├── .gitignore ├── Docs ├── Shahi-FEM-handbook.pdf ├── fem_package_nrc.gif ├── fem_toolbox.jpg └── fem_toolbox.png ├── Instructions.pdf ├── LICENSE ├── README.md ├── Source Code ├── GUI │ ├── FiniteElementGUI.fig │ ├── FiniteElementGUI.m │ ├── Model.mat │ ├── PlotMeshX.p │ ├── Solution.mat │ ├── inpFileReader.p │ ├── printResult.m │ └── printSummary.m ├── PlaneFrame │ ├── input1.txt │ ├── input2.txt │ ├── lib │ │ ├── beamShapeFunctions.m │ │ ├── facenodes.m │ │ ├── integrationpoints.m │ │ ├── integrationweights.m │ │ ├── nfacenodes.m │ │ ├── numberofintegrationpoints.m │ │ ├── planeFrameAnalysis.m │ │ ├── planeFrameExplicit.m │ │ ├── planeFrameNumerical.m │ │ ├── shapefunctionderivs.m │ │ └── shapefunctions.m │ ├── lib_io │ │ ├── inpFileReader.p │ │ ├── plotmesh.p │ │ ├── printResult.m │ │ ├── printStiff.m │ │ └── printSummary.m │ └── main.m ├── PlaneStress PlaneStrain │ ├── input1.txt │ ├── input2.txt │ ├── input3.txt │ ├── lib │ │ ├── eldload.m │ │ ├── elstif.m │ │ ├── facenodes.m │ │ ├── femGeneral.m │ │ ├── globalstiffness.m │ │ ├── globaltraction.m │ │ ├── integrationpoints.m │ │ ├── integrationweights.m │ │ ├── materialstiffness.m │ │ ├── materialstress.m │ │ ├── nfacenodes.m │ │ ├── numberofintegrationpoints.m │ │ ├── plotmesh.m │ │ ├── print_results.m │ │ ├── shapefunctionderivs.m │ │ ├── shapefunctions.m │ │ └── solution.m │ ├── lib_io │ │ ├── inpFileReader.p │ │ ├── printResult.m │ │ └── printSummary.m │ └── main.m ├── PlaneTruss │ ├── input1.txt │ ├── input2.txt │ ├── input3.txt │ ├── lib │ │ ├── shapefunctionderivs.m │ │ ├── shapefunctions.m │ │ ├── trussAnalysisExplicit.m │ │ └── trussAnalysisNumerical.m │ ├── lib_io │ │ ├── inpFileReader.p │ │ ├── plotModel.p │ │ ├── printResult.m │ │ ├── printStiff.m │ │ └── printSummary.m │ └── main.m └── fem.m └── Toolbox Installation File └── FEM Package.mltbx /.gitignore: -------------------------------------------------------------------------------- 1 | .DS_Store 2 | -------------------------------------------------------------------------------- /Docs/Shahi-FEM-handbook.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/shahrokhx/FEM_Toolbox/8dda726b82d707d2e3404996893c95b8e2de3ef9/Docs/Shahi-FEM-handbook.pdf -------------------------------------------------------------------------------- /Docs/fem_package_nrc.gif: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/shahrokhx/FEM_Toolbox/8dda726b82d707d2e3404996893c95b8e2de3ef9/Docs/fem_package_nrc.gif -------------------------------------------------------------------------------- /Docs/fem_toolbox.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/shahrokhx/FEM_Toolbox/8dda726b82d707d2e3404996893c95b8e2de3ef9/Docs/fem_toolbox.jpg -------------------------------------------------------------------------------- /Docs/fem_toolbox.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/shahrokhx/FEM_Toolbox/8dda726b82d707d2e3404996893c95b8e2de3ef9/Docs/fem_toolbox.png -------------------------------------------------------------------------------- /Instructions.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/shahrokhx/FEM_Toolbox/8dda726b82d707d2e3404996893c95b8e2de3ef9/Instructions.pdf -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | Apache License 2 | Version 2.0, January 2004 3 | http://www.apache.org/licenses/ 4 | 5 | TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 6 | 7 | 1. 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We also recommend that a 185 | file or class name and description of purpose be included on the 186 | same "printed page" as the copyright notice for easier 187 | identification within third-party archives. 188 | 189 | Copyright [yyyy] [name of copyright owner] 190 | 191 | Licensed under the Apache License, Version 2.0 (the "License"); 192 | you may not use this file except in compliance with the License. 193 | You may obtain a copy of the License at 194 | 195 | http://www.apache.org/licenses/LICENSE-2.0 196 | 197 | Unless required by applicable law or agreed to in writing, software 198 | distributed under the License is distributed on an "AS IS" BASIS, 199 | WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 200 | See the License for the specific language governing permissions and 201 | limitations under the License. 202 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # FEM_Toolbox 2 | A general FEM toolbox to analyze planar (2D) and 3D structures, including trusses, beams, frames, plane stress/strain, and 3D solid structures. The package including a graphical user interface (GUI) and visulization tools to fascilitate modeling and analyzing process. This toolbox can also be employed for educational purposes. 3 | 4 | 5 | |
Developed by Shahrokh Shahi
| 6 | |:----------| 7 | |
Georgia Institute of Technology
College of Computing and College of Engineering
2018-2020
| 8 | |
www.sshahi.com
| 9 | 10 | 11 |
12 | 13 | #### Details: 14 | This repository is part of a set of FEM-related codes, where you can find more details in this blog post. 15 | 16 | 17 | > In general, finite element method (FEM) is used as an effective numerical method to solve differential equations and widely employed in engineering and mathematical modeling, where a mechanical system is divided into discrete subdomains known as finite elements. The technical process of creating finite element meshes and using Gaussian numerical integration to calculate the stiffness of each element, assembly process, and solving the obtained system of equations have always been challenging to implement and understand by both undergrad and graduate students in engineering fields such as Civil Engineering, Mechanical Engineering, Aerospace Engineering, etc. Therefore, as a TA in FEM and advanced FEM course, who also held several sessions and workshops for MATLAB programming and developing FEM codes, I started to develop many demonstrations and educational toolboxes to help students internalize these technical steps. The following is the datails regarding these packages and codes predented in the three sub-sections. 18 | 19 | > In addition to the set of snippets and demos, a general FEM toolbox is developed in MATLA, which can be used for both educational and research purposes. This package is based on the implementation of the book, “Applied Mechanics of Solids”, by Allan F. Bower, and handled by a simple, yet user-friendly, graphical user interface (GUI) in MATLAB, and can be employed to analyze 2D and 3D mechanical structures, including trusses, frames, plane stress and plane strain, and general 3D solid. 20 | 21 | --- 22 | 23 | #### Sample runs: 24 | ![](Docs/fem_toolbox.jpg) 25 | 26 | --- 27 | 28 | ![](Docs/fem_package_nrc.gif) 29 | 30 | --- 31 | 32 | > A complete handbook is also provided in Docs folder. -------------------------------------------------------------------------------- /Source Code/GUI/FiniteElementGUI.fig: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/shahrokhx/FEM_Toolbox/8dda726b82d707d2e3404996893c95b8e2de3ef9/Source Code/GUI/FiniteElementGUI.fig -------------------------------------------------------------------------------- /Source Code/GUI/Model.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/shahrokhx/FEM_Toolbox/8dda726b82d707d2e3404996893c95b8e2de3ef9/Source Code/GUI/Model.mat -------------------------------------------------------------------------------- /Source Code/GUI/PlotMeshX.p: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/shahrokhx/FEM_Toolbox/8dda726b82d707d2e3404996893c95b8e2de3ef9/Source Code/GUI/PlotMeshX.p -------------------------------------------------------------------------------- /Source Code/GUI/Solution.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/shahrokhx/FEM_Toolbox/8dda726b82d707d2e3404996893c95b8e2de3ef9/Source Code/GUI/Solution.mat -------------------------------------------------------------------------------- /Source Code/GUI/inpFileReader.p: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/shahrokhx/FEM_Toolbox/8dda726b82d707d2e3404996893c95b8e2de3ef9/Source Code/GUI/inpFileReader.p -------------------------------------------------------------------------------- /Source Code/GUI/printResult.m: -------------------------------------------------------------------------------- 1 | function printResult(Solution,fid) 2 | 3 | if nargin < 2 4 | fid = 1; 5 | end 6 | 7 | BULLET_CHAR = char(15); 8 | 9 | fprintf(fid,'\n\n'); 10 | printDLine(fid) 11 | printCTitle(fid,'O U T P U T S U M M A R Y') 12 | printDLine(fid) 13 | 14 | if isfield(Solution,'info') 15 | fprintf(fid,'%c About: \n',BULLET_CHAR); 16 | fprintf(fid,'%s\n', Solution.info); 17 | end 18 | printLine(fid) 19 | 20 | 21 | if isfield(Solution, 'nodalDisplacements') 22 | u = Solution.nodalDisplacements; 23 | [nNode,nDof] = size(u); 24 | printCTitle(fid,'Nodal Displacements'); 25 | printSLine(fid); 26 | for i = 1 : nNode 27 | formatStr = repmat('%10.5f\t',1,nDof); 28 | fprintf(fid,['[%3d] ',formatStr,'\n'],i,u(i,:)); 29 | end 30 | end 31 | printLine(fid) 32 | if isfield(Solution, 'reactionForces') 33 | rf = Solution.reactionForces; 34 | [nNode,nDof] = size(rf); 35 | printCTitle(fid,'Reaction Forces'); 36 | printSLine(fid); 37 | for i = 1 : nNode 38 | formatStr = repmat('%10.5f\t',1,nDof); 39 | fprintf(fid,['[%3d] ',formatStr,'\n'],i,rf(i,:)); 40 | end 41 | end 42 | printLine(fid) 43 | if isfield(Solution, 'elementStresses') 44 | stress = Solution.elementStresses.sigma11; 45 | [nElem,nComponenet] = size(stress); 46 | printCTitle(fid,'Stresses'); 47 | printSLine(fid); 48 | for i = 1 : nElem 49 | formatStr = repmat('%10.5f\t',1,nComponenet); 50 | fprintf(fid,['[%3d] ',formatStr,'\n'],i,stress(i,:)); 51 | end 52 | end 53 | printLine(fid) 54 | if isfield(Solution, 'internalForces') 55 | internalForces = Solution.internalForces.axial; 56 | [nElem,nComponenet] = size(internalForces); 57 | printCTitle(fid,'Internal Forces (Axial)'); 58 | printSLine(fid); 59 | for i = 1 : nElem 60 | formatStr = repmat('%10.5f\t',1,nComponenet); 61 | fprintf(fid,['[%3d] ',formatStr,'\n'],i,internalForces(i,:)); 62 | end 63 | end 64 | printDLine(fid); 65 | end 66 | 67 | %-------------------------------------------------------------------------- 68 | % Helper Functions 69 | function printLine(fid,n) 70 | if nargin < 2 71 | n = 80; 72 | end 73 | if nargin < 1 74 | fid = 1; 75 | end 76 | fprintf(fid,'%s\n',repmat('_',1,n)); 77 | end 78 | 79 | %-------------------------------------------------------------------------- 80 | function printDLine(fid,n) 81 | if nargin < 2 82 | n = 80; 83 | end 84 | if nargin < 1 85 | fid = 1; 86 | end 87 | fprintf(fid,'%s\n',repmat('=',1,n)); 88 | end 89 | 90 | %-------------------------------------------------------------------------- 91 | function printSLine(fid,n) 92 | if nargin < 2 93 | n = 80; 94 | end 95 | if nargin < 1 96 | fid = 1; 97 | end 98 | fprintf(fid,'%s\n',repmat('-',1,n)); 99 | end 100 | 101 | %-------------------------------------------------------------------------- 102 | % printing centered text title 103 | function printCTitle(fid,text,n) 104 | if nargin < 3 105 | n = 80; 106 | end 107 | if nargin < 2 108 | text =''; 109 | end 110 | if nargin < 1 111 | fid = 1; 112 | end 113 | tLen = length(text); 114 | space = floor((n-tLen)/2); 115 | fprintf(fid,'%s\n',[repmat(' ',1,space),text]); 116 | end 117 | %-------------------------------------------------------------------------- -------------------------------------------------------------------------------- /Source Code/GUI/printSummary.m: -------------------------------------------------------------------------------- 1 | function printSummary(Model,fid) 2 | % PURPOSE: reads input files and generates a structure including all data 3 | % 4 | % INPUT(S): 5 | % - Model: a structure including the following fields 6 | % - fid : file id to store 7 | % 8 | % OUTPUT(S): 9 | % 10 | % 11 | % USAGE: 12 | % >> printSummary(Model) print input details on command window 13 | % >> printSummary(Model,fid) print input details on a file with fid 14 | % identifier 15 | 16 | % DEVELOPMENT HISTORY: 17 | % [2018, Oct, 29] Shahrokh Shahi -- initial development 18 | % [2018, XXX, XX] Shahrokh Shahi -- 19 | 20 | if nargin < 2 21 | fid = 1; 22 | end 23 | BULLET_CHAR = char(15); 24 | 25 | printDLine(fid) 26 | tText = 'A S U M M A R Y O F T H E I N P U T M O D E L'; 27 | printCTitle(fid,tText) 28 | printDLine(fid) 29 | 30 | 31 | if isfield(Model,'info') 32 | fprintf(fid,'%c About: \n',BULLET_CHAR); 33 | fprintf(fid,'%s\n', Model.info); 34 | end 35 | if isfield(Model,'analysisType') 36 | fprintf(fid,'\n%c Structure Type: \n',BULLET_CHAR); 37 | fprintf(fid,'%s\n', Model.analysisType); 38 | end 39 | printLine(fid) 40 | 41 | 42 | fprintf(fid,'%c Control Variables: \n',BULLET_CHAR); 43 | fprintf(fid,' - Dimension: %dD\n' ,Model.nDim); 44 | fprintf(fid,' - Number of DOF(s): %d \n' ,Model.nDof); 45 | fprintf(fid,'\n'); 46 | fprintf(fid,' - Number of Nodes: %4d \n' ,Model.nNode); 47 | fprintf(fid,' - Number of Elements: %4d \n' ,Model.nElem); 48 | fprintf(fid,' - Nodes per Elements: %d\n',Model.nElemNode); 49 | fprintf(fid,'\n'); 50 | fprintf(fid,' - Number of Sections: %d \n',Model.nSection); 51 | printDLine(fid) 52 | 53 | 54 | printCTitle(fid,'N O D A L I N F O R M A T I O N') 55 | printLine(fid) 56 | headerTxt = ['Node Coordinates Nodal Loads ',... 57 | ' Nodal Restraints \n']; 58 | fprintf(fid,headerTxt); 59 | printSLine(fid) 60 | switch Model.nDim 61 | case 1 62 | headerTxt1 =' ID X '; 63 | headerTxt2 =' Fx '; 64 | headerTxt3 =' ux \n'; 65 | 66 | case 2 67 | headerTxt1 =' ID X Y '; 68 | headerTxt2 =' Fx Fy '; 69 | headerTxt3 =' ux uy \n'; 70 | 71 | case 3 72 | headerTxt1 =' ID X Y Z '; 73 | headerTxt2 =' Fx Fy Fz '; 74 | headerTxt3 =' ux uy uz \n'; 75 | end 76 | fprintf(fid,[headerTxt1,headerTxt2,headerTxt3]); 77 | printLine(fid) 78 | 79 | % nodal forces to displaying 80 | F = zeros(Model.nNode,Model.nDof); 81 | for i = 1 : Model.nNodalForce 82 | node = Model.loading.nodalForces(i,1); 83 | F(node, 1:Model.nDof) = Model.loading.nodalForces(i,2:end); 84 | end 85 | 86 | % printing table contents 87 | for i = 1 : Model.nNode 88 | coord = Model.geometry.coordinates(i,:); 89 | fprintf(fid,'%2d ',i); 90 | for j = 1 : length(coord) 91 | fprintf(fid,'%7.2f ',coord(j)); 92 | end 93 | fprintf(fid,'\t'); 94 | for j = 1 : size(F,2) 95 | fprintf(fid,'%10.2f ',F(i,j)); 96 | end 97 | 98 | fprintf(fid,'\t'); 99 | index = find(Model.boundary(:,1)==i); 100 | dx='-';dy='-';dz='-';bc=''; 101 | 102 | if ~isempty(index) 103 | for k = 1 : length(index) 104 | if Model.boundary(index(k),2)==1 105 | dx=num2str(Model.boundary(index(k),3)); 106 | elseif Model.boundary(index(k),2)==2 107 | dy=num2str(Model.boundary(index(k),3)); 108 | elseif Model.boundary(index(k),2)==3 109 | dz=num2str(Model.boundary(index(k),3)); 110 | end 111 | end 112 | if length(index)==1 113 | bc = 'Roller '; 114 | elseif length(index)==2 115 | bc = 'Pin'; 116 | elseif length(index)==3 117 | bc = 'Fixed'; 118 | end 119 | end 120 | presc = [dx, dy, dz]; %prescribed values 121 | for j = 1 : Model.nDof 122 | fprintf(fid,' %s',presc(j)); 123 | end 124 | fprintf(fid,' %s\n',bc); 125 | end 126 | printDLine(fid); 127 | 128 | printCTitle(fid,'E L E M E N T S I N F O R M A T I O N') 129 | printLine(fid) 130 | fprintf(fid,' ID\t '); 131 | for i = 1 : Model.nElemNode 132 | fprintf(fid,'Node%d\t',i); 133 | end 134 | fprintf(fid,' Section No. Material Properties\n'); 135 | printLine(fid); 136 | 137 | for i = 1 : Model.nElem 138 | fprintf(fid,'%2d\t ',i); 139 | for j = 1 : Model.nElemNode 140 | fprintf(fid,'%2d\t\t',Model.geometry.elements(i,j)); 141 | end 142 | fprintf(fid,'\t'); 143 | fprintf(fid,'\t%2d\t\t\t[',Model.elemSectId(i)); 144 | for j = 1 : Model.nMaterialProp 145 | fprintf(fid,'%g\t\t',Model.sections(Model.elemSectId(i),j)); 146 | end 147 | fprintf(fid,']\n'); 148 | end 149 | 150 | printDLine(fid); 151 | 152 | end 153 | 154 | 155 | % Helper Functions 156 | function printLine(fid,n) 157 | if nargin < 2 158 | n = 80; 159 | end 160 | if nargin < 1 161 | fid = 1; 162 | end 163 | fprintf(fid,'%s\n',repmat('_',1,n)); 164 | end 165 | 166 | function printDLine(fid,n) 167 | if nargin < 2 168 | n = 80; 169 | end 170 | if nargin < 1 171 | fid = 1; 172 | end 173 | fprintf(fid,'%s\n',repmat('=',1,n)); 174 | end 175 | 176 | function printSLine(fid,n) 177 | if nargin < 2 178 | n = 80; 179 | end 180 | if nargin < 1 181 | fid = 1; 182 | end 183 | fprintf(fid,'%s\n',repmat('-',1,n)); 184 | end 185 | % printing centered text title 186 | function printCTitle(fid,text,n) 187 | if nargin < 3 188 | n = 80; 189 | end 190 | if nargin < 2 191 | text =''; 192 | end 193 | if nargin < 1 194 | fid = 1; 195 | end 196 | tLen = length(text); 197 | space = floor((n-tLen)/2); 198 | fprintf(fid,'%s\n',[repmat(' ',1,space),text]); 199 | end -------------------------------------------------------------------------------- /Source Code/PlaneFrame/input1.txt: -------------------------------------------------------------------------------- 1 | * INFO 2 | A planar frame example with HINGE 3 | 4 | * ANALYSIS TYPE 5 | Beam 6 | 7 | * COORDINATES 8 | 1 0.0 0.0 9 | 2 2.0 0.0 10 | 3 3.0 0.0 11 | 4 4.0 0.0 12 | 13 | * HINGE 14 | 3 15 | 16 | * ELEMENTS 17 | 1 1 1 2 18 | 2 1 2 3 19 | 3 1 3 4 20 | 21 | * SECTIONS 22 | 1 210e9 2e-4 1 23 | 24 | 25 | * TRACTION FORCES 26 | 3 1 0 -10e3 27 | 28 | * BOUNDARY 29 | 1 1 0.0 30 | 1 2 0.0 31 | 1 3 0.0 32 | 2 1 0.0 33 | 2 2 0.0 34 | 4 1 0.0 35 | 4 2 0.0 36 | 4 3 0.0 37 | 38 | 39 | -------------------------------------------------------------------------------- /Source Code/PlaneFrame/input2.txt: -------------------------------------------------------------------------------- 1 | * INFO 2 | A planar frame example 3 | 4 | * ANALYSIS TYPE 5 | Beam 6 | 7 | * COORDINATES 8 | 1 0.0 0.0 9 | 2 0.0 16.0 10 | 3 20.0 16.0 11 | 4 20.0 0.0 12 | 13 | 14 | * ELEMENTS 15 | 1 1 1 2 16 | 2 2 2 3 17 | 3 1 3 4 18 | 19 | * SECTIONS 20 | 1 3e7 600 100 21 | 2 3e10 1000 100 22 | 23 | # E I A 24 | 25 | * NODAL FORCES 26 | 2 0.0 -6.0 -28.8 27 | 3 0.0 -4.0 19.2 28 | 29 | # Uniform distributed load 30 | * TRACTION FORCES 31 | 1 1 0 -500 32 | 33 | 34 | * BOUNDARY 35 | 4 1 0.0 36 | 4 2 0.0 37 | 4 3 0.0 38 | 39 | -------------------------------------------------------------------------------- /Source Code/PlaneFrame/lib/beamShapeFunctions.m: -------------------------------------------------------------------------------- 1 | function [N,dNdxi] = beamShapeFunctions(xi) 2 | N = [ ((xi - 1)^2*(xi + 2))/4 3 | ((xi - 1)^2*(xi + 1))/4 4 | -((xi + 1)^2*(xi - 2))/4 5 | ((xi - 1)*(xi + 1)^2)/4 ]; 6 | dNdxi = [ (xi - 1)^2/4 + ((2*xi - 2)*(xi + 2))/4 7 | (xi - 1)^2/4 + ((2*xi - 2)*(xi + 1))/4 8 | -(xi + 1)^2/4 - ((2*xi + 2)*(xi - 2))/4 9 | (xi + 1)^2/4 + ((2*xi + 2)*(xi - 1))/4 ]; 10 | end -------------------------------------------------------------------------------- /Source Code/PlaneFrame/lib/facenodes.m: -------------------------------------------------------------------------------- 1 | %======================= Lists of nodes on element faces ============= 2 | % 3 | % This procedure returns the list of nodes on an element face 4 | % The nodes are ordered so that the element face forms either 5 | % a 1D line element or a 2D surface element for 2D or 3D problems 6 | % 7 | function list = facenodes(ncoord,nelnodes,face) 8 | 9 | i3 = [2,3,1]; 10 | i4 = [2,3,4,1]; 11 | 12 | list = zeros(nfacenodes(ncoord,nelnodes,face),1); 13 | 14 | if (ncoord == 2) 15 | if (nelnodes == 2) 16 | list = [1,2]; 17 | elseif (nelnodes == 3) 18 | list(1) = face; 19 | list(2) = i3(face); 20 | elseif (nelnodes == 6) 21 | list(1) = face; 22 | list(2) = i3(face); 23 | list(3) = face+3; 24 | elseif (nelnodes==4) 25 | list(1) = face; 26 | list(2) = i4(face); 27 | elseif (nelnodes==8) 28 | list(1) = face; 29 | list(2) = i4(face); 30 | list(3) = face+4; 31 | end 32 | elseif (ncoord == 3) 33 | if (nelnodes==4) 34 | if (face == 1) 35 | list = [1,2,3]; 36 | elseif (face == 2) 37 | list = [1,4,2]; 38 | elseif (face == 3) 39 | list = [2,4,3]; 40 | elseif (face == 4) 41 | list = [3,4,1]; 42 | end 43 | elseif (nelnodes == 10) 44 | if (face == 1) 45 | list = [1,2,3,5,6,7]; 46 | elseif (face == 2) 47 | list = [1,4,2,8,9,5]; 48 | elseif (face == 3) 49 | list = [2,4,3,9,10,6]; 50 | elseif (face == 4) 51 | list = [3,4,1,10,8,7]; 52 | end 53 | elseif (nelnodes == 8) 54 | if (face == 1) 55 | list = [1,2,3,4]; 56 | elseif (face == 2) 57 | list = [5,8,7,6]; 58 | elseif (face == 3) 59 | list = [1,5,6,2]; 60 | elseif (face == 4) 61 | list = [2,3,7,6]; 62 | elseif (face == 5) 63 | list = [3,7,8,4]; 64 | elseif (face == 6) 65 | list = [4,8,5,1]; 66 | end 67 | elseif (nelnodes == 20) 68 | if (face == 1) 69 | list = [1,2,3,4,9,10,11,12]; 70 | elseif (face == 2) 71 | list = [5,8,7,6,16,15,14,13]; 72 | elseif (face == 3) 73 | list = [1,5,6,2,17,13,18,9]; 74 | elseif (face == 4) 75 | list = [2,6,7,3,18,14,19,10]; 76 | elseif (face == 5) 77 | list = [3,7,8,4,19,15,20,11]; 78 | elseif (face == 6) 79 | list = [4,8,5,1,20,16,17,12]; 80 | end 81 | end 82 | end 83 | end -------------------------------------------------------------------------------- /Source Code/PlaneFrame/lib/integrationpoints.m: -------------------------------------------------------------------------------- 1 | %====================== INTEGRATION POINTS ================================== 2 | % 3 | % Defines positions of integration points 4 | % 5 | function xi = integrationpoints(ncoord,nelnodes,npoints) 6 | 7 | xi = zeros(ncoord,npoints); 8 | % 9 | % 1D elements 10 | % 11 | if (ncoord == 1) 12 | if (npoints==1) 13 | xi(1,1) = 0.; 14 | elseif (npoints == 2) 15 | xi(1,1) = -0.5773502692; 16 | xi(1,2) = -xi(1,1); 17 | elseif (npoints == 3) 18 | xi(1,1) = -0.7745966692; 19 | xi(1,2) = 0.0; 20 | xi(1,3) = -xi(1,1); 21 | end 22 | % 23 | % 2D elements 24 | % 25 | elseif (ncoord == 2) 26 | % 27 | % Triangular element 28 | % 29 | if ( nelnodes == 3 || nelnodes == 6 ) 30 | if (npoints == 1) 31 | xi(1,1) = 1./3.; 32 | xi(2,1) = 1./3.; 33 | elseif (npoints == 3) 34 | xi(1,1) = 0.6; 35 | xi(2,1) = 0.2; 36 | xi(1,2) = 0.2; 37 | xi(2,2) = 0.6; 38 | xi(1,3) = 0.2; 39 | xi(2,3) = 0.2; 40 | elseif (npoints == 4) 41 | xi(1,1) = 1./3.; 42 | xi(2,1) = 1./3.; 43 | xi(1,2) = 0.6; 44 | xi(2,2) = 0.2; 45 | xi(1,3) = 0.2; 46 | xi(2,3) = 0.6; 47 | xi(1,4) = 0.2; 48 | xi(2,4) = 0.2; 49 | end 50 | % 51 | % Rectangular element 52 | % 53 | elseif ( nelnodes==4 || nelnodes==8 ) 54 | 55 | if (npoints == 1) 56 | xi(1,1) = 0.; 57 | xi(2,1) = 0.; 58 | elseif (npoints == 4) 59 | xi(1,1) = -0.5773502692; 60 | xi(2,1) = xi(1,1); 61 | xi(1,2) = -xi(1,1); 62 | xi(2,2) = xi(1,1); 63 | xi(1,3) = xi(1,1); 64 | xi(2,3) = -xi(1,1); 65 | xi(1,4) = -xi(1,1); 66 | xi(2,4) = -xi(1,1); 67 | elseif (npoints == 9) 68 | xi(1,1) = -0.7745966692; 69 | xi(2,1) = xi(1,1); 70 | xi(1,2) = 0.0; 71 | xi(2,2) = xi(1,1); 72 | xi(1,3) = -xi(1,1); 73 | xi(2,3) = xi(1,1); 74 | xi(1,4) = xi(1,1); 75 | xi(2,4) = 0.0; 76 | xi(1,5) = 0.0; 77 | xi(2,5) = 0.0; 78 | xi(1,6) = -xi(1,1); 79 | xi(2,6) = 0.0; 80 | xi(1,7) = xi(1,1); 81 | xi(2,7) = -xi(1,1); 82 | xi(1,8) = 0.; 83 | xi(2,8) = -xi(1,1); 84 | xi(1,9) = -xi(1,1); 85 | xi(2,9) = -xi(1,1); 86 | end 87 | end 88 | % 89 | % 3D elements 90 | % 91 | elseif (ncoord == 3) 92 | % 93 | % 3D elements 94 | % 95 | if (nelnodes == 4 || nelnodes==10 ) 96 | if (npoints == 1) 97 | xi(1,1) = 0.25; 98 | xi(2,1) = 0.25; 99 | xi(3,1) = 0.25; 100 | elseif (npoints == 4) 101 | xi(1,1) = 0.58541020; 102 | xi(2,1) = 0.13819660; 103 | xi(3,1) = xi(2,1); 104 | xi(1,2) = xi(2,1); 105 | xi(2,2) = xi(1,1); 106 | xi(3,2) = xi(2,1); 107 | xi(1,3) = xi(2,1); 108 | xi(2,3) = xi(2,1); 109 | xi(3,3) = xi(1,1); 110 | xi(1,4) = xi(2,1); 111 | xi(2,4) = xi(2,1); 112 | xi(3,4) = xi(2,1); 113 | end 114 | elseif ( nelnodes==8 || nelnodes==20 ) 115 | if (npoints == 1) 116 | xi(1,1) = 0.; 117 | xi(2,1) = 0.; 118 | xi(3,1) = 0.; 119 | elseif (npoints == 8) 120 | x1D = [-0.5773502692,0.5773502692]; 121 | for k = 1:2 122 | for j = 1:2 123 | for i = 1:2 124 | n = 4*(k-1) + 2*(j-1) + i; 125 | xi(1,n) = x1D(i); 126 | xi(2,n) = x1D(j); 127 | xi(3,n) = x1D(k); 128 | end 129 | end 130 | end 131 | elseif (npoints == 27) 132 | x1D = [-0.7745966692,0.,0.7745966692]; 133 | for k = 1:3 134 | for j = 1:3 135 | for i = 1:3 136 | n = 9*(k-1) + 3*(j-1) + i; 137 | xi(1,n) = x1D(i); 138 | xi(2,n) = x1D(j); 139 | xi(3,n) = x1D(k); 140 | end 141 | end 142 | end 143 | end 144 | end 145 | end 146 | end -------------------------------------------------------------------------------- /Source Code/PlaneFrame/lib/integrationweights.m: -------------------------------------------------------------------------------- 1 | %================= INTEGRATION WEIGHTS ================================== 2 | % 3 | % Defines integration weights w_i 4 | % 5 | function w = integrationweights(ncoord,nelnodes,npoints) 6 | 7 | w = zeros(npoints,1); 8 | 9 | % 10 | % 1D elements 11 | % 12 | if (ncoord == 1) 13 | if (npoints == 1) 14 | w(1) = 2.; 15 | elseif (npoints == 2) 16 | w = [1.,1.]; 17 | elseif (npoints == 3) 18 | w = [0.555555555,0.888888888,0.555555555]; 19 | end 20 | % 21 | % 2D elements 22 | % 23 | elseif (ncoord == 2) 24 | % 25 | % Triangular element 26 | % 27 | if ( nelnodes == 3 || nelnodes == 6 ) 28 | if (npoints == 1) 29 | w(1) = 0.5; 30 | elseif (npoints == 3) 31 | w(1) = 1./6.; 32 | w(2) = 1./6.; 33 | w(3) = 1./6.; 34 | elseif (npoints == 4) 35 | w = [-27./96.,25./96.,25/96.,25/96.]; 36 | end 37 | % 38 | % Rectangular element 39 | % 40 | elseif ( nelnodes==4 || nelnodes==8 ) 41 | 42 | if (npoints == 1) 43 | w(1) = 4.; 44 | elseif (npoints == 4) 45 | w = [1.,1.,1.,1.]; 46 | elseif (npoints == 9 ) 47 | w1D = [0.555555555,0.888888888,0.55555555555]; 48 | for j = 1:3 49 | for i = 1:3 50 | n = 3*(j-1)+i; 51 | w(n) = w1D(i)*w1D(j); 52 | end 53 | end 54 | end 55 | end 56 | 57 | elseif (ncoord == 3) 58 | % 59 | % 3D elements 60 | % 61 | if (nelnodes == 4 || nelnodes==10 ) 62 | if (npoints == 1) 63 | w(1) = 1./6.; 64 | elseif (npoints == 4) 65 | w = [1./24.,1./24.,1./24.,1./24.]; 66 | end 67 | elseif ( nelnodes==8 || nelnodes==20 ) 68 | if (npoints == 1) 69 | w(1) = 8.; 70 | elseif (npoints == 8) 71 | w = [1.,1.,1.,1.,1.,1.,1.,1.]; 72 | elseif (npoints == 27) 73 | w1D = [0.555555555,0.888888888,0.55555555555]; 74 | for k = 1:3 75 | for j = 1:3 76 | for i = 1:3 77 | n = 9*(k-1)+3*(j-1)+i; 78 | w(n) = w1D(i)*w1D(j)*w1D(k); 79 | end 80 | end 81 | end 82 | end 83 | end 84 | end 85 | end -------------------------------------------------------------------------------- /Source Code/PlaneFrame/lib/nfacenodes.m: -------------------------------------------------------------------------------- 1 | %====================== No. nodes on element faces ================ 2 | % 3 | % This procedure returns the number of nodes on each element face 4 | % for various element types. This info is needed for computing 5 | % the surface integrals associated with the element traction vector 6 | % 7 | function n = nfacenodes(ncoord,nelnodes,elident,face) 8 | if (ncoord == 2) 9 | n = 2; 10 | if (nelnodes == 3 || nelnodes == 4) 11 | n = 2; 12 | elseif (nelnodes == 6 || nelnodes == 8) 13 | n=3; 14 | end 15 | elseif (ncoord == 3) 16 | if (nelnodes == 4) 17 | n = 3; 18 | elseif (nelnodes == 10) 19 | n = 6; 20 | elseif (nelnodes == 8) 21 | n = 4; 22 | elseif (nelnodes == 20) 23 | n = 8; 24 | end 25 | end 26 | end -------------------------------------------------------------------------------- /Source Code/PlaneFrame/lib/numberofintegrationpoints.m: -------------------------------------------------------------------------------- 1 | %====================== No. integration points ============================= 2 | % 3 | % Defines the number of integration points:be used for 4 | % each element type 5 | % 6 | function n = numberofintegrationpoints(ncoord,nelnodes) 7 | 8 | if (ncoord == 1) 9 | n = nelnodes; 10 | elseif (ncoord == 2) 11 | if (nelnodes == 2) 12 | n = 1; 13 | end 14 | if (nelnodes == 3) 15 | n = 1; 16 | end 17 | if (nelnodes == 6) 18 | n = 3; 19 | end 20 | if (nelnodes == 4) 21 | n = 4; 22 | end 23 | if (nelnodes == 8) 24 | n = 9; 25 | end 26 | elseif (ncoord == 3) 27 | if (nelnodes == 4) 28 | n = 1 ; 29 | end 30 | if (nelnodes == 10) 31 | n = 4; 32 | end 33 | if (nelnodes == 8) 34 | n = 8; 35 | end 36 | if (nelnodes == 20) 37 | n = 27; 38 | end 39 | end 40 | end -------------------------------------------------------------------------------- /Source Code/PlaneFrame/lib/planeFrameAnalysis.m: -------------------------------------------------------------------------------- 1 | function Solution = planeFrameAnalysis(Model) 2 | 3 | Solution.info = ['Solution obtained on ', date]; 4 | 5 | FirstNode = Model.geometry.elements(:,1); 6 | SecondNode = Model.geometry.elements(:,2); 7 | ifix = Model.bound.ifix; 8 | 9 | % processing element load information 10 | ndof = Model.nNode * Model.nDof; 11 | K = zeros(ndof,ndof); %initialize the global stiffness matrix of size ndof 12 | Feq = zeros(ndof,1); %nodal force vector due to element loads 13 | ke_local (:,:,Model.nElem) = zeros(6); 14 | ke_global(:,:,Model.nElem) = zeros(6); 15 | T6(:,:,Model.nElem) = zeros(6); 16 | 17 | for e = 1 : Model.nElem 18 | c = Model.geometry.Cx(e); 19 | s = Model.geometry.Cy(e); 20 | le = Model.geometry.L(e); 21 | 22 | ae = Model.properties.A(e) * Model.properties.E(e); %axial rigidity 23 | ei = Model.properties.E(e) * Model.properties.Iz(e); %flexural rigidity 24 | %Degrees of freedom for element e with nodes m and n are 3m-2, 3m-1 ,3m, 3n-2, 3n-1 ,3n 25 | %These degrees of freedom are stored in the vector {dof} as shown below 26 | dof = [3*FirstNode(e)-2, 3*FirstNode(e)-1, 3*FirstNode(e), ... 27 | 3*SecondNode(e)-2, 3*SecondNode(e)-1, 3*SecondNode(e)]; 28 | 29 | % rotation transformation matrix for element e 30 | T=[c s 0 0 0 0; 31 | -s c 0 0 0 0; 32 | 0 0 1 0 0 0; 33 | 0 0 0 c s 0; 34 | 0 0 0 -s c 0; 35 | 0 0 0 0 0 1;]; 36 | 37 | % element stiffness matrix w.r.t local axes 38 | estif = [ ae/le 0 0 -ae/le 0 0; 39 | 0 12*ei/le^3 6*ei/le^2 0 -12*ei/le^3 6*ei/le^2; 40 | 0 6*ei/le^2 4*ei/le 0 -6*ei/le^2 2*ei/le ; 41 | -ae/le 0 0 ae/le 0 0; 42 | 0 -12*ei/le^3 -6*ei/le^2 0 12*ei/le^3 -6*ei/le^2; 43 | 0 6*ei/le^2 2*ei/le 0 -6*ei/le^2 4*ei/le ]; 44 | 45 | if Model.geometry.hingIndex(SecondNode(e)) == 1 % if the right node is a hinge 46 | % Modifications due to the hing on the right hand 47 | estif( 6 , : ) = 0; 48 | estif( : , 6 ) = 0; 49 | estif([2,5],[2,5]) = (1/4) * estif([2,5],[2,5]); 50 | estif([2,5], 3 ) = (1/2) * estif([2,5], 3 ); 51 | estif( 3 ,[2,5]) = (1/2) * estif( 3 ,[2,5]); 52 | estif( 3 , 3 ) = (3/4) * estif( 3 , 3 ); 53 | end 54 | 55 | 56 | ke=(T'*estif*T) ; %element stiffness matrix with reference to global axes 57 | 58 | ke_local(:,:,e) = estif; 59 | T6(:,:,e)= T; 60 | ke_global(:,:,e) = ke; 61 | 62 | 63 | K(dof,dof)=K(dof,dof)+ke; %assembly of global stiffness matrix K 64 | %{Feq} is vector of equivalent nodal forces due to element loads 65 | Feq(dof) = Feq(dof) + T'*Model.loading.eforce(:,e); 66 | end 67 | 68 | Fc = Model.loading.F+Feq; %combined force vector {Fc} is obtained by adding vector of nodal loads {F} to {Feq} 69 | 70 | Solution.data.ke_local = ke_local; 71 | Solution.data.ke_global = ke_global; 72 | Solution.data.T6 = T6; 73 | Solution.data.F_global = Fc; 74 | 75 | %------------------------------------------------------------------------- 76 | %applying boundary conditions (specified by restraints along X and Y axes) 77 | %on global stiffness matrix and global force vector 78 | K(ifix,:)=0; %Elements in rows with d.o.f corresponding to ifix are made 0 79 | K(:,ifix)=0; %Elements in columns with d.o.f corresponding to ifix are made 0 80 | K(ifix,ifix)=eye(length(ifix));%Diagonal elements with d.o.f corresponding to ifix are made 1 81 | Fc(ifix) = 0; %corresponding columns of Global force vector are also made zero 82 | %--------------------------------------------------------------------- 83 | %obtaining vector of nodal displacements along global axes 84 | u=inv(K)*Fc; 85 | 86 | Solution.data.u = u; 87 | 88 | 89 | 90 | %--------------------------------------------------------------------- 91 | %P O S T P R O C E S S I N G 92 | %--------------------------------------------------------------------- 93 | %Computation of internal forces and moments in elements of Plane Frame 94 | for e = 1 : Model.nElem 95 | %degrees of freedom corresponding to element e 96 | dof=[3*FirstNode(e)-2 3*FirstNode(e)-1 3*FirstNode(e) 3*SecondNode(e)-2 3*SecondNode(e)-1 3*SecondNode(e)]; 97 | c = Model.geometry.Cx(e);%direction cosines 98 | s = Model.geometry.Cy(e); 99 | le = Model.geometry.L(e); 100 | ae = Model.properties.A(e)*Model.properties.E(e); %axial rigidity 101 | ei = Model.properties.E(e)*Model.properties.Iz(e); %flexural rigidity 102 | %rotation transformation matrix for element e 103 | T=[c s 0 0 0 0; 104 | -s c 0 0 0 0; 105 | 0 0 1 0 0 0; 106 | 0 0 0 c s 0; 107 | 0 0 0 -s c 0; 108 | 0 0 0 0 0 1;]; 109 | %element stiffness matrix w.r.t local axes 110 | estif = [ ae/le 0 0 -ae/le 0 0; 111 | 0 12*ei/le^3 6*ei/le^2 0 -12*ei/le^3 6*ei/le^2; 112 | 0 6*ei/le^2 4*ei/le 0 -6*ei/le^2 2*ei/le ; 113 | -ae/le 0 0 ae/le 0 0; 114 | 0 -12*ei/le^3 -6*ei/le^2 0 12*ei/le^3 -6*ei/le^2; 115 | 0 6*ei/le^2 2*ei/le 0 -6*ei/le^2 4*ei/le ]; 116 | 117 | lforce(:,e) = estif*T*u(dof)-Model.loading.eforce(:,e); %Vector of internal forces of element w.r.t. local axes 118 | end 119 | Solution.data.lforce = lforce; 120 | Solution.nodalDisplacements = reshape(u,Model.nDof,Model.nNode)'; 121 | 122 | 123 | % Calculating the Reactions 124 | reactionForces = []; 125 | for i = 1 : Model.nNode 126 | if(Model.bound.resnode(i)==0) %restrained nodes (at support) are identified 127 | Rx = 0.0; %components of support reactions along global X and Y directions are initialized 128 | Ry = 0.0; 129 | Mz = 0.0;%support moment is initialized 130 | for e = 1 : Model.nElem %elements with "node i" as one of the nodes are identified 131 | %components of force in element e along global X and Y 132 | %directions are extracted using direction cosines and are 133 | %then its contribution to Rx and Ry is computed 134 | if(i == FirstNode(e)) %"node i" is the first node of element e 135 | Rx = Rx + Model.geometry.Cx(e)*lforce(1,e) - Model.geometry.Cy(e)*lforce(2,e); 136 | Ry = Ry + Model.geometry.Cy(e)*lforce(1,e) + Model.geometry.Cx(e)*lforce(2,e); 137 | Mz = Mz + lforce(3,e); 138 | end 139 | if(i == SecondNode(e)) %"node i" is the second node of element e 140 | Rx = Rx + Model.geometry.Cx(e)*lforce(4,e) - Model.geometry.Cy(e)*lforce(5,e); 141 | Ry = Ry + Model.geometry.Cy(e)*lforce(4,e) + Model.geometry.Cx(e)*lforce(5,e); 142 | Mz = Mz + lforce(6,e); 143 | end 144 | end 145 | %support reactions are set zero for any unrestrained degree of freedom 146 | %associated with a support 147 | if(Model.bound.resx(i) == 1) 148 | Rx = 0.0; 149 | end 150 | if(Model.bound.resy(i) == 1) 151 | Ry = 0.0; 152 | end 153 | if(Model.bound.resz(i) == 1) 154 | Mz = 0.0; 155 | end 156 | reactionForces = [reactionForces; i,Rx,Ry,Mz]; 157 | end 158 | end 159 | Solution.data.reactionForces = reactionForces; 160 | 161 | end -------------------------------------------------------------------------------- /Source Code/PlaneFrame/lib/planeFrameExplicit.m: -------------------------------------------------------------------------------- 1 | function Solution = planeFrameExplicit(Model) 2 | 3 | Model = ModelRevise(Model); 4 | 5 | Solution.info = ['Solution obtained on ', date]; 6 | 7 | FirstNode = Model.geometry.elements(:,1); 8 | SecondNode = Model.geometry.elements(:,2); 9 | ifix = Model.bound.ifix; 10 | 11 | % processing element load information 12 | ndof = Model.nNode * Model.nDof; 13 | K = zeros(ndof,ndof); %initialize the global stiffness matrix of size ndof 14 | Feq = zeros(ndof,1); %nodal force vector due to element loads 15 | ke_local (:,:,Model.nElem) = zeros(6); 16 | ke_global(:,:,Model.nElem) = zeros(6); 17 | T6(:,:,Model.nElem) = zeros(6); 18 | 19 | for e = 1 : Model.nElem 20 | c = Model.geometry.Cx(e); 21 | s = Model.geometry.Cy(e); 22 | le = Model.geometry.L(e); 23 | 24 | ae = Model.properties.A(e) * Model.properties.E(e); %axial rigidity 25 | ei = Model.properties.E(e) * Model.properties.Iz(e); %flexural rigidity 26 | %Degrees of freedom for element e with nodes m and n are 3m-2, 3m-1 ,3m, 3n-2, 3n-1 ,3n 27 | %These degrees of freedom are stored in the vector {dof} as shown below 28 | dof = [3*FirstNode(e)-2, 3*FirstNode(e)-1, 3*FirstNode(e), ... 29 | 3*SecondNode(e)-2, 3*SecondNode(e)-1, 3*SecondNode(e)]; 30 | 31 | % rotation transformation matrix for element e 32 | T=[c s 0 0 0 0; 33 | -s c 0 0 0 0; 34 | 0 0 1 0 0 0; 35 | 0 0 0 c s 0; 36 | 0 0 0 -s c 0; 37 | 0 0 0 0 0 1;]; 38 | 39 | % element stiffness matrix w.r.t local axes 40 | estif = [ ae/le 0 0 -ae/le 0 0; 41 | 0 12*ei/le^3 6*ei/le^2 0 -12*ei/le^3 6*ei/le^2; 42 | 0 6*ei/le^2 4*ei/le 0 -6*ei/le^2 2*ei/le ; 43 | -ae/le 0 0 ae/le 0 0; 44 | 0 -12*ei/le^3 -6*ei/le^2 0 12*ei/le^3 -6*ei/le^2; 45 | 0 6*ei/le^2 2*ei/le 0 -6*ei/le^2 4*ei/le ]; 46 | 47 | if Model.geometry.hingIndex(SecondNode(e)) == 1 % if the right node is a hinge 48 | % Modifications due to the hing on the right hand 49 | estif( 6 , : ) = 0; 50 | estif( : , 6 ) = 0; 51 | estif([2,5],[2,5]) = (1/4) * estif([2,5],[2,5]); 52 | estif([2,5], 3 ) = (1/2) * estif([2,5], 3 ); 53 | estif( 3 ,[2,5]) = (1/2) * estif( 3 ,[2,5]); 54 | estif( 3 , 3 ) = (3/4) * estif( 3 , 3 ); 55 | end 56 | 57 | 58 | ke=(T'*estif*T) ; %element stiffness matrix with reference to global axes 59 | 60 | ke_local(:,:,e) = estif; 61 | T6(:,:,e)= T; 62 | ke_global(:,:,e) = ke; 63 | 64 | 65 | K(dof,dof)=K(dof,dof)+ke; %assembly of global stiffness matrix K 66 | %{Feq} is vector of equivalent nodal forces due to element loads 67 | Feq(dof) = Feq(dof) + T'*Model.loading.eforce(:,e); 68 | end 69 | 70 | Fc = Model.loading.F+Feq; %combined force vector {Fc} is obtained by adding vector of nodal loads {F} to {Feq} 71 | 72 | Solution.data.ke_local = ke_local; 73 | Solution.data.ke_global = ke_global; 74 | Solution.data.T6 = T6; 75 | Solution.data.F_global = Fc; 76 | 77 | %------------------------------------------------------------------------- 78 | %applying boundary conditions (specified by restraints along X and Y axes) 79 | %on global stiffness matrix and global force vector 80 | K(ifix,:)=0; %Elements in rows with d.o.f corresponding to ifix are made 0 81 | K(:,ifix)=0; %Elements in columns with d.o.f corresponding to ifix are made 0 82 | K(ifix,ifix)=eye(length(ifix));%Diagonal elements with d.o.f corresponding to ifix are made 1 83 | Fc(ifix) = 0; %corresponding columns of Global force vector are also made zero 84 | %--------------------------------------------------------------------- 85 | %obtaining vector of nodal displacements along global axes 86 | u=inv(K)*Fc; 87 | 88 | Solution.data.u = u; 89 | 90 | 91 | 92 | %--------------------------------------------------------------------- 93 | %P O S T P R O C E S S I N G 94 | %--------------------------------------------------------------------- 95 | %Computation of internal forces and moments in elements of Plane Frame 96 | for e = 1 : Model.nElem 97 | %degrees of freedom corresponding to element e 98 | dof=[3*FirstNode(e)-2 3*FirstNode(e)-1 3*FirstNode(e) 3*SecondNode(e)-2 3*SecondNode(e)-1 3*SecondNode(e)]; 99 | 100 | % Vector of internal forces of element w.r.t. local axes 101 | % lforce(:,e) = estif*T*u(dof)-Model.loading.eforce(:,e); 102 | lforce(:,e) = ke_local(:,:,e) * T6(:,:,e) * u(dof)-Model.loading.eforce(:,e); 103 | end 104 | 105 | Solution.data.lforce = lforce; 106 | Solution.nodalDisplacements = reshape(u,Model.nDof,Model.nNode)'; 107 | 108 | 109 | % Calculating the Reactions 110 | reactionForces = []; 111 | for i = 1 : Model.nNode 112 | if(Model.bound.resnode(i)==0) %restrained nodes (at support) are identified 113 | Rx = 0.0; %components of support reactions along global X and Y directions are initialized 114 | Ry = 0.0; 115 | Mz = 0.0;%support moment is initialized 116 | for e = 1 : Model.nElem %elements with "node i" as one of the nodes are identified 117 | %components of force in element e along global X and Y 118 | %directions are extracted using direction cosines and are 119 | %then its contribution to Rx and Ry is computed 120 | if(i == FirstNode(e)) %"node i" is the first node of element e 121 | Rx = Rx + Model.geometry.Cx(e)*lforce(1,e) - Model.geometry.Cy(e)*lforce(2,e); 122 | Ry = Ry + Model.geometry.Cy(e)*lforce(1,e) + Model.geometry.Cx(e)*lforce(2,e); 123 | Mz = Mz + lforce(3,e); 124 | end 125 | if(i == SecondNode(e)) %"node i" is the second node of element e 126 | Rx = Rx + Model.geometry.Cx(e)*lforce(4,e) - Model.geometry.Cy(e)*lforce(5,e); 127 | Ry = Ry + Model.geometry.Cy(e)*lforce(4,e) + Model.geometry.Cx(e)*lforce(5,e); 128 | Mz = Mz + lforce(6,e); 129 | end 130 | end 131 | %support reactions are set zero for any unrestrained degree of freedom 132 | %associated with a support 133 | if(Model.bound.resx(i) == 1) 134 | Rx = 0.0; 135 | end 136 | if(Model.bound.resy(i) == 1) 137 | Ry = 0.0; 138 | end 139 | if(Model.bound.resz(i) == 1) 140 | Mz = 0.0; 141 | end 142 | reactionForces = [reactionForces; i,Rx,Ry,Mz]; 143 | end 144 | end 145 | Solution.reactionForces = reactionForces; 146 | 147 | 148 | 149 | 150 | 151 | 152 | %-------------------------------------------------------------------------- 153 | % this part will be moved in the future 154 | if isfield(Model,'analysis') 155 | if Model.analysis.showResults 156 | printResult(Solution,1) 157 | end 158 | if Model.analysis.showDetails 159 | % print stiffness matrices 160 | printStiff(Solution,1) 161 | end 162 | if Model.analysis.saveToFile 163 | outFile = fopen(Model.analysis.outputFileName, 'w'); 164 | printSummary(Model,outFile); 165 | printResult(Solution,outFile); 166 | 167 | fclose(outFile); 168 | end 169 | end 170 | %-------------------------------------------------------------------------- 171 | end 172 | 173 | 174 | 175 | %-------------------------------------------------------------------------- 176 | 177 | function Model = ModelRevise(Model) 178 | 179 | %-------------------------------------------------------------------------- 180 | % G E N E R A L I N F O R M A T I O N 181 | %-------------------------------------------------------------------------- 182 | nNode = Model.nNode; 183 | nElem = Model.nElem; 184 | nDof = Model.nDof; 185 | 186 | %-------------------------------------------------------------------------- 187 | % R E A D I N G N O D A L I N F O R M A T I O N 188 | %-------------------------------------------------------------------------- 189 | 190 | Xval = Model.geometry.coordinates(:,1); % x coordinates of nodes 191 | Yval = Model.geometry.coordinates(:,2); % y coordinates of nodes 192 | 193 | % restraints of a node 194 | res = ones(nNode,nDof); 195 | for i = 1 : Model.nBoundary 196 | row = Model.boundary(i,1); 197 | col = Model.boundary(i,2); 198 | res(row,col) = 0; 199 | end 200 | resx = res(:,1); % restraint along x-direction 201 | resy = res(:,2); % restraint along y-direction 202 | resz = res(:,3); % restraint about z-direction 203 | 204 | %-------------------------------------------------------------------------- 205 | % Generation of nodal force vector (F) (of size ndof) along global axes 206 | %-------------------------------------------------------------------------- 207 | 208 | hingeIndex = zeros(nNode,1); 209 | if isfield(Model,'hinge') 210 | if ~isempty(Model.hinge) 211 | hingeIndex(Model.hinge)=1; 212 | end 213 | end 214 | % hinge = 1 regular node = 0 215 | 216 | % nodal forces 217 | F = zeros(nNode,nDof); 218 | for i = 1 : Model.nNodalForce 219 | node = Model.loading.nodalForces(i,1); 220 | F(node, 1:Model.nDof) = Model.loading.nodalForces(i,2:end); 221 | end 222 | % reshape to vector form 223 | F = reshape(F',1,nDof*nNode)'; 224 | 225 | %-------------------------------------------------------------------------- 226 | % B O U N D A R Y C O N D I T I O N I N F O R M A T I O N 227 | %-------------------------------------------------------------------------- 228 | % bn is a counter for the total number of restraints 229 | bn = 0; % initialized to zero 230 | %-------------------------------------------------------------------------- 231 | % notation used to indicate restraint associated with a given dof 232 | % 0 indicates RESTRAINED degree of freedom 233 | % 1 indicates UNRESTRAINED degree of freedom 234 | %-------------------------------------------------------------------------- 235 | % A new vector "{resnode}" of size nNode is initialized with ones 236 | % {resnode} is used to indicate the status of restraint for nodes: 237 | % - Restrained nodes (at supports): 0 238 | % (with atleast one RESTRAINED degree of freedom) 239 | % - Unrestrained nodes : 1resnode = ones(nNode,1); 240 | 241 | resnode = ones(nNode,1); % nodes are initialized as UNRESTRAINED by default 242 | 243 | for i = 1 : nNode 244 | if(resx(i) == 0) % if this dof along x-direction is restrained 245 | bn = bn+1; 246 | ifix(bn) = 3*i-2; % add to the list of restrained dofs 247 | resnode(i) = 0; 248 | end 249 | if(resy(i) == 0) % if this dof along x-direction is restrained 250 | bn = bn+1; 251 | ifix(bn) = 3*i-1; % add to the list of restrained dofs 252 | resnode(i) = 0; 253 | end 254 | if(resz(i) == 0) % if this dof ABOUT z-direction is restrained 255 | bn = bn+1; 256 | ifix(bn) = 3*i; % add to the list of restrained dofs 257 | resnode(i) = 0; 258 | end 259 | end 260 | % NOTE: bn is incremented by 3 for a fixed support 261 | % bn is incremented by 2 for a pin support 262 | % bn is incremented by 1 for a roller support in the above for-loop 263 | % at the end of the above loop, 264 | % bn is total number of restrained degrees of freedom 265 | % ifix is list of restrained degrees of freedom for the Plane Frame 266 | 267 | %-------------------------------------------------------------------------- 268 | % R E A D I N G E L E M E N T I N F O R M A T I O N 269 | %-------------------------------------------------------------------------- 270 | 271 | Cx = zeros(nElem,1); % direction cosines of elements Cx and Cy 272 | Cy = zeros(nElem,1); 273 | L = zeros(nElem,1); % length of each element 274 | eforce = zeros(6,nElem); % element force vector with six dofs 275 | % (3 at each node of element) 276 | FirstNode = Model.geometry.elements(:,1); 277 | SecondNode = Model.geometry.elements(:,2); 278 | 279 | 280 | sectProp = Model.sections(Model.elemSectId,:); 281 | A = sectProp(:,3); 282 | E = sectProp(:,1); 283 | Iz = sectProp(:,2); 284 | 285 | 286 | for e = 1 : nElem 287 | x1 = Xval(FirstNode(e)); 288 | y1 = Yval(FirstNode(e)); %x and y coordinates of first node 289 | x2 = Xval(SecondNode(e)); 290 | y2 = Yval(SecondNode(e)); %x and y coordinates of second node 291 | le = sqrt((x2-x1)^2+(y2-y1)^2); %length of element e 292 | %direction cosines of element e 293 | c = (x2-x1)/le; 294 | s = (y2-y1)/le; 295 | %Storing values of direction cosines c and s in vectors {Cx} and {Cy} for subsequent use 296 | Cx(e) = c; 297 | Cy(e) = s; 298 | L (e) = le; 299 | end 300 | 301 | distLoad = zeros(nElem,4); 302 | for i = 1 : Model.nTractionForce 303 | e = Model.loading.tractionForces(i).element; 304 | Ty = Model.loading.tractionForces(i).eq{2}; 305 | distLoad(e,:) = [Ty(0), 0, Ty(L(e)), L(e)]; 306 | end 307 | % reading element load information 308 | % uniformly distributed load of intensity w1 acts from a distance of d1 to d2 309 | % as measured from left end of element 310 | wr = distLoad(:,1); % distributed load w1 acting on elements from column 7 311 | d1 = distLoad(:,2); % left limit d1 of distributed load w1 from columns 8 312 | wl = distLoad(:,3); % distributed load w2 acting on elements from column 9 313 | d2 = distLoad(:,4); % right limit d2 of distributed load w1 from column 10 314 | 315 | %----------------------- 316 | w1 = -wr; 317 | % w1 = wr; 318 | 319 | %Computation of equivalent nodal loads owing to uniformly distributed load over some portion of the span 320 | for e = 1 : nElem 321 | %computation of equivalent nodal loads owing to uniformly distributed load over some portion of the span 322 | c1 = d2(e) - d1(e); 323 | a = d1(e) + 0.5*c1; 324 | b = 0.5*c1 + le - d2(e); 325 | p1 = (-w1(e)*c1 / (12*le^2)) * (12*a*b^2 + c1^2*(le-3*b)); 326 | p2 = ( w1(e)*c1 / (12*le^2)) * (12*a^2*b+c1^2*(le-3*a)); 327 | p3 = ( w1(e)*c1 * b/le) - (p1+p2)/le; 328 | p4 = ( w1(e)*c1 * a/le) + (p1+p2)/le; 329 | eforce(:,e) = eforce(:,e) + [0.0 -p3 p1 0.0 -p4 p2]'; 330 | %Negative of vector of fixed end forces in added to the element force vector 331 | end 332 | %-------------------------------------------------------------------------- 333 | % F O R M I N G M O D E L S T R U C T U R E 334 | %-------------------------------------------------------------------------- 335 | % Model.info = 'Plane Beam/Frame Program'; 336 | % Model.analysisType = 'BEAM'; 337 | % Model.nDim = 2; % 2D (plane beam/frame) 338 | % Model.nNode = nNode; 339 | % Model.nElem = nElem; 340 | % Model.nDof = 3; 341 | % Model.nElemNode = 2; 342 | 343 | % Model.geometry.coordinates = [Xval, Yval]; 344 | % Model.geometry.elements = [FirstNode, SecondNode]; 345 | Model.geometry.Cx = Cx; 346 | Model.geometry.Cy = Cy; 347 | Model.geometry.L = L; 348 | Model.geometry.hingIndex = hingeIndex; 349 | 350 | Model.properties.A = A; 351 | Model.properties.E = E; 352 | Model.properties.Iz= Iz; 353 | 354 | Model.nBoundary = bn; 355 | Model.bound.resx = resx; 356 | Model.bound.resy = resy; 357 | Model.bound.resz = resz; 358 | Model.bound.resnode = resnode; 359 | Model.bound.ifix = ifix; 360 | 361 | Model.loading.F = F; 362 | Model.loading.eforce = eforce; 363 | Model.loading.data = [d1,d2,wl,wr]; 364 | end -------------------------------------------------------------------------------- /Source Code/PlaneFrame/lib/shapefunctionderivs.m: -------------------------------------------------------------------------------- 1 | %================= SHAPE FUNCTION DERIVATIVES ====================== 2 | % 3 | function dNdxi = shapefunctionderivs(nDim,nElemNode,xi) 4 | 5 | dNdxi = zeros(nElemNode,nDim); 6 | % 7 | % 1D elements 8 | % 9 | if (nDim == 1) 10 | if (nElemNode==2) 11 | dNdxi(1,1) = 0.5; 12 | dNdxi(2,1) = -0.5; 13 | elseif (nElemNode == 3) 14 | dNdxi(1,1) = -0.5+xi(1); 15 | dNdxi(2,1) = 0.5+xi(1); 16 | dNdxi(3,1) = -2.*xi(1); 17 | end 18 | % 19 | % 2D elements 20 | % 21 | elseif (nDim == 2) 22 | % 23 | % Triangular element 24 | % 25 | if ( nElemNode == 3 ) 26 | dNdxi(1,1) = 1.; 27 | dNdxi(2,2) = 1.; 28 | dNdxi(3,1) = -1.; 29 | dNdxi(3,2) = -1.; 30 | elseif ( nElemNode == 6 ) 31 | xi3 = 1.-xi(1)-xi(2); 32 | dNdxi(1,1) = 4.*xi(1)-1.; 33 | dNdxi(2,2) = 4.*xi(2)-1.; 34 | dNdxi(3,1) = -(4.*xi3-1.); 35 | dNdxi(3,2) = -(4.*xi3-1.); 36 | dNdxi(4,1) = 4.*xi(2); 37 | dNdxi(4,2) = 4.*xi(1); 38 | dNdxi(5,1) = -4.*xi(2); 39 | dNdxi(5,2) = -4.*xi(1); 40 | dNdxi(6,1) = 4.*xi3 - 4.*xi(1); 41 | dNdxi(6,2) = 4.*xi3 - 4.*xi(2); 42 | % 43 | % Rectangular element 44 | % 45 | elseif ( nElemNode == 4 ) 46 | dNdxi(1,1) = -0.25*(1.-xi(2)); 47 | dNdxi(1,2) = -0.25*(1.-xi(1)); 48 | dNdxi(2,1) = 0.25*(1.-xi(2)); 49 | dNdxi(2,2) = -0.25*(1.+xi(1)); 50 | dNdxi(3,1) = 0.25*(1.+xi(2)); 51 | dNdxi(3,2) = 0.25*(1.+xi(1)); 52 | dNdxi(4,1) = -0.25*(1.+xi(2)); 53 | dNdxi(4,2) = 0.25*(1.-xi(1)); 54 | elseif (nElemNode == 8) 55 | dNdxi(1,1) = 0.25*(1.-xi(2))*(2.*xi(1)+xi(2)); 56 | dNdxi(1,2) = 0.25*(1.-xi(1))*(xi(1)+2.*xi(2)); 57 | dNdxi(2,1) = 0.25*(1.-xi(2))*(2.*xi(1)-xi(2)); 58 | dNdxi(2,2) = 0.25*(1.+xi(1))*(2.*xi(2)-xi(1)); 59 | dNdxi(3,1) = 0.25*(1.+xi(2))*(2.*xi(1)+xi(2)); 60 | dNdxi(3,2) = 0.25*(1.+xi(1))*(2.*xi(2)+xi(1)); 61 | dNdxi(4,1) = 0.25*(1.+xi(2))*(2.*xi(1)-xi(2)); 62 | dNdxi(4,2) = 0.25*(1.-xi(1))*(2.*xi(2)-xi(1)); 63 | dNdxi(5,1) = -xi(1)*(1.-xi(2)); 64 | dNdxi(5,2) = -0.5*(1.-xi(1)*xi(1)); 65 | dNdxi(6,1) = 0.5*(1.-xi(2)*xi(2)); 66 | dNdxi(6,2) = -(1.+xi(1))*xi(2); 67 | dNdxi(7,1) = -xi(1)*(1.+xi(2)); 68 | dNdxi(7,2) = 0.5*(1.-xi(1)*xi(1)); 69 | dNdxi(8,1) = -0.5*(1.-xi(2)*xi(2)); 70 | dNdxi(8,2) = -(1.-xi(1))*xi(2); 71 | end 72 | % 73 | % 3D elements 74 | % 75 | elseif (nDim==3) 76 | 77 | if (nElemNode == 4) 78 | dNdxi(1,1) = 1.; 79 | dNdxi(2,2) = 1.; 80 | dNdxi(3,3) = 1.; 81 | dNdxi(4,1) = -1.; 82 | dNdxi(4,2) = -1.; 83 | dNdxi(4,3) = -1.; 84 | elseif (nElemNode == 10) 85 | xi4 = 1.-xi(1)-xi(2)-xi(3); 86 | dNdxi(1,1) = (4.*xi(1)-1.); 87 | dNdxi(2,2) = (4.*xi(2)-1.); 88 | dNdxi(3,3) = (4.*xi(3)-1.); 89 | dNdxi(4,1) = -(4.*xi4-1.); 90 | dNdxi(4,2) = -(4.*xi4-1.); 91 | dNdxi(4,3) = -(4.*xi4-1.); 92 | dNdxi(5,1) = 4.*xi(2); 93 | dNdxi(5,2) = 4.*xi(1); 94 | dNdxi(6,2) = 4.*xi(3); 95 | dNdxi(6,3) = 4.*xi(2); 96 | dNdxi(7,1) = 4.*xi(3); 97 | dNdxi(7,3) = 4.*xi(1); 98 | dNdxi(8,1) = 4.*(xi4-xi(1)); 99 | dNdxi(8,2) = -4.*xi(1); 100 | dNdxi(8,3) = -4.*xi(1); 101 | dNdxi(9,1) = -4.*xi(2); 102 | dNdxi(9,2) = 4.*(xi4-xi(2)); 103 | dNdxi(9,3) = -4.*xi(2); 104 | dNdxi(10,1) = -4.*xi(3)*xi4; 105 | dNdxi(10,2) = -4.*xi(3); 106 | dNdxi(10,3) = 4.*(xi4-xi(3)); 107 | elseif (nElemNode == 8) 108 | dNdxi(1,1) = -(1.-xi(2))*(1.-xi(3))/8.; 109 | dNdxi(1,2) = -(1.-xi(1))*(1.-xi(3))/8.; 110 | dNdxi(1,3) = -(1.-xi(1))*(1.-xi(2))/8.; 111 | dNdxi(2,1) = (1.-xi(2))*(1.-xi(3))/8.; 112 | dNdxi(2,2) = -(1.+xi(1))*(1.-xi(3))/8.; 113 | dNdxi(2,3) = -(1.+xi(1))*(1.-xi(2))/8.; 114 | dNdxi(3,1) = (1.+xi(2))*(1.-xi(3))/8.; 115 | dNdxi(3,2) = (1.+xi(1))*(1.-xi(3))/8.; 116 | dNdxi(3,3) = -(1.+xi(1))*(1.+xi(2))/8.; 117 | dNdxi(4,1) = -(1.+xi(2))*(1.-xi(3))/8.; 118 | dNdxi(4,2) = (1.-xi(1))*(1.-xi(3))/8.; 119 | dNdxi(4,3) = -(1.-xi(1))*(1.+xi(2))/8.; 120 | dNdxi(5,1) = -(1.-xi(2))*(1.+xi(3))/8.; 121 | dNdxi(5,2) = -(1.-xi(1))*(1.+xi(3))/8.; 122 | dNdxi(5,3) = (1.-xi(1))*(1.-xi(2))/8.; 123 | dNdxi(6,1) = (1.-xi(2))*(1.+xi(3))/8.; 124 | dNdxi(6,2) = -(1.+xi(1))*(1.+xi(3))/8.; 125 | dNdxi(6,3) = (1.+xi(1))*(1.-xi(2))/8.; 126 | dNdxi(7,1) = (1.+xi(2))*(1.+xi(3))/8.; 127 | dNdxi(7,2) = (1.+xi(1))*(1.+xi(3))/8.; 128 | dNdxi(7,3) = (1.+xi(1))*(1.+xi(2))/8.; 129 | dNdxi(8,1) = -(1.+xi(2))*(1.+xi(3))/8.; 130 | dNdxi(8,2) = (1.-xi(1))*(1.+xi(3))/8.; 131 | dNdxi(8,3) = (1.-xi(1))*(1.+xi(2))/8.; 132 | elseif (nElemNode == 20) 133 | dNdxi(1,1) = (-(1.-xi(2))*(1.-xi(3))*(-xi(1)-xi(2)-xi(3)-2.)-(1.-xi(1))*(1.-xi(2))*(1.-xi(3)))/8.; 134 | dNdxi(1,2) = (-(1.-xi(1))*(1.-xi(3))*(-xi(1)-xi(2)-xi(3)-2.)-(1.-xi(1))*(1.-xi(2))*(1.-xi(3)))/8.; 135 | dNdxi(1,3) = (-(1.-xi(1))*(1.-xi(2))*(-xi(1)-xi(2)-xi(3)-2.)-(1.-xi(1))*(1.-xi(2))*(1.-xi(3)))/8.; 136 | 137 | dNdxi(2,1) = ((1.-xi(2))*(1.-xi(3))*(xi(1)-xi(2)-xi(3)-2.)+(1.+xi(1))*(1.-xi(2))*(1.-xi(3)))/8.; 138 | dNdxi(2,2) = (-(1.+xi(1))*(1.-xi(3))*(xi(1)-xi(2)-xi(3)-2.)-(1.+xi(1))*(1.-xi(2))*(1.-xi(3)))/8.; 139 | dNdxi(2,3) = (-(1.+xi(1))*(1.-xi(2))*(xi(1)-xi(2)-xi(3)-2.)-(1.+xi(1))*(1.-xi(2))*(1.-xi(3)))/8.; 140 | 141 | dNdxi(3,1) = ((1.+xi(2))*(1.-xi(3))*(xi(1)+xi(2)-xi(3)-2.)+(1.+xi(1))*(1.+xi(2))*(1.-xi(3)))/8.; 142 | dNdxi(3,2) = ((1.+xi(1))*(1.-xi(3))*(xi(1)+xi(2)-xi(3)-2.)+(1.+xi(1))*(1.+xi(2))*(1.-xi(3)))/8.; 143 | dNdxi(3,3) = (-(1.+xi(1))*(1.+xi(2))*(xi(1)+xi(2)-xi(3)-2.)-(1.+xi(1))*(1.+xi(2))*(1.-xi(3)))/8.; 144 | 145 | dNdxi(4,1) = (-(1.+xi(2))*(1.-xi(3))*(-xi(1)+xi(2)-xi(3)-2.)-(1.-xi(1))*(1.+xi(2))*(1.-xi(3)))/8.; 146 | dNdxi(4,2) = ((1.-xi(1))*(1.-xi(3))*(-xi(1)+xi(2)-xi(3)-2.)+(1.-xi(1))*(1.+xi(2))*(1.-xi(3)))/8.; 147 | dNdxi(4,3) = (-(1.-xi(1))*(1.+xi(2))*(-xi(1)+xi(2)-xi(3)-2.)-(1.-xi(1))*(1.+xi(2))*(1.-xi(3)))/8.; 148 | dNdxi(5,1) = (-(1.-xi(2))*(1.+xi(3))*(-xi(1)-xi(2)+xi(3)-2.)-(1.-xi(1))*(1.-xi(2))*(1.+xi(3)))/8.; 149 | dNdxi(5,2) = (-(1.-xi(1))*(1.+xi(3))*(-xi(1)-xi(2)+xi(3)-2.)-(1.-xi(1))*(1.-xi(2))*(1.+xi(3)))/8.; 150 | dNdxi(5,3) = ((1.-xi(1))*(1.-xi(2))*(-xi(1)-xi(2)+xi(3)-2.)+(1.-xi(1))*(1.-xi(2))*(1.+xi(3)))/8.; 151 | dNdxi(6,1) = ((1.-xi(2))*(1.+xi(3))*(xi(1)-xi(2)+xi(3)-2.)+(1.+xi(1))*(1.-xi(2))*(1.+xi(3)))/8.; 152 | dNdxi(6,2) = (-(1.+xi(1))*(1.+xi(3))*(xi(1)-xi(2)+xi(3)-2.)-(1.+xi(1))*(1.-xi(2))*(1.+xi(3)))/8.; 153 | dNdxi(6,3) = ((1.+xi(1))*(1.-xi(2))*(xi(1)-xi(2)+xi(3)-2.)+(1.+xi(1))*(1.-xi(2))*(1.+xi(3)))/8.; 154 | dNdxi(7,1) = ((1.+xi(2))*(1.+xi(3))*(xi(1)+xi(2)+xi(3)-2.)+(1.+xi(1))*(1.+xi(2))*(1.+xi(3)))/8.; 155 | dNdxi(7,2) = ((1.+xi(1))*(1.+xi(3))*(xi(1)+xi(2)+xi(3)-2.)+(1.+xi(1))*(1.+xi(2))*(1.+xi(3)))/8.; 156 | dNdxi(7,3) = ((1.+xi(1))*(1.+xi(2))*(xi(1)+xi(2)+xi(3)-2.)+(1.+xi(1))*(1.+xi(2))*(1.+xi(3)))/8.; 157 | dNdxi(8,1) = (-(1.+xi(2))*(1.+xi(3))*(-xi(1)+xi(2)+xi(3)-2.)-(1.-xi(1))*(1.+xi(2))*(1.+xi(3)))/8.; 158 | dNdxi(8,2) = ((1.-xi(1))*(1.+xi(3))*(-xi(1)+xi(2)+xi(3)-2.)+(1.-xi(1))*(1.+xi(2))*(1.+xi(3)))/8.; 159 | dNdxi(8,3) = ((1.-xi(1))*(1.+xi(2))*(-xi(1)+xi(2)+xi(3)-2.)+(1.-xi(1))*(1.+xi(2))*(1.+xi(3)))/8.; 160 | dNdxi(9,1) = -2.*xi(1)*(1.-xi(2))*(1.-xi(3))/4.; 161 | dNdxi(9,2) = -(1.-xi(1)^2)*(1.-xi(3))/4.; 162 | dNdxi(9,3) = -(1.-xi(1)^2)*(1.-xi(2))/4.; 163 | dNdxi(10,1) = (1.-xi(2)^2)*(1.-xi(3))/4.; 164 | dNdxi(10,2) = -2.*xi(2)*(1.+xi(1))*(1.-xi(3))/4.; 165 | dNdxi(10,3) = -(1.-xi(2)^2)*(1.+xi(1))/4.; 166 | dNdxi(11,1) = -2.*xi(1)*(1.+xi(2))*(1.-xi(3))/4.; 167 | dNdxi(11,2) = (1.-xi(1)^2)*(1.-xi(3))/4.; 168 | dNdxi(11,3) = -(1.-xi(1)^2)*(1.+xi(2))/4.; 169 | dNdxi(12,1) = -(1.-xi(2)^2)*(1.-xi(3))/4.; 170 | dNdxi(12,2) = -2.*xi(2)*(1.-xi(1))*(1.-xi(3))/4.; 171 | dNdxi(12,3) = -(1.-xi(2)^2)*(1.-xi(1))/4.; 172 | dNdxi(13,1) = -2.*xi(1)*(1.-xi(2))*(1.+xi(3))/4.; 173 | dNdxi(13,2) = -(1.-xi(1)^2)*(1.+xi(3))/4.; 174 | dNdxi(13,3) = (1.-xi(1)^2)*(1.-xi(2))/4.; 175 | dNdxi(14,1) = (1.-xi(2)^2)*(1.+xi(3))/4.; 176 | dNdxi(14,2) = -2.*xi(2)*(1.+xi(1))*(1.+xi(3))/4.; 177 | dNdxi(14,3) = (1.-xi(2)^2)*(1.+xi(1))/4.; 178 | dNdxi(15,1) = -2.*xi(1)*(1.+xi(2))*(1.+xi(3))/4.; 179 | dNdxi(15,2) = (1.-xi(1)^2)*(1.+xi(3))/4.; 180 | dNdxi(15,3) = (1.-xi(1)^2)*(1.+xi(2))/4.; 181 | dNdxi(16,1) = -(1.-xi(2)^2)*(1.+xi(3))/4.; 182 | dNdxi(16,2) = -2.*xi(2)*(1.-xi(1))*(1.+xi(3))/4.; 183 | dNdxi(16,3) = (1.-xi(2)^2)*(1.-xi(1))/4.; 184 | dNdxi(17,1) = -(1.-xi(2))*(1.-xi(3)^2)/4.; 185 | dNdxi(17,2) = -(1.-xi(1))*(1.-xi(3)^2)/4.; 186 | dNdxi(17,3) = -xi(3)*(1.-xi(1))*(1.-xi(2))/2.; 187 | dNdxi(18,1) = (1.-xi(2))*(1.-xi(3)^2)/4.; 188 | dNdxi(18,2) = -(1.+xi(1))*(1.-xi(3)^2)/4.; 189 | dNdxi(18,3) = -xi(3)*(1.+xi(1))*(1.-xi(2))/2.; 190 | dNdxi(19,1) = (1.+xi(2))*(1.-xi(3)^2)/4.; 191 | dNdxi(19,2) = (1.+xi(1))*(1.-xi(3)^2)/4.; 192 | dNdxi(19,3) = -xi(3)*(1.+xi(1))*(1.+xi(2))/2.; 193 | dNdxi(20,1) = -(1.+xi(2))*(1.-xi(3)^2)/4.; 194 | dNdxi(20,2) = (1.-xi(1))*(1.-xi(3)^2)/4.; 195 | dNdxi(20,3) = -xi(3)*(1.-xi(1))*(1.+xi(2))/2.; 196 | end 197 | end 198 | 199 | end 200 | -------------------------------------------------------------------------------- /Source Code/PlaneFrame/lib/shapefunctions.m: -------------------------------------------------------------------------------- 1 | % 2 | %================= SHAPE FUNCTIONS ================================== 3 | % 4 | % Calculates shape functions for various element types 5 | % 6 | function N = shapefunctions(nDim,nElemNode,xi) 7 | 8 | 9 | N = zeros(nElemNode,1); 10 | % 11 | % 1D elements 12 | % 13 | if (nDim == 1) 14 | if (nElemNode==2) 15 | N(1) = 0.5*(1.+xi(1)); 16 | N(2) = 0.5*(1.-xi(1)); 17 | elseif (nElemNode == 3) 18 | N(1) = -0.5*xi(1)*(1.-xi(1)); 19 | N(2) = 0.5*xi(1)*(1.+xi(1)); 20 | N(3) = (1.-xi(1))*(1.+xi(1)); 21 | end 22 | % 23 | % 2D elements 24 | % 25 | elseif (nDim == 2) 26 | % 27 | % Triangular element 28 | % 29 | if ( nElemNode == 3 ) 30 | N(1) = xi(1); 31 | N(2) = xi(2); 32 | N(3) = 1.-xi(1)-xi(2); 33 | elseif ( nElemNode == 6 ) 34 | xi3 = 1.-xi(1)-xi(2); 35 | N(1) = (2.*xi(1)-1.)*xi(1); 36 | N(2) = (2.*xi(2)-1.)*xi(2); 37 | N(3) = (2.*xi3-1.)*xi3; 38 | N(4) = 4.*xi(1)*xi(2); 39 | N(5) = 4.*xi(2)*xi3; 40 | N(6) = 4.*xi3*xi(1); 41 | % 42 | % Rectangular element 43 | % 44 | elseif ( nElemNode == 4 ) 45 | N(1) = 0.25*(1.-xi(1))*(1.-xi(2)); 46 | N(2) = 0.25*(1.+xi(1))*(1.-xi(2)); 47 | N(3) = 0.25*(1.+xi(1))*(1.+xi(2)); 48 | N(4) = 0.25*(1.-xi(1))*(1.+xi(2)); 49 | elseif (nElemNode == 8) 50 | N(1) = -0.25*(1.-xi(1))*(1.-xi(2))*(1.+xi(1)+xi(2)); 51 | N(2) = 0.25*(1.+xi(1))*(1.-xi(2))*(xi(1)-xi(2)-1.); 52 | N(3) = 0.25*(1.+xi(1))*(1.+xi(2))*(xi(1)+xi(2)-1.); 53 | N(4) = 0.25*(1.-xi(1))*(1.+xi(2))*(xi(2)-xi(1)-1.); 54 | N(5) = 0.5*(1.-xi(1)*xi(1))*(1.-xi(2)); 55 | N(6) = 0.5*(1.+xi(1))*(1.-xi(2)*xi(2)); 56 | N(7) = 0.5*(1.-xi(1)*xi(1))*(1.+xi(2)); 57 | N(8) = 0.5*(1.-xi(1))*(1.-xi(2)*xi(2)); 58 | end 59 | % 60 | elseif (nDim==3) 61 | 62 | if (nElemNode == 4) 63 | N(1) = xi(1); 64 | N(2) = xi(2); 65 | N(3) = xi(3); 66 | N(4) = 1.-xi(1)-xi(2)-xi(3); 67 | elseif (nElemNode == 10) 68 | xi4 = 1.-xi(1)-xi(2)-xi(3); 69 | N(1) = (2.*xi(1)-1.)*xi(1); 70 | N(2) = (2.*xi(2)-1.)*xi(2); 71 | N(3) = (2.*xi(3)-1.)*xi(3); 72 | N(4) = (2.*xi4-1.)*xi4; 73 | N(5) = 4.*xi(1)*xi(2); 74 | N(6) = 4.*xi(2)*xi(3); 75 | N(7) = 4.*xi(3)*xi(1); 76 | N(8) = 4.*xi(1)*xi4; 77 | N(9) = 4.*xi(2)*xi4; 78 | N(10) = 4.*xi(3)*xi4; 79 | elseif (nElemNode == 8) 80 | N(1) = (1.-xi(1))*(1.-xi(2))*(1.-xi(3))/8.; 81 | N(2) = (1.+xi(1))*(1.-xi(2))*(1.-xi(3))/8.; 82 | N(3) = (1.+xi(1))*(1.+xi(2))*(1.-xi(3))/8.; 83 | N(4) = (1.-xi(1))*(1.+xi(2))*(1.-xi(3))/8.; 84 | N(5) = (1.-xi(1))*(1.-xi(2))*(1.+xi(3))/8.; 85 | N(6) = (1.+xi(1))*(1.-xi(2))*(1.+xi(3))/8.; 86 | N(7) = (1.+xi(1))*(1.+xi(2))*(1.+xi(3))/8.; 87 | N(8) = (1.-xi(1))*(1.+xi(2))*(1.+xi(3))/8.; 88 | elseif (nElemNode == 20) 89 | N(1) = (1.-xi(1))*(1.-xi(2))*(1.-xi(3))*(-xi(1)-xi(2)-xi(3)-2.)/8.; 90 | N(2) = (1.+xi(1))*(1.-xi(2))*(1.-xi(3))*(xi(1)-xi(2)-xi(3)-2.)/8.; 91 | N(3) = (1.+xi(1))*(1.+xi(2))*(1.-xi(3))*(xi(1)+xi(2)-xi(3)-2.)/8.; 92 | N(4) = (1.-xi(1))*(1.+xi(2))*(1.-xi(3))*(-xi(1)+xi(2)-xi(3)-2.)/8.; 93 | N(5) = (1.-xi(1))*(1.-xi(2))*(1.+xi(3))*(-xi(1)-xi(2)+xi(3)-2.)/8.; 94 | N(6) = (1.+xi(1))*(1.-xi(2))*(1.+xi(3))*(xi(1)-xi(2)+xi(3)-2.)/8.; 95 | N(7) = (1.+xi(1))*(1.+xi(2))*(1.+xi(3))*(xi(1)+xi(2)+xi(3)-2.)/8.; 96 | N(8) = (1.-xi(1))*(1.+xi(2))*(1.+xi(3))*(-xi(1)+xi(2)+xi(3)-2.)/8.; 97 | N(9) = (1.-xi(1)^2)*(1.-xi(2))*(1.-xi(3))/4.; 98 | N(10) = (1.+xi(1))*(1.-xi(2)^2)*(1.-xi(3))/4.; 99 | N(11) = (1.-xi(1)^2)*(1.+xi(2))*(1.-xi(3))/4.; 100 | N(12) = (1.-xi(1))*(1.-xi(2)^2)*(1.-xi(3))/4.; 101 | N(13) = (1.-xi(1)^2)*(1.-xi(2))*(1.+xi(3))/4.; 102 | N(14) = (1.+xi(1))*(1.-xi(2)^2)*(1.+xi(3))/4.; 103 | N(15) = (1.-xi(1)^2)*(1.+xi(2))*(1.+xi(3))/4.; 104 | N(16) = (1.-xi(1))*(1.-xi(2)^2)*(1.+xi(3))/4.; 105 | N(17) = (1.-xi(1))*(1.-xi(2))*(1.-xi(3)^2)/4.; 106 | N(18) = (1.+xi(1))*(1.-xi(2))*(1.-xi(3)^2)/4.; 107 | N(19) = (1.+xi(1))*(1.+xi(2))*(1.-xi(3)^2)/4.; 108 | N(20) = (1.-xi(1))*(1.+xi(2))*(1.-xi(3)^2)/4.; 109 | end 110 | end 111 | 112 | end 113 | -------------------------------------------------------------------------------- /Source Code/PlaneFrame/lib_io/inpFileReader.p: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/shahrokhx/FEM_Toolbox/8dda726b82d707d2e3404996893c95b8e2de3ef9/Source Code/PlaneFrame/lib_io/inpFileReader.p -------------------------------------------------------------------------------- /Source Code/PlaneFrame/lib_io/plotmesh.p: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/shahrokhx/FEM_Toolbox/8dda726b82d707d2e3404996893c95b8e2de3ef9/Source Code/PlaneFrame/lib_io/plotmesh.p -------------------------------------------------------------------------------- /Source Code/PlaneFrame/lib_io/printResult.m: -------------------------------------------------------------------------------- 1 | function printResult(Solution,fid) 2 | 3 | if nargin < 2 4 | fid = 1; 5 | end 6 | BULLET_CHAR = char(15); 7 | 8 | fprintf(fid,'\n\n'); 9 | printDLine(fid,96) 10 | printCTitle(fid,'O U T P U T S U M M A R Y',96) 11 | printDLine(fid,96) 12 | 13 | if isfield(Solution,'info') 14 | fprintf(fid,'%c About: \n',BULLET_CHAR); 15 | fprintf(fid,'%s\n', Solution.info); 16 | end 17 | 18 | 19 | uNodal = Solution.nodalDisplacements; 20 | u = Solution.data.u; 21 | [nNode,~] = size(uNodal); 22 | 23 | printDLine(fid,96) 24 | printCTitle(fid,'N O D A L D I S P L A C E M E N T S',96) 25 | printSLine(fid,96) 26 | fprintf(fid,'Node X- displacement Y- displacement Z-rotation\n'); 27 | printLine(fid,96) 28 | for i=1 : nNode 29 | fprintf(fid,'%2d %22.10e %22.10e %22.10e\n',i,u(3*i-2),u(3*i-1),u(3*i)); 30 | end 31 | 32 | lforce = Solution.data.lforce; 33 | printDLine(fid,96) 34 | printCTitle(fid,'F O R C E S A N D M O M E N T S I N E L E M E N T S',96); 35 | printSLine(fid,96); 36 | fprintf(fid,'ELEMENT Axial Shear Bending Axial Shear Bending\n'); 37 | fprintf(fid,' Force Force Moment Force Force Moment\n'); 38 | fprintf(fid,' ---------------------------- ------------------------------\n'); 39 | fprintf(fid,' at FIRST NODE at SECOND NODE\n'); 40 | fprintf(fid,'--------------------------------------------------------------------------\n'); 41 | for e = 1 : size(lforce,2) 42 | f1= lforce(1,e); 43 | f2= lforce(2,e); 44 | f3= lforce(3,e); 45 | f4= lforce(4,e); 46 | f5= lforce(5,e); 47 | f6= lforce(6,e); 48 | fprintf(fid,'%3d %10.3f %10.3f %10.3f %10.3f %10.3f %10.3f\n',e,f1,f2,f3,f4,f5,f6); 49 | end 50 | 51 | 52 | 53 | rf = Solution.reactionForces; 54 | printDLine(fid,96); 55 | printCTitle(fid,'S U P P O R T R E A C T I O N S',96); 56 | fprintf(fid,'Support node Rx Ry Mz\n'); 57 | printSLine(fid,96); 58 | for i = 1 : size(rf,1) 59 | fprintf(fid,' %2d %10.3f %10.3f %10.3f\n',... 60 | rf(i,1), rf(i,2), rf(i,3), rf(i,4)); 61 | end 62 | % % printDLine(fid,96); 63 | 64 | % n = input('Press Enter to Display Stiffness Matrices...'); 65 | % % printCTitle(fid,'S T I F F N E S S M A T R I C E S',96); 66 | % % 67 | % % nElem = size(Solution.data.ke_local,3); 68 | % % for i = 1 : nElem 69 | % % printLine(fid,96); 70 | % % fprintf(fid,'%c Element No = %d \n',BULLET_CHAR,i); 71 | % % fprintf (fid,' - Local Stiffness Matrix: \n'); 72 | % % disp_mat(Solution.data.ke_local,1,fid) 73 | % % printSLine(fid,96); 74 | % % 75 | % % fprintf (fid,' - Transformation Matrix: \n'); 76 | % % disp_mat(Solution.data.T6,2,fid) 77 | % % printSLine(fid,96); 78 | % % 79 | % % fprintf (fid,' - GlobalStiffness Matrix: K=T`kT = \n'); 80 | % % disp_mat(Solution.data.ke_global,3,fid) 81 | % % end 82 | % % 83 | % format shortEng 84 | % fprintf('Global Load Vector:') 85 | % disp(Fc) 86 | % 87 | % fprintf('\n') 88 | % format short 89 | % fprintf('Global Assembled Stiffness Matrix:') 90 | % disp(K) 91 | % format long 92 | % 93 | printDLine(fid,96); 94 | end 95 | 96 | 97 | % Helper Functions 98 | function printLine(fid,n) 99 | if nargin < 2 100 | n = 80; 101 | end 102 | if nargin < 1 103 | fid = 1; 104 | end 105 | fprintf(fid,'%s\n',repmat('_',1,n)); 106 | end 107 | 108 | function printDLine(fid,n) 109 | if nargin < 2 110 | n = 80; 111 | end 112 | if nargin < 1 113 | fid = 1; 114 | end 115 | fprintf(fid,'%s\n',repmat('=',1,n)); 116 | end 117 | 118 | function printSLine(fid,n) 119 | if nargin < 2 120 | n = 80; 121 | end 122 | if nargin < 1 123 | fid = 1; 124 | end 125 | fprintf(fid,'%s\n',repmat('-',1,n)); 126 | end 127 | % printing centered text title 128 | function printCTitle(fid,text,n) 129 | if nargin < 3 130 | n = 80; 131 | end 132 | if nargin < 2 133 | text =''; 134 | end 135 | if nargin < 1 136 | fid = 1; 137 | end 138 | tLen = length(text); 139 | space = floor((n-tLen)/2); 140 | fprintf(fid,'%s\n',[repmat(' ',1,space),text]); 141 | end 142 | 143 | 144 | function disp_mat(mat,mode,fid) 145 | format compact 146 | 147 | if mode==1 148 | format shortEng 149 | fprintf(fid,' +---- ----+ +---- ----+ \n'); 150 | fprintf(fid,' | k11 k12 k13 k14 k15 k16 | | EA/L 0 0 -EA/L 0 0 | \n'); 151 | fprintf(fid,' | k21 k22 k23 k24 k25 k26 | | 0 12EI/L^3 6EI/L^2 0 -12EI/L^3 6EI/L^2 | \n'); 152 | fprintf(fid,' | k31 k32 k33 k34 k35 k36 | | 0 6EI/L^2 4EI/L 0 -6EI /L^2 2EI/L | \n'); 153 | fprintf(fid,' | k41 k42 k43 k44 k45 k46 | = |-EA/L 0 0 EA/L 0 0 |=\n'); 154 | fprintf(fid,' | k51 k52 k53 k54 k55 k56 | | 0 -12EI/L^3 -6EI/L^2 0 12EI/L^3 -6EI/L2 | \n'); 155 | fprintf(fid,' | k61 k62 k63 k64 k65 k66 | | 0 6EI/L^2 2EI/L 0 -6EI /L^2 4EI/L | \n'); 156 | fprintf(fid,' +---- ----+ +---- ----+ \n'); 157 | for i = 1 : 6 158 | for j = 1 : 6 159 | fprintf(fid,'%14.3e\t',mat(i,j)); 160 | end 161 | fprintf(fid,'\n'); 162 | end 163 | 164 | elseif mode==2 165 | format short g 166 | c=mat(1,1); 167 | s=mat(1,2); 168 | fprintf(fid,' +--- ---+ +--- ---+\n'); 169 | fprintf(fid,' | c s 0 0 0 0 | | %5.2f %5.2f %5.2f %5.2f %5.2f %5.2f |\n',c ,s ,0,0,0,0); 170 | fprintf(fid,' | -s c 0 0 0 0 | | %5.2f %5.2f %5.2f %5.2f %5.2f %5.2f |\n',-s,c ,0,0,0,0); 171 | fprintf(fid,' | 0 0 1 0 0 0 | | %5.2f %5.2f %5.2f %5.2f %5.2f %5.2f |\n',0 ,0 ,1,0,0,0); 172 | fprintf(fid,' | 0 0 0 c s 0 | = | %5.2f %5.2f %5.2f %5.2f %5.2f %5.2f |\n',0 ,0 ,0,c,s,0); 173 | fprintf(fid,' | 0 0 0 -s c 0 | | %5.2f %5.2f %5.2f %5.2f %5.2f %5.2f |\n',0 ,0 ,0,-s,c,0); 174 | fprintf(fid,' | 0 0 0 0 0 1 | | %5.2f %5.2f %5.2f %5.2f %5.2f %5.2f |\n',0 ,0 ,0,0,0,1); 175 | fprintf(fid,' +--- ---+ +--- ---+\n'); 176 | 177 | elseif mode==3 178 | for i = 1 : 6 179 | for j = 1 : 6 180 | fprintf(fid,'%14.3e\t',mat(i,j)); 181 | end 182 | fprintf(fid,'\n'); 183 | end 184 | end 185 | 186 | 187 | fprintf('\n') 188 | format long 189 | end -------------------------------------------------------------------------------- /Source Code/PlaneFrame/lib_io/printStiff.m: -------------------------------------------------------------------------------- 1 | function printStiff(Solution,fid) 2 | 3 | if isfield(Solution,'data') 4 | printCTitle(fid,'S T I F F N E S S M A T R I C E S',96); 5 | 6 | nElem = size(Solution.data.ke_local,3); 7 | for i = 1 : nElem 8 | printLine(fid,96); 9 | fprintf(fid,' element No = %d \n',i); 10 | fprintf (fid,' - Local Stiffness Matrix: \n'); 11 | disp_mat(Solution.data.ke_local(:,:,i),1,fid) 12 | printSLine(fid,96); 13 | 14 | fprintf (fid,' - Transformation Matrix: \n'); 15 | disp_mat(Solution.data.T6(:,:,i),2,fid) 16 | printSLine(fid,96); 17 | 18 | fprintf (fid,' - GlobalStiffness Matrix: K=T`kT = \n'); 19 | disp_mat(Solution.data.ke_global(:,:,i),3,fid) 20 | end 21 | 22 | printDLine(fid); 23 | end 24 | 25 | end 26 | 27 | 28 | % Helper Functions 29 | function printLine(fid,n) 30 | if nargin < 2 31 | n = 80; 32 | end 33 | if nargin < 1 34 | fid = 1; 35 | end 36 | fprintf(fid,'%s\n',repmat('_',1,n)); 37 | end 38 | 39 | function printDLine(fid,n) 40 | if nargin < 2 41 | n = 80; 42 | end 43 | if nargin < 1 44 | fid = 1; 45 | end 46 | fprintf(fid,'%s\n',repmat('=',1,n)); 47 | end 48 | 49 | function printSLine(fid,n) 50 | if nargin < 2 51 | n = 80; 52 | end 53 | if nargin < 1 54 | fid = 1; 55 | end 56 | fprintf(fid,'%s\n',repmat('-',1,n)); 57 | end 58 | % printing centered text title 59 | function printCTitle(fid,text,n) 60 | if nargin < 3 61 | n = 80; 62 | end 63 | if nargin < 2 64 | text =''; 65 | end 66 | if nargin < 1 67 | fid = 1; 68 | end 69 | tLen = length(text); 70 | space = floor((n-tLen)/2); 71 | fprintf(fid,'%s\n',[repmat(' ',1,space),text]); 72 | end 73 | 74 | 75 | function disp_mat(mat,mode,fid) 76 | format compact 77 | 78 | if mode==1 79 | format shortEng 80 | fprintf(fid,' +---- ----+ +---- ----+ \n'); 81 | fprintf(fid,' | k11 k12 k13 k14 k15 k16 | | EA/L 0 0 -EA/L 0 0 | \n'); 82 | fprintf(fid,' | k21 k22 k23 k24 k25 k26 | | 0 12EI/L^3 6EI/L^2 0 -12EI/L^3 6EI/L^2 | \n'); 83 | fprintf(fid,' | k31 k32 k33 k34 k35 k36 | | 0 6EI/L^2 4EI/L 0 -6EI /L^2 2EI/L | \n'); 84 | fprintf(fid,' | k41 k42 k43 k44 k45 k46 | = |-EA/L 0 0 EA/L 0 0 |=\n'); 85 | fprintf(fid,' | k51 k52 k53 k54 k55 k56 | | 0 -12EI/L^3 -6EI/L^2 0 12EI/L^3 -6EI/L2 | \n'); 86 | fprintf(fid,' | k61 k62 k63 k64 k65 k66 | | 0 6EI/L^2 2EI/L 0 -6EI /L^2 4EI/L | \n'); 87 | fprintf(fid,' +---- ----+ +---- ----+ \n'); 88 | for i = 1 : 6 89 | for j = 1 : 6 90 | fprintf(fid,'%14.3e\t',mat(i,j)); 91 | end 92 | fprintf(fid,'\n'); 93 | end 94 | 95 | elseif mode==2 96 | format short g 97 | c=mat(1,1); 98 | s=mat(1,2); 99 | fprintf(fid,' +--- ---+ +--- ---+\n'); 100 | fprintf(fid,' | c s 0 0 0 0 | | %5.2f %5.2f %5.2f %5.2f %5.2f %5.2f |\n',c ,s ,0,0,0,0); 101 | fprintf(fid,' | -s c 0 0 0 0 | | %5.2f %5.2f %5.2f %5.2f %5.2f %5.2f |\n',-s,c ,0,0,0,0); 102 | fprintf(fid,' | 0 0 1 0 0 0 | | %5.2f %5.2f %5.2f %5.2f %5.2f %5.2f |\n',0 ,0 ,1,0,0,0); 103 | fprintf(fid,' | 0 0 0 c s 0 | = | %5.2f %5.2f %5.2f %5.2f %5.2f %5.2f |\n',0 ,0 ,0,c,s,0); 104 | fprintf(fid,' | 0 0 0 -s c 0 | | %5.2f %5.2f %5.2f %5.2f %5.2f %5.2f |\n',0 ,0 ,0,-s,c,0); 105 | fprintf(fid,' | 0 0 0 0 0 1 | | %5.2f %5.2f %5.2f %5.2f %5.2f %5.2f |\n',0 ,0 ,0,0,0,1); 106 | fprintf(fid,' +--- ---+ +--- ---+\n'); 107 | 108 | elseif mode==3 109 | for i = 1 : 6 110 | for j = 1 : 6 111 | fprintf(fid,'%14.3e\t',mat(i,j)); 112 | end 113 | fprintf(fid,'\n'); 114 | end 115 | end 116 | 117 | 118 | fprintf('\n') 119 | format long 120 | end -------------------------------------------------------------------------------- /Source Code/PlaneFrame/lib_io/printSummary.m: -------------------------------------------------------------------------------- 1 | function printSummary(Model,fid) 2 | % PURPOSE: reads input files and generates a structure including all data 3 | % 4 | % INPUT(S): 5 | % - Model: a structure including the following fields 6 | % - fid : file id to store 7 | % 8 | % OUTPUT(S): 9 | % 10 | % 11 | % USAGE: 12 | % >> printSummary(Model) print input details on command window 13 | % >> printSummary(Model,fid) print input details on a file with fid 14 | % identifier 15 | 16 | % DEVELOPMENT HISTORY: 17 | % [2018, Oct, 29] Shahrokh Shahi -- initial development 18 | % [2018, XXX, XX] Shahrokh Shahi -- 19 | 20 | if nargin < 2 21 | fid = 1; 22 | end 23 | BULLET_CHAR = char(15); 24 | 25 | printDLine(fid) 26 | tText = 'A S U M M A R Y O F T H E I N P U T M O D E L'; 27 | printCTitle(fid,tText) 28 | printDLine(fid) 29 | 30 | 31 | if isfield(Model,'info') 32 | fprintf(fid,'%c About: \n',BULLET_CHAR); 33 | fprintf(fid,'%s\n', Model.info); 34 | end 35 | if isfield(Model,'analysisType') 36 | fprintf(fid,'\n%c Structure Type: \n',BULLET_CHAR); 37 | fprintf(fid,'%s\n', Model.analysisType); 38 | end 39 | printLine(fid) 40 | 41 | 42 | fprintf(fid,'%c Control Variables: \n',BULLET_CHAR); 43 | fprintf(fid,' - Dimension: %dD\n' ,Model.nDim); 44 | fprintf(fid,' - Number of DOF(s): %d \n' ,Model.nDof); 45 | fprintf(fid,'\n'); 46 | fprintf(fid,' - Number of Nodes: %4d \n' ,Model.nNode); 47 | fprintf(fid,' - Number of Elements: %4d \n' ,Model.nElem); 48 | fprintf(fid,' - Nodes per Elements: %d\n',Model.nElemNode); 49 | fprintf(fid,'\n'); 50 | fprintf(fid,' - Number of Sections: %d \n',Model.nSection); 51 | printDLine(fid) 52 | 53 | 54 | printCTitle(fid,'N O D A L I N F O R M A T I O N') 55 | printLine(fid) 56 | headerTxt = ['Node Coordinates Nodal Loads ',... 57 | ' Nodal Restraints \n']; 58 | fprintf(fid,headerTxt); 59 | printSLine(fid) 60 | switch Model.nDim 61 | case 1 62 | headerTxt1 =' ID X '; 63 | headerTxt2 =' Fx '; 64 | headerTxt3 =' ux \n'; 65 | 66 | case 2 67 | headerTxt1 =' ID X Y '; 68 | headerTxt2 =' Fx Fy '; 69 | headerTxt3 =' ux uy \n'; 70 | 71 | case 3 72 | headerTxt1 =' ID X Y Z '; 73 | headerTxt2 =' Fx Fy Fz '; 74 | headerTxt3 =' ux uy uz \n'; 75 | end 76 | fprintf(fid,[headerTxt1,headerTxt2,headerTxt3]); 77 | printLine(fid) 78 | 79 | % nodal forces to displaying 80 | F = zeros(Model.nNode,Model.nDof); 81 | for i = 1 : Model.nNodalForce 82 | node = Model.loading.nodalForces(i,1); 83 | F(node, 1:Model.nDof) = Model.loading.nodalForces(i,2:end); 84 | end 85 | 86 | % printing table contents 87 | for i = 1 : Model.nNode 88 | coord = Model.geometry.coordinates(i,:); 89 | fprintf(fid,'%2d ',i); 90 | for j = 1 : length(coord) 91 | fprintf(fid,'%7.2f ',coord(j)); 92 | end 93 | fprintf(fid,'\t'); 94 | for j = 1 : size(F,2) 95 | fprintf(fid,'%10.2f ',F(i,j)); 96 | end 97 | 98 | fprintf(fid,'\t'); 99 | index = find(Model.boundary(:,1)==i); 100 | dx='-';dy='-';dz='-';bc=''; 101 | 102 | if ~isempty(index) 103 | for k = 1 : length(index) 104 | if Model.boundary(index(k),2)==1 105 | dx=num2str(Model.boundary(index(k),3)); 106 | elseif Model.boundary(index(k),2)==2 107 | dy=num2str(Model.boundary(index(k),3)); 108 | elseif Model.boundary(index(k),2)==3 109 | dz=num2str(Model.boundary(index(k),3)); 110 | end 111 | end 112 | if length(index)==1 113 | bc = 'Roller '; 114 | elseif length(index)==2 115 | bc = 'Pin'; 116 | elseif length(index)==3 117 | bc = 'Fixed'; 118 | end 119 | end 120 | presc = [dx, dy, dz]; %prescribed values 121 | for j = 1 : Model.nDof 122 | fprintf(fid,' %s',presc(j)); 123 | end 124 | fprintf(fid,' %s\n',bc); 125 | end 126 | printDLine(fid); 127 | 128 | printCTitle(fid,'E L E M E N T S I N F O R M A T I O N') 129 | printLine(fid) 130 | fprintf(fid,' ID\t '); 131 | for i = 1 : Model.nElemNode 132 | fprintf(fid,'Node%d\t',i); 133 | end 134 | fprintf(fid,' Section No. Material Properties\n'); 135 | printLine(fid); 136 | 137 | for i = 1 : Model.nElem 138 | fprintf(fid,'%2d\t ',i); 139 | for j = 1 : Model.nElemNode 140 | fprintf(fid,'%2d\t\t',Model.geometry.elements(i,j)); 141 | end 142 | fprintf(fid,'\t'); 143 | fprintf(fid,'\t%2d\t\t\t[',Model.elemSectId(i)); 144 | for j = 1 : Model.nMaterialProp 145 | fprintf(fid,'%g\t\t',Model.sections(Model.elemSectId(i),j)); 146 | end 147 | fprintf(fid,']\n'); 148 | end 149 | 150 | printDLine(fid); 151 | 152 | end 153 | 154 | 155 | % Helper Functions 156 | function printLine(fid,n) 157 | if nargin < 2 158 | n = 80; 159 | end 160 | if nargin < 1 161 | fid = 1; 162 | end 163 | fprintf(fid,'%s\n',repmat('_',1,n)); 164 | end 165 | 166 | function printDLine(fid,n) 167 | if nargin < 2 168 | n = 80; 169 | end 170 | if nargin < 1 171 | fid = 1; 172 | end 173 | fprintf(fid,'%s\n',repmat('=',1,n)); 174 | end 175 | 176 | function printSLine(fid,n) 177 | if nargin < 2 178 | n = 80; 179 | end 180 | if nargin < 1 181 | fid = 1; 182 | end 183 | fprintf(fid,'%s\n',repmat('-',1,n)); 184 | end 185 | % printing centered text title 186 | function printCTitle(fid,text,n) 187 | if nargin < 3 188 | n = 80; 189 | end 190 | if nargin < 2 191 | text =''; 192 | end 193 | if nargin < 1 194 | fid = 1; 195 | end 196 | tLen = length(text); 197 | space = floor((n-tLen)/2); 198 | fprintf(fid,'%s\n',[repmat(' ',1,space),text]); 199 | end -------------------------------------------------------------------------------- /Source Code/PlaneFrame/main.m: -------------------------------------------------------------------------------- 1 | %% M A I N F U N C T I O N 2 | %__________________________________________________________________________ 3 | % 4 | % Finite Element Methods 5 | % Developed by SHAHROKH SHAHI 6 | % (www.sshahi.com) 7 | % 8 | % Georgia Institute of Technology 9 | %__________________________________________________________________________ 10 | % This file is the main function to handle the PLANE BEAM/FRAME analysis 11 | % by employing the functions in the folder "lib" 12 | 13 | % DEVELOPMENT HISTORY: 14 | % [2018, Nov, 01] Shahrokh Shahi -- transform to function formats 15 | % [2018, XXX, XX] Shahrokh Shahi -- 16 | 17 | %% Initial Setup ( You do NOT need to change this section) 18 | clc 19 | clear 20 | close all 21 | 22 | format short g 23 | format compact 24 | 25 | % adding "lib" folder to the path 26 | path = mfilename('fullpath'); 27 | path(end-length(mfilename):end)=[]; 28 | addpath(fullfile(path,'lib')) 29 | addpath(fullfile(path,'lib_io')) 30 | 31 | %% Reading the Input File 32 | 33 | % input file name: 34 | inpFileName = 'input1.txt'; 35 | inpFileName = 'input2.txt'; 36 | 37 | %-------------------------------------------------------------------------- 38 | % E X T R A C T M O D E L F R O M I N P U T F I L E 39 | %-------------------------------------------------------------------------- 40 | Model = inpFileReader(inpFileName) 41 | 42 | 43 | %-------------------------------------------------------------------------- 44 | % P R I N T I N P U T S U M M A R Y 45 | %-------------------------------------------------------------------------- 46 | printSummary(Model) 47 | 48 | 49 | %-------------------------------------------------------------------------- 50 | % S I M P L E P L O T 51 | %-------------------------------------------------------------------------- 52 | plotmesh(Model,'b'); 53 | 54 | %% Run Analysis 55 | 56 | Solution1 = planeFrameExplicit(Model); 57 | Solution2 = planeFrameNumerical(Model); 58 | 59 | printResult(Solution2) -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/input1.txt: -------------------------------------------------------------------------------- 1 | * INFO 2 | [TRI] BASIC EXAMPLE -- PLANE STRESS W/ TRIANGULAR ELEMENTS 3 | 4 | * ANALYSIS TYPE 5 | Plane Stress 6 | 7 | * COORDINATES 8 | 1 0.0 0.0 9 | 2 1.0 0.0 10 | 3 1.0 1.0 11 | 4 0.0 1.0 12 | 13 | 14 | * ELEMENTS 15 | 1 1 1 2 4 16 | 2 1 2 3 4 17 | 18 | * SECTIONS 19 | 1 26.0 0.3 1.0 20 | 21 | 22 | * TRACTION FORCES 23 | 2 1 1.0 0.0 24 | 25 | * BOUNDARY 26 | 1 1 0.0 27 | 1 2 0.0 28 | 4 1 0.0 29 | 30 | -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/input2.txt: -------------------------------------------------------------------------------- 1 | * INFO 2 | [QUAD4] THIS IS A VERY BASIC INPUT FILE FOR TESTING PURPOSE 3 | 4 | * ANALYSIS TYPE 5 | Plane Stress 6 | 7 | * COORDINATES 8 | 1 0.0 0.0 9 | 2 1.0 0.0 10 | 3 2.0 0.0 11 | 4 3.0 0.0 12 | 5 4.0 0.0 13 | 6 0.0 1.0 14 | 7 1.0 1.0 15 | 8 2.0 1.0 16 | 9 3.0 1.0 17 | 10 4.0 1.0 18 | 11 0.0 2.0 19 | 12 1.0 2.0 20 | 13 2.0 2.0 21 | 14 3.0 2.0 22 | 15 4.0 2.0 23 | 24 | 25 | * ELEMENTS 26 | 1 1 1 2 7 6 27 | 2 1 2 3 8 7 28 | 3 1 3 4 9 8 29 | 4 1 4 5 10 9 30 | 5 1 6 7 12 11 31 | 6 1 7 8 13 12 32 | 7 1 8 9 14 13 33 | 8 1 9 10 15 14 34 | 35 | * SECTIONS 36 | 1 26.0 0.3 1.0 37 | 38 | 39 | * TRACTION FORCES 40 | 4 2 1.0 0.0 41 | 8 2 1.0 0.0 42 | 43 | * BOUNDARY 44 | 1 1 0.0 45 | 1 2 0.0 46 | 6 1 0.0 47 | 11 1 0.0 48 | 49 | -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/input3.txt: -------------------------------------------------------------------------------- 1 | * INFO 2 | BASIC EXAMPLE -- 3D GENERAL BRICK ELEMENT 3 | 4 | * ANALYSIS TYPE 5 | General 3D 6 | 7 | * COORDINATES 8 | 1 0.0 -1.0 0.0 9 | 2 1.0 -1.0 0.0 10 | 3 2.0 -1.0 0.0 11 | 4 3.0 -1.0 0.0 12 | 5 0.0 0.0 0.0 13 | 6 1.0 0.0 0.0 14 | 7 2.0 0.0 0.0 15 | 8 3.0 0.0 0.0 16 | 9 0.0 1.0 0.0 17 | 10 1.0 1.0 0.0 18 | 11 2.0 1.0 0.0 19 | 12 3.0 1.0 0.0 20 | 13 0.0 -1.0 1.0 21 | 14 1.0 -1.0 1.0 22 | 15 2.0 -1.0 1.0 23 | 16 3.0 -1.0 1.0 24 | 17 0.0 0.0 1.0 25 | 18 1.0 0.0 1.0 26 | 19 2.0 0.0 1.0 27 | 20 3.0 0.0 1.0 28 | 21 0.0 1.0 1.0 29 | 22 1.0 1.0 1.0 30 | 23 2.0 1.0 1.0 31 | 24 3.0 1.0 1.0 32 | 33 | 34 | * ELEMENTS 35 | 1 1 1 2 6 5 13 14 18 17 36 | 2 1 2 3 7 6 14 15 19 18 37 | 3 1 3 4 8 7 15 16 20 19 38 | 4 1 5 6 10 9 17 18 22 21 39 | 5 1 6 7 11 10 18 19 23 22 40 | 6 1 7 8 12 11 19 20 24 23 41 | 42 | * SECTIONS 43 | 1 26.0 0.3 44 | 45 | 46 | * TRACTION FORCES 47 | 3 4 1.0 0.0 0.0 48 | 6 4 1.0 0.0 0.0 49 | 50 | * BOUNDARY 51 | 1 1 0.0 52 | 1 2 0.0 53 | 1 3 0.0 54 | 13 1 0.0 55 | 13 2 0.0 56 | 5 1 0.0 57 | 17 1 0.0 58 | 21 1 0.0 59 | 9 1 0.0 60 | 61 | -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib/eldload.m: -------------------------------------------------------------------------------- 1 | %====================== ELEMENT DISTRIBUTED LOAD VECTOR ============== 2 | % 3 | function r = eldload(ncoord,ndof,nfacenodes,elident,coords,loadEq) 4 | 5 | npoints = numberofintegrationpoints(ncoord-1,nfacenodes); 6 | xi = zeros(ncoord-1,1); 7 | dxdxi = zeros(ncoord,ncoord-1); 8 | r = zeros(ndof*nfacenodes,1); 9 | 10 | xilist = integrationpoints(ncoord-1,nfacenodes,npoints); 11 | w = integrationweights(ncoord-1,nfacenodes,npoints); 12 | 13 | for intpt = 1:npoints 14 | 15 | for i = 1:ncoord-1 16 | xi(i) = xilist(i,intpt); 17 | end 18 | 19 | N = shapefunctions(nfacenodes,ncoord-1,elident,xi); 20 | dNdxi = shapefunctionderivs(nfacenodes,ncoord-1,elident,xi); 21 | % 22 | % Compute the jacobian matrix && its determinant 23 | % 24 | for i = 1:ncoord 25 | for j = 1:ncoord-1 26 | dxdxi(i,j) = 0.; 27 | for a = 1:nfacenodes 28 | dxdxi(i,j) = dxdxi(i,j) + coords(i,a)*dNdxi(a,j); 29 | end 30 | end 31 | end 32 | if (ncoord == 2) 33 | dt = sqrt(dxdxi(1,1)^2+dxdxi(2,1)^2); 34 | elseif (ncoord == 3) 35 | dt = sqrt( ((dxdxi(2,1)*dxdxi(3,2))-(dxdxi(2,2)*dxdxi(3,1)))^2 ... 36 | + ((dxdxi(1,1)*dxdxi(3,2))-(dxdxi(1,2)*dxdxi(3,1)))^2 ... 37 | + ((dxdxi(1,1)*dxdxi(2,2))-(dxdxi(1,2)*dxdxi(2,1)))^2 ); 38 | end 39 | 40 | 41 | L = norm(diff(coords')); 42 | traction = zeros(length(loadEq),1); 43 | x = (1+xi)/2 * L; 44 | for i = 1 : length(traction) 45 | traction(i,1) = loadEq{i}(x); 46 | end 47 | traction; 48 | 49 | for a = 1:nfacenodes 50 | for i = 1:ndof 51 | row = ndof*(a-1)+i; 52 | r(row) = r(row) + N(a)*traction(i)*w(intpt)*dt; 53 | end 54 | end 55 | end 56 | end -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib/elstif.m: -------------------------------------------------------------------------------- 1 | % 2 | %================= ELEMENT STIFFNESS MATRIX ================================ 3 | % 4 | function kel = elstif(ncoord,ndof,nelnodes,elident,coord,materialprops,displacement) 5 | % 6 | % Assemble the element stiffness 7 | % 8 | % Arguments; 9 | % 10 | % ncoord No. coordinates (2 or 3 for 2D or 3D problem) 11 | % ndof No. degrees of freedom per node (often ndof = ncoord) 12 | % nelnodes No. nodes on the element 13 | % elident Element identifier (not used here - for future enhancements!) 14 | % coords(i,a) ith coord of ath node 15 | % materialprops Material properties passed on:constitutive procedures 16 | % displacement(i,a) ith displacement component at ath node 17 | % 18 | % Local variables 19 | % npoints No. integration points 20 | % xi(i,inpt) ith local coord of integration point no. intpt 21 | % w(intpt) weight for integration point no. intpt 22 | % N(a) Shape function associated with ath node on element 23 | % dNdxi(a,i) Derivative of ath shape function wrt ith local coord 24 | % dNdx(a,i) Derivative of ath shape function wrt ith global coord 25 | % dxdxi(i,j) Derivative of ith global coord wrt jth local coord 26 | % dxidx(i,j) Derivative of ith local coord wrt jth global coord 27 | % det Determinant of jacobian 28 | % strain(i,j) strain_ij components 29 | % dsde(i,j,k,l) Derivative of stress_ij with respect:strain_kl 30 | % kel(row,col) Rows && cols of element stiffness 31 | % 32 | % 33 | npoints = numberofintegrationpoints(ncoord,nelnodes,elident); 34 | dNdx = zeros(nelnodes,ncoord); 35 | dxdxi = zeros(ncoord,ncoord); 36 | strain = zeros(ndof,ncoord); 37 | kel = zeros(ndof*nelnodes,ndof*nelnodes); 38 | % 39 | % Set up integration points && weights 40 | % 41 | xilist = integrationpoints(ncoord,nelnodes,npoints,elident); 42 | w = integrationweights(ncoord,nelnodes,npoints,elident); 43 | % 44 | % Loop over the integration points 45 | % 46 | for intpt = 1:npoints 47 | 48 | % Compute shape functions && derivatives wrt local coords 49 | % 50 | for i = 1:ncoord 51 | xi(i) = xilist(i,intpt); 52 | end 53 | N = shapefunctions(nelnodes,ncoord,elident,xi); 54 | dNdxi = shapefunctionderivs(nelnodes,ncoord,elident,xi); 55 | 56 | 57 | % 58 | % Compute the jacobian matrix && its determinant 59 | % 60 | for i = 1:ncoord 61 | for j = 1:ncoord 62 | dxdxi(i,j) = 0.; 63 | for a = 1:nelnodes 64 | dxdxi(i,j) = dxdxi(i,j) + coord(i,a)*dNdxi(a,j); 65 | end 66 | end 67 | end 68 | 69 | dxidx = inv(dxdxi); 70 | dt = det(dxdxi); 71 | % 72 | % Convert shape function derivatives:derivatives wrt global coords 73 | % 74 | for a = 1:nelnodes 75 | for i = 1:ncoord 76 | dNdx(a,i) = 0.; 77 | for j = 1:ncoord 78 | dNdx(a,i) = dNdx(a,i) + dNdxi(a,j)*dxidx(j,i); 79 | end 80 | end 81 | end 82 | % 83 | % Compute the (infinitesimal) strain by differentiating displacements 84 | % This step is not really necessary for linear elasticity calculations 85 | % where stiffness is independent of strain. It is included:allow 86 | % extension:nonlinear materials later. 87 | % 88 | for i = 1:ncoord 89 | for j = 1:ncoord 90 | strain(i,j) = 0.; 91 | for a = 1:nelnodes 92 | strain(i,j) = strain(i,j) + 0.5*(displacement(i,a)*dNdx(a,j)+displacement(j,a)*dNdx(a,i)); 93 | end 94 | end 95 | end 96 | % 97 | % Compute the material tangent stiffness (d stress/d strain) 98 | % ds/de is just C_ijkl for linear elasticity - this notation is used 99 | % to allow extension to nonlinear problems 100 | % 101 | dsde = materialstiffness(ndof,ncoord,strain,materialprops); 102 | % 103 | % Compute the element stiffness 104 | % 105 | for a = 1:nelnodes 106 | for i = 1:ndof 107 | for b = 1:nelnodes 108 | for k = 1:ndof 109 | row = ndof*(a-1)+i; 110 | col = ndof*(b-1)+k; 111 | for j = 1:ncoord 112 | for l = 1:ncoord 113 | kel(col,row) = kel(col,row) + dsde(i,j,k,l)*dNdx(b,l)*dNdx(a,j)*w(intpt)*dt; 114 | end 115 | end 116 | end 117 | end 118 | end 119 | end 120 | end 121 | 122 | end -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib/facenodes.m: -------------------------------------------------------------------------------- 1 | %======================= Lists of nodes on element faces ============= 2 | % 3 | % This procedure returns the list of nodes on an element face 4 | % The nodes are ordered so that the element face forms either 5 | % a 1D line element or a 2D surface element for 2D or 3D problems 6 | % 7 | function list = facenodes(ncoord,nelnodes,elident,face) 8 | 9 | i3 = [2,3,1]; 10 | i4 = [2,3,4,1]; 11 | 12 | list = zeros(nfacenodes(ncoord,nelnodes,face),1); 13 | 14 | if (ncoord == 2) 15 | if (nelnodes == 3) 16 | list(1) = face; 17 | list(2) = i3(face); 18 | elseif (nelnodes == 6) 19 | list(1) = face; 20 | list(2) = i3(face); 21 | list(3) = face+3; 22 | elseif (nelnodes==4) 23 | list(1) = face; 24 | list(2) = i4(face); 25 | elseif (nelnodes==8) 26 | list(1) = face; 27 | list(2) = i4(face); 28 | list(3) = face+4; 29 | end 30 | elseif (ncoord == 3) 31 | if (nelnodes==4) 32 | if (face == 1) 33 | list = [1,2,3]; 34 | elseif (face == 2) 35 | list = [1,4,2]; 36 | elseif (face == 3) 37 | list = [2,4,3]; 38 | elseif (face == 4) 39 | list = [3,4,1]; 40 | end 41 | elseif (nelnodes == 10) 42 | if (face == 1) 43 | list = [1,2,3,5,6,7]; 44 | elseif (face == 2) 45 | list = [1,4,2,8,9,5]; 46 | elseif (face == 3) 47 | list = [2,4,3,9,10,6]; 48 | elseif (face == 4) 49 | list = [3,4,1,10,8,7]; 50 | end 51 | elseif (nelnodes == 8) 52 | if (face == 1) 53 | list = [1,2,3,4]; 54 | elseif (face == 2) 55 | list = [5,8,7,6]; 56 | elseif (face == 3) 57 | list = [1,5,6,2]; 58 | elseif (face == 4) 59 | list = [2,3,7,6]; 60 | elseif (face == 5) 61 | list = [3,7,8,4]; 62 | elseif (face == 6) 63 | list = [4,8,5,1]; 64 | end 65 | elseif (nelnodes == 20) 66 | if (face == 1) 67 | list = [1,2,3,4,9,10,11,12]; 68 | elseif (face == 2) 69 | list = [5,8,7,6,16,15,14,13]; 70 | elseif (face == 3) 71 | list = [1,5,6,2,17,13,18,9]; 72 | elseif (face == 4) 73 | list = [2,6,7,3,18,14,19,10]; 74 | elseif (face == 5) 75 | list = [3,7,8,4,19,15,20,11]; 76 | elseif (face == 6) 77 | list = [4,8,5,1,20,16,17,12]; 78 | end 79 | end 80 | end 81 | end -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib/femGeneral.m: -------------------------------------------------------------------------------- 1 | function Solution = femGeneral(Model) 2 | % PURPOSE: finite element analysis of a given model 3 | % 4 | % INPUT(S): 5 | % - Model: a structure including the following fields 6 | 7 | % DEVELOPMENT HISTORY: 8 | % [2018, May, 25] Shahrokh Shahi -- transformation of the basic one 9 | % [2018, XXX, XX] Shahrokh Shahi -- 10 | % [2018, XXX, XX] Shahrokh Shahi -- 11 | 12 | %% 2D Plane Stress/Strain and General 3D case 13 | 14 | nprops = Model.nSection; 15 | materialprops = Model.sections; % NOTE: 16 | % in gui the first material property is "E"; however, in my 17 | % elasticity-based FEM code, the first material property is "mu" (shear 18 | % modulus), so, a transformation is inevitable here: 19 | % G or mu = E / 2(1+nu) 20 | materialprops(:,1) = materialprops(:,1) ./ ... 21 | (2 .* (1 + materialprops(:,2))); 22 | 23 | ncoord = Model.nDim; 24 | ndof = Model.nDof; 25 | nnode = Model.nNode; 26 | coords = Model.geometry.coordinates'; % trn 27 | nelem = Model.nElem; 28 | maxnodes = double(Model.nElemNode); 29 | connect = Model.geometry.elements'; % trn 30 | nelnodes = ones(nelem, 1) * maxnodes; 31 | elident = Model.elemSectId;% use this reserved var. as a key 32 | nfix = Model.nBoundary; 33 | fixnodes = Model.boundary'; %trn 34 | ndload = Model.nTractionForce; 35 | 36 | % dloads = Model.loading.tractionForces'; %trn 37 | traction = Model.loading.tractionForces; 38 | 39 | Solution.info = ['Solution obtained on ', date]; 40 | 41 | 42 | % fem linear procedure: 43 | dofs = zeros(ndof*nnode,1); 44 | 45 | K = globalstiffness(ncoord,ndof,nnode,coords,nelem,maxnodes, ... 46 | elident,nelnodes,connect,materialprops,dofs); 47 | 48 | % traction forces vector 49 | r = globaltraction(ncoord,ndof,nnode,ndload,coords,nelnodes, ... 50 | elident,connect,traction,dofs); 51 | 52 | R = r; 53 | 54 | % imposing displacement boundary conditions 55 | debc = (fixnodes(1,:) - 1) * ndof + fixnodes(2,:); 56 | ebcVals = fixnodes(3,:)'; 57 | 58 | [dofs, rf] = solution(K, R, debc, ebcVals); 59 | 60 | 61 | if isfield(Model,'analysis') 62 | if Model.analysis.saveToFile 63 | fileSaveId = fopen(Model.analysis.outputFileName, 'w'); 64 | printSummary(Model,fileSaveId); 65 | print_results(fileSaveId, ... 66 | nprops,materialprops,ncoord,ndof,nnode,coords, ... 67 | nelem,maxnodes,connect,nelnodes,elident, ... 68 | nfix,fixnodes,ndload,traction,dofs); 69 | fclose(fileSaveId); 70 | end 71 | 72 | if Model.analysis.showDetails 73 | % print stiffness matrices 74 | end 75 | end 76 | 77 | 78 | % temporary displyin on command window (TODO: improve the output format) 79 | print_results(1, ... 80 | nprops,materialprops,ncoord,ndof,nnode,coords, ... 81 | nelem,maxnodes,connect,nelnodes,elident, ... 82 | nfix,fixnodes,ndload,traction,dofs); 83 | 84 | Solution.nodalDisplacements = reshape(dofs,ncoord,nnode)'; 85 | end 86 | 87 | 88 | 89 | 90 | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 | 101 | 102 | -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib/globalstiffness.m: -------------------------------------------------------------------------------- 1 | %====================== Assemble the global stiffness matrix ================= 2 | % 3 | function Stif = globalstiffness(ncoord,ndof,nnode,coords,nelem,maxnodes,elident,nelnodes,connect,materialprops,dofs) 4 | % 5 | % Assemble the global stiffness matrix 6 | % 7 | 8 | Stif = zeros(ndof*nnode,ndof*nnode); 9 | lmncoord = zeros(ncoord,maxnodes); 10 | lmndof = zeros(ndof,maxnodes); 11 | % 12 | % Loop over all the elements 13 | % 14 | for lmn = 1:nelem 15 | % 16 | % Extract coords of nodes, DOF for the current element 17 | % 18 | for a = 1:nelnodes(lmn) 19 | for i = 1:ncoord 20 | lmncoord(i,a) = coords(i,connect(a,lmn)); 21 | end 22 | for i = 1:ndof 23 | lmndof(i,a) = dofs(ndof*(connect(a,lmn)-1)+i); 24 | end 25 | end 26 | n = nelnodes(lmn); 27 | ident = elident(lmn); 28 | 29 | % simple case: only 1 section (material properties) is defined: 30 | % kel = elstif(ncoord,ndof,n,ident,lmncoord,materialprops,lmndof); 31 | 32 | % general case: multi-material properties: 33 | kel = elstif(ncoord,ndof,n,ident,lmncoord,materialprops(ident,:),lmndof); 34 | % 35 | % Add the current element stiffness:the global stiffness 36 | % 37 | for a = 1:nelnodes(lmn) 38 | for i = 1:ndof 39 | for b = 1:nelnodes(lmn) 40 | for k = 1:ndof 41 | rw = ndof*(connect(a,lmn)-1)+i; 42 | cl = ndof*(connect(b,lmn)-1)+k; 43 | Stif(rw,cl) = Stif(rw,cl) + kel(ndof*(a-1)+i,ndof*(b-1)+k); 44 | end 45 | end 46 | end 47 | end 48 | 49 | 50 | end 51 | end -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib/globaltraction.m: -------------------------------------------------------------------------------- 1 | %===================== Assemble the global traction vector ============= 2 | % 3 | function r = globaltraction(ncoord,ndof,nnodes,ndload,coords,nelnodes,elident,connect,dloads,dofs) 4 | 5 | r = zeros(ndof*nnodes,1); 6 | % traction = zeros(ndof,1); 7 | nTraction = length(dloads); 8 | for load = 1 : nTraction % ndload 9 | % 10 | % Extract the coords of the nodes on the appropriate element face 11 | % 12 | traction = dloads(load); 13 | 14 | lmn = traction.element; % dloads(1,load); 15 | face = traction.face; % dloads(2,load); 16 | n = nelnodes(lmn); 17 | ident = elident(lmn); 18 | nfnodes = nfacenodes(ncoord,n,ident,face); 19 | nodelist = facenodes(ncoord,n,ident,face); 20 | lmncoord = zeros(ncoord,nfnodes); 21 | for a = 1:nfnodes 22 | for i = 1:ncoord 23 | lmncoord(i,a) = coords(i,connect(nodelist(a),lmn)); %,dloads(1,load))); 24 | end 25 | for i = 1:ndof 26 | % lmndof(i,a) = dofs(ndof*(connect(nodelist(a),dloads(1,load))-1)+i); 27 | lmndof(i,a) = dofs(ndof*(connect(nodelist(a),lmn)-1)+i); 28 | end 29 | end 30 | % 31 | % Compute the element load vector 32 | % 33 | 34 | % for i = 1:ndof 35 | % traction(i) = dloads(i+2,load); 36 | % end 37 | 38 | loadEq = traction.eq; 39 | 40 | rel = eldload(ncoord,ndof,nfnodes,ident,lmncoord,loadEq); %traction); 41 | % 42 | % Assemble the element load vector into global vector 43 | % 44 | for a = 1:nfnodes 45 | for i = 1:ndof 46 | % rw = (connect(nodelist(a),dloads(1,load))-1)*ndof+i; 47 | rw = (connect(nodelist(a),lmn)-1)*ndof+i; 48 | r(rw) = r(rw) + rel((a-1)*ndof+i); 49 | end 50 | end 51 | 52 | end 53 | end -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib/integrationpoints.m: -------------------------------------------------------------------------------- 1 | %====================== INTEGRATION POINTS ================================== 2 | % 3 | % Defines positions of integration points 4 | % 5 | function xi = integrationpoints(ncoord,nelnodes,npoints,elident) 6 | 7 | xi = zeros(ncoord,npoints); 8 | % 9 | % 1D elements 10 | % 11 | if (ncoord == 1) 12 | if (npoints==1) 13 | xi(1,1) = 0.; 14 | elseif (npoints == 2) 15 | xi(1,1) = -0.5773502692; 16 | xi(1,2) = -xi(1,1); 17 | elseif (npoints == 3) 18 | xi(1,1) = -0.7745966692; 19 | xi(1,2) = 0.0; 20 | xi(1,3) = -xi(1,1); 21 | end 22 | % 23 | % 2D elements 24 | % 25 | elseif (ncoord == 2) 26 | % 27 | % Triangular element 28 | % 29 | if ( nelnodes == 3 || nelnodes == 6 ) 30 | if (npoints == 1) 31 | xi(1,1) = 1./3.; 32 | xi(2,1) = 1./3.; 33 | elseif (npoints == 3) 34 | xi(1,1) = 0.6; 35 | xi(2,1) = 0.2; 36 | xi(1,2) = 0.2; 37 | xi(2,2) = 0.6; 38 | xi(1,3) = 0.2; 39 | xi(2,3) = 0.2; 40 | elseif (npoints == 4) 41 | xi(1,1) = 1./3.; 42 | xi(2,1) = 1./3.; 43 | xi(1,2) = 0.6; 44 | xi(2,2) = 0.2; 45 | xi(1,3) = 0.2; 46 | xi(2,3) = 0.6; 47 | xi(1,4) = 0.2; 48 | xi(2,4) = 0.2; 49 | end 50 | % 51 | % Rectangular element 52 | % 53 | elseif ( nelnodes==4 || nelnodes==8 ) 54 | 55 | if (npoints == 1) 56 | xi(1,1) = 0.; 57 | xi(2,1) = 0.; 58 | elseif (npoints == 4) 59 | xi(1,1) = -0.5773502692; 60 | xi(2,1) = xi(1,1); 61 | xi(1,2) = -xi(1,1); 62 | xi(2,2) = xi(1,1); 63 | xi(1,3) = xi(1,1); 64 | xi(2,3) = -xi(1,1); 65 | xi(1,4) = -xi(1,1); 66 | xi(2,4) = -xi(1,1); 67 | elseif (npoints == 9) 68 | xi(1,1) = -0.7745966692; 69 | xi(2,1) = xi(1,1); 70 | xi(1,2) = 0.0; 71 | xi(2,2) = xi(1,1); 72 | xi(1,3) = -xi(1,1); 73 | xi(2,3) = xi(1,1); 74 | xi(1,4) = xi(1,1); 75 | xi(2,4) = 0.0; 76 | xi(1,5) = 0.0; 77 | xi(2,5) = 0.0; 78 | xi(1,6) = -xi(1,1); 79 | xi(2,6) = 0.0; 80 | xi(1,7) = xi(1,1); 81 | xi(2,7) = -xi(1,1); 82 | xi(1,8) = 0.; 83 | xi(2,8) = -xi(1,1); 84 | xi(1,9) = -xi(1,1); 85 | xi(2,9) = -xi(1,1); 86 | end 87 | end 88 | % 89 | % 3D elements 90 | % 91 | elseif (ncoord == 3) 92 | % 93 | % 3D elements 94 | % 95 | if (nelnodes == 4 || nelnodes==10 ) 96 | if (npoints == 1) 97 | xi(1,1) = 0.25; 98 | xi(2,1) = 0.25; 99 | xi(3,1) = 0.25; 100 | elseif (npoints == 4) 101 | xi(1,1) = 0.58541020; 102 | xi(2,1) = 0.13819660; 103 | xi(3,1) = xi(2,1); 104 | xi(1,2) = xi(2,1); 105 | xi(2,2) = xi(1,1); 106 | xi(3,2) = xi(2,1); 107 | xi(1,3) = xi(2,1); 108 | xi(2,3) = xi(2,1); 109 | xi(3,3) = xi(1,1); 110 | xi(1,4) = xi(2,1); 111 | xi(2,4) = xi(2,1); 112 | xi(3,4) = xi(2,1); 113 | end 114 | elseif ( nelnodes==8 || nelnodes==20 ) 115 | if (npoints == 1) 116 | xi(1,1) = 0.; 117 | xi(2,1) = 0.; 118 | xi(3,1) = 0.; 119 | elseif (npoints == 8) 120 | x1D = [-0.5773502692,0.5773502692]; 121 | for k = 1:2 122 | for j = 1:2 123 | for i = 1:2 124 | n = 4*(k-1) + 2*(j-1) + i; 125 | xi(1,n) = x1D(i); 126 | xi(2,n) = x1D(j); 127 | xi(3,n) = x1D(k); 128 | end 129 | end 130 | end 131 | elseif (npoints == 27) 132 | x1D = [-0.7745966692,0.,0.7745966692]; 133 | for k = 1:3 134 | for j = 1:3 135 | for i = 1:3 136 | n = 9*(k-1) + 3*(j-1) + i; 137 | xi(1,n) = x1D(i); 138 | xi(2,n) = x1D(j); 139 | xi(3,n) = x1D(k); 140 | end 141 | end 142 | end 143 | end 144 | end 145 | end 146 | end -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib/integrationweights.m: -------------------------------------------------------------------------------- 1 | %================= INTEGRATION WEIGHTS ================================== 2 | % 3 | % Defines integration weights w_i 4 | % 5 | function w = integrationweights(ncoord,nelnodes,npoints,elident) 6 | 7 | w = zeros(npoints,1); 8 | 9 | % 10 | % 1D elements 11 | % 12 | if (ncoord == 1) 13 | if (npoints == 1) 14 | w(1) = 2.; 15 | elseif (npoints == 2) 16 | w = [1.,1.]; 17 | elseif (npoints == 3) 18 | w = [0.555555555,0.888888888,0.555555555]; 19 | end 20 | % 21 | % 2D elements 22 | % 23 | elseif (ncoord == 2) 24 | % 25 | % Triangular element 26 | % 27 | if ( nelnodes == 3 || nelnodes == 6 ) 28 | if (npoints == 1) 29 | w(1) = 0.5; 30 | elseif (npoints == 3) 31 | w(1) = 1./6.; 32 | w(2) = 1./6.; 33 | w(3) = 1./6.; 34 | elseif (npoints == 4) 35 | w = [-27./96.,25./96.,25/96.,25/96.]; 36 | end 37 | % 38 | % Rectangular element 39 | % 40 | elseif ( nelnodes==4 || nelnodes==8 ) 41 | 42 | if (npoints == 1) 43 | w(1) = 4.; 44 | elseif (npoints == 4) 45 | w = [1.,1.,1.,1.]; 46 | elseif (npoints == 9 ) 47 | w1D = [0.555555555,0.888888888,0.55555555555]; 48 | for j = 1:3 49 | for i = 1:3 50 | n = 3*(j-1)+i; 51 | w(n) = w1D(i)*w1D(j); 52 | end 53 | end 54 | end 55 | end 56 | 57 | elseif (ncoord == 3) 58 | % 59 | % 3D elements 60 | % 61 | if (nelnodes == 4 || nelnodes==10 ) 62 | if (npoints == 1) 63 | w(1) = 1./6.; 64 | elseif (npoints == 4) 65 | w = [1./24.,1./24.,1./24.,1./24.]; 66 | end 67 | elseif ( nelnodes==8 || nelnodes==20 ) 68 | if (npoints == 1) 69 | w(1) = 8.; 70 | elseif (npoints == 8) 71 | w = [1.,1.,1.,1.,1.,1.,1.,1.]; 72 | elseif (npoints == 27) 73 | w1D = [0.555555555,0.888888888,0.55555555555]; 74 | for k = 1:3 75 | for j = 1:3 76 | for i = 1:3 77 | n = 9*(k-1)+3*(j-1)+i; 78 | w(n) = w1D(i)*w1D(j)*w1D(k); 79 | end 80 | end 81 | end 82 | end 83 | end 84 | end 85 | end -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib/materialstiffness.m: -------------------------------------------------------------------------------- 1 | %================= Material Stiffness ================================== 2 | % 3 | % Computes elasticity tensor C_{ijkl} = shear modulus and Poissons ratio 4 | % Currently coded either for plane strain, plane stress or general 3D. 5 | % 6 | function C = materialstiffness(ndof,ncoord,strain,materialprops) 7 | 8 | mu = materialprops(1); 9 | nu = materialprops(2); 10 | 11 | C = zeros(ndof,ncoord,ndof,ncoord); 12 | 13 | if (ncoord == 2) 14 | 15 | % planestrain = 0 => plane stress, 16 | % planestrain = 1 => plane strain 17 | planestrain = materialprops(3); 18 | 19 | for i = 1:2 20 | for j = 1:2 21 | for k = 1:2 22 | for l = 1:2 23 | if (planestrain==1) 24 | if (i==j && k==l) 25 | C(i,j,k,l) = C(i,j,k,l)+2*mu*nu/(1-2*nu); 26 | end 27 | else 28 | if (i==j && k==l) 29 | C(i,j,k,l) = C(i,j,k,l)+2*mu*nu/(1-nu); 30 | end 31 | end 32 | if (i==l && k==j) 33 | C(i,j,k,l) = C(i,j,k,l)+mu; 34 | end 35 | if (i==k && j==l) 36 | C(i,j,k,l) = C(i,j,k,l)+mu; 37 | end 38 | end 39 | end 40 | end 41 | end 42 | 43 | elseif (ncoord == 3) 44 | 45 | for i = 1:3 46 | for j = 1:3 47 | for k = 1:3 48 | for l = 1:3 49 | if (i==j && k==l) 50 | C(i,j,k,l)=C(i,j,k,l) + 2.*mu*nu/(1.-2.*nu); 51 | end 52 | if (i==k && j==l) 53 | C(i,j,k,l)=C(i,j,k,l) + mu; 54 | end 55 | if (i==l && j==k) 56 | C(i,j,k,l)=C(i,j,k,l) + mu; 57 | end 58 | end 59 | end 60 | end 61 | end 62 | end 63 | 64 | end -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib/materialstress.m: -------------------------------------------------------------------------------- 1 | %================= Material Stress ================================== 2 | % 3 | % Computes stress sigma_{ij} given strain epsilon_{ij} 4 | % 5 | function stress = materialstress(ndof,ncoord,strain,materialprops) 6 | 7 | C = materialstiffness(ndof,ncoord,strain,materialprops); 8 | stress = zeros(ndof,ncoord); 9 | for i = 1 : ndof 10 | for j = 1 : ncoord 11 | for k = 1 : ndof 12 | for l = 1: ncoord 13 | stress(i,j) = stress(i,j) + C(i,j,k,l)*strain(k,l); 14 | end 15 | end 16 | end 17 | end 18 | end -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib/nfacenodes.m: -------------------------------------------------------------------------------- 1 | %====================== No. nodes on element faces ================ 2 | % 3 | % This procedure returns the number of nodes on each element face 4 | % for various element types. This info is needed for computing 5 | % the surface integrals associated with the element traction vector 6 | % 7 | function n = nfacenodes(ncoord,nelnodes,elident,face) 8 | if (ncoord == 2) 9 | if (nelnodes == 3 || nelnodes == 4) 10 | n = 2; 11 | elseif (nelnodes == 6 || nelnodes == 8) 12 | n=3; 13 | end 14 | elseif (ncoord == 3) 15 | if (nelnodes == 4) 16 | n = 3; 17 | elseif (nelnodes == 10) 18 | n = 6; 19 | elseif (nelnodes == 8) 20 | n = 4; 21 | elseif (nelnodes == 20) 22 | n = 8; 23 | end 24 | end 25 | end -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib/numberofintegrationpoints.m: -------------------------------------------------------------------------------- 1 | %====================== No. integration points ============================= 2 | % 3 | % Defines the number of integration points:be used for 4 | % each element type 5 | % 6 | function n = numberofintegrationpoints(ncoord,nelnodes,elident) 7 | 8 | if (ncoord == 1) 9 | n = nelnodes; 10 | elseif (ncoord == 2) 11 | if (nelnodes == 2) 12 | n = 1; 13 | end 14 | if (nelnodes == 3) 15 | n = 1; 16 | end 17 | if (nelnodes == 6) 18 | n = 3; 19 | end 20 | if (nelnodes == 4) 21 | n = 4; 22 | end 23 | if (nelnodes == 8) 24 | n = 9; 25 | end 26 | elseif (ncoord == 3) 27 | if (nelnodes == 4) 28 | n = 1 ; 29 | end 30 | if (nelnodes == 10) 31 | n = 4; 32 | end 33 | if (nelnodes == 8) 34 | n = 8; 35 | end 36 | if (nelnodes == 20) 37 | n = 27; 38 | end 39 | end 40 | end -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib/plotmesh.m: -------------------------------------------------------------------------------- 1 | function plotmesh(Model,color) 2 | 3 | ncoord = Model.nDim; 4 | coords = Model.geometry.coordinates'; % trn 5 | nelem = Model.nElem; 6 | maxnodes = double(Model.nElemNode); 7 | connect = Model.geometry.elements'; % trn 8 | nelnodes = ones(nelem, 1) * maxnodes; 9 | 10 | if nargin < 2 11 | color = 'b'; 12 | end 13 | 14 | % Function to plot a mesh. 15 | f2D_2 = [1,2]; 16 | f2D_3 = [1,2,3]; 17 | f2D_4 = [1,2,3,4]; 18 | f2D_6 = [1,4,2,5,3,6]; 19 | f2D_8 = [1,5,2,6,3,7,4,8]; 20 | f3D_4 = [[1,2,3];[1,4,2];[2,4,3];[3,4,1]]; 21 | f3D_10 = [[1,5,2,6,3,7];[1,8,4,9,2,5];[2,9,4,10,3,6];[3,10,4,8,1,7]]; 22 | f3D_8 = [[1,2,3,4];[5,8,7,6];[1,5,6,2];[2,3,7,6];[3,7,8,4];[4,8,5,1]]; 23 | f3D_20 = [[1,9,2,10,3,11,4,12];[5,16,8,15,7,14,6,13]; 24 | [1,17,5,13,6,18,2,9];[2,18,6,14,7,19,3,10]; 25 | [3,19,7,15,8,20,4,11];[4,20,8,16,5,17,1,12]]; 26 | 27 | hold on 28 | if (ncoord==2) % Plot a 2D mesh 29 | for lmn = 1:nelem 30 | for i = 1:nelnodes(lmn) 31 | x(i,1:2) = coords(1:2,connect(i,lmn)); 32 | end 33 | scatter(x(:,1),x(:,2),'MarkerFaceColor','r'); 34 | if (nelnodes(lmn)==2) 35 | patch('Vertices',x,'Faces',f2D_2,'FaceColor','none','EdgeColor',color); 36 | elseif (nelnodes(lmn)==3) 37 | patch('Vertices',x,'Faces',f2D_3,'FaceColor','none','EdgeColor',color); 38 | elseif (nelnodes(lmn)==4) 39 | patch('Vertices',x,'Faces',f2D_4,'FaceColor','none','EdgeColor',color); 40 | elseif (nelnodes(lmn)==6) 41 | patch('Vertices',x,'Faces',f2D_6,'FaceColor','none','EdgeColor',color); 42 | elseif (nelnodes(lmn)==8 || nelnodes(lmn)==9) 43 | patch('Vertices',x,'Faces',f2D_8,'FaceColor','none','EdgeColor',color); 44 | end 45 | end 46 | elseif (ncoord==3) % Plot a 3D mesh 47 | for lmn = 1:nelem 48 | for i = 1:nelnodes(lmn) 49 | x(i,1:3) = coords(1:3,connect(i,lmn)); 50 | end 51 | scatter3(x(:,1),x(:,2),x(:,3),'MarkerFaceColor','r'); 52 | if (nelnodes(lmn)==4) 53 | patch('Vertices',x,'Faces',f3D_4,'FaceColor','none','EdgeColor',color); 54 | elseif (nelnodes(lmn)==10) 55 | patch('Vertices',x,'Faces',f3D_10,'FaceColor','none','EdgeColor',color); 56 | elseif (nelnodes(lmn)==8) 57 | patch('Vertices',x,'Faces',f3D_8,'FaceColor','none','EdgeColor',color); 58 | elseif (nelnodes(lmn)==20) 59 | patch('Vertices',x,'Faces',f3D_20,'FaceColor','none','EdgeColor',color); 60 | end 61 | end 62 | end 63 | axis equal 64 | hold off 65 | end 66 | -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib/print_results.m: -------------------------------------------------------------------------------- 1 | function print_results(outfile, ... 2 | nprops,materialprops,ncoord,ndof,nnode,coords, ... 3 | nelem,maxnodes,connect,nelnodes,elident, ... 4 | nfix,fixnodes,ndload,dloads,dofs) 5 | % Print nodal displacements, element strains && stresses:a file 6 | fprintf(outfile,'\n\n'); 7 | printDLine(outfile) 8 | printCTitle(outfile,'O U T P U T S U M M A R Y') 9 | printDLine(outfile) 10 | 11 | printCTitle(outfile,'N O D A L D I S P L A C E M E N T S'); 12 | printLine(outfile) 13 | if (ndof == 2) 14 | fprintf(outfile,' Node Coords u1 u2 \n'); 15 | for i = 1:nnode 16 | fprintf(outfile,'%3d %8.4f %8.4f %8.4f %8.4f\n', ... 17 | i,coords(1,i),coords(2,i),dofs(2*i-1),dofs(2*i)); 18 | end 19 | elseif (ndof == 3) 20 | fprintf(outfile,' Node Coords u1 u2 u3 \n'); 21 | for i = 1:nnode 22 | fprintf(outfile,'%3d %8.4f %8.4f %8.4f %8.4f %8.4f %8.4f \n', ... 23 | i,coords(1,i),coords(2,i),coords(3,i),dofs(3*i-2),dofs(3*i-1),dofs(3*i)); 24 | end 25 | end 26 | 27 | printDLine(outfile) 28 | printCTitle(outfile,'S T R E S S E S A N D S T R A I N S') 29 | 30 | lmncoord = zeros(ncoord,maxnodes); 31 | displacements = zeros(ndof,maxnodes); 32 | 33 | % 34 | % Loop over all the elements 35 | % 36 | for lmn = 1:nelem 37 | printLine(outfile) 38 | fprintf(outfile,' \n Element: %d ',lmn); 39 | if (ncoord == 2) 40 | fprintf(outfile,' \n int pt Coords e_11 e_22 e_12 s_11 s_22 s_12 \n'); 41 | 42 | elseif (ncoord == 3) 43 | fprintf(outfile,'\n int pt Coords e_11 e_22 e_33 e_12 e_13 e_23 s_11 s_22 s_33 s_12 s_13 s_23 \n'); 44 | end 45 | % 46 | % Extract coords of nodes, DOF for the current element 47 | % 48 | for a = 1:nelnodes(lmn) 49 | for i = 1:ncoord 50 | lmncoord(i,a) = coords(i,connect(a,lmn)); 51 | end 52 | for i = 1:ndof 53 | displacements(i,a) = dofs(ndof*(connect(a,lmn)-1)+i); 54 | end 55 | end 56 | n = nelnodes(lmn); 57 | ident = elident(lmn); 58 | 59 | npoints = numberofintegrationpoints(ncoord,n); 60 | dNdx = zeros(n,ncoord); 61 | dxdxi = zeros(ncoord,ncoord); 62 | strain = zeros(ndof,ncoord); 63 | xi = zeros(ncoord,1); 64 | x = zeros(ncoord,1); 65 | % 66 | % Set up integration points 67 | % 68 | xilist = integrationpoints(ncoord,n,npoints); 69 | % 70 | % Loop over the integration points 71 | % 72 | for intpt = 1:npoints 73 | 74 | % Compute shape functions && derivatives wrt local coords 75 | % 76 | for i = 1:ncoord 77 | xi(i) = xilist(i,intpt); 78 | end 79 | N = shapefunctions(n,ncoord,ident,xi); 80 | dNdxi = shapefunctionderivs(n,ncoord,ident,xi); 81 | % 82 | % Compute the coords of the integration point 83 | % 84 | for i = 1:ncoord 85 | x(i) = 0.; 86 | for a = 1:n 87 | x(i) = x(i) + lmncoord(i,a)*N(a); 88 | end 89 | end 90 | % 91 | % Compute the jacobian matrix && its determinant 92 | % 93 | for i = 1:ncoord 94 | for j = 1:ncoord 95 | dxdxi(i,j) = 0.; 96 | for a = 1:n 97 | dxdxi(i,j) = dxdxi(i,j) + lmncoord(i,a)*dNdxi(a,j); 98 | end 99 | end 100 | end 101 | 102 | dxidx = inv(dxdxi); 103 | % 104 | % Convert shape function derivatives:derivatives wrt global coords 105 | % 106 | for a = 1:n 107 | for i = 1:ncoord 108 | dNdx(a,i) = 0.; 109 | for j = 1:ncoord 110 | dNdx(a,i) = dNdx(a,i) + dNdxi(a,j)*dxidx(j,i); 111 | end 112 | end 113 | end 114 | % 115 | % Compute the (infinitesimal) strain by differentiating displacements 116 | % 117 | for i = 1:ncoord 118 | for j = 1:ncoord 119 | strain(i,j) = 0.; 120 | for a = 1:n 121 | strain(i,j) = strain(i,j) + 0.5*(displacements(i,a)*dNdx(a,j)+displacements(j,a)*dNdx(a,i)); 122 | end 123 | end 124 | end 125 | 126 | stress = materialstress(ndof,ncoord,strain,materialprops); 127 | 128 | if (ncoord == 2) 129 | 130 | fprintf(outfile,'%5d %7.4f %7.4f %9.4f %9.4f %9.4f %9.4f %9.4f %9.4f \n', ... 131 | intpt,x(1),x(2),strain(1,1),strain(2,2),strain(1,2),stress(1,1),stress(2,2),stress(1,2)); 132 | 133 | 134 | elseif (ncoord == 3) 135 | 136 | fprintf(outfile,'%5d %7.4f %7.4f %7.4f %9.4f %9.4f %9.4f %9.4f %9.4f %9.4f %9.4f %9.4f %9.4f %9.4f %9.4f %9.4f \n',... 137 | intpt,x(1),x(2),x(3), ... 138 | strain(1,1),strain(2,2),strain(3,3),strain(1,2),strain(1,3),strain(2,3), ... 139 | stress(1,1),stress(2,2),stress(3,3),stress(1,2),stress(1,3),stress(2,3)); 140 | end 141 | end 142 | 143 | end 144 | printDLine(outfile) 145 | end 146 | 147 | 148 | 149 | % Helper Functions 150 | function printLine(fid,n) 151 | if nargin < 2 152 | n = 80; 153 | end 154 | if nargin < 1 155 | fid = 1; 156 | end 157 | fprintf(fid,'%s\n',repmat('_',1,n)); 158 | end 159 | 160 | function printDLine(fid,n) 161 | if nargin < 2 162 | n = 80; 163 | end 164 | if nargin < 1 165 | fid = 1; 166 | end 167 | fprintf(fid,'%s\n',repmat('=',1,n)); 168 | end 169 | 170 | function printSLine(fid,n) 171 | if nargin < 2 172 | n = 80; 173 | end 174 | if nargin < 1 175 | fid = 1; 176 | end 177 | fprintf(fid,'%s\n',repmat('-',1,n)); 178 | end 179 | % printing centered text title 180 | function printCTitle(fid,text,n) 181 | if nargin < 3 182 | n = 80; 183 | end 184 | if nargin < 2 185 | text =''; 186 | end 187 | if nargin < 1 188 | fid = 1; 189 | end 190 | tLen = length(text); 191 | space = floor((n-tLen)/2); 192 | fprintf(fid,'%s\n',[repmat(' ',1,space),text]); 193 | end -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib/shapefunctionderivs.m: -------------------------------------------------------------------------------- 1 | %================= SHAPE FUNCTION DERIVATIVES ====================== 2 | % 3 | function dNdxi = shapefunctionderivs(nelnodes,ncoord,elident,xi) 4 | 5 | dNdxi = zeros(nelnodes,ncoord); 6 | % 7 | % 1D elements 8 | % 9 | if (ncoord == 1) 10 | if (nelnodes==2) 11 | dNdxi(1,1) = 0.5; 12 | dNdxi(2,1) = -0.5; 13 | elseif (nelnodes == 3) 14 | dNdxi(1,1) = -0.5+xi(1); 15 | dNdxi(2,1) = 0.5+xi(1); 16 | dNdxi(3,1) = -2.*xi(1); 17 | end 18 | % 19 | % 2D elements 20 | % 21 | elseif (ncoord == 2) 22 | % 23 | % Triangular element 24 | % 25 | if ( nelnodes == 3 ) 26 | dNdxi(1,1) = 1.; 27 | dNdxi(2,2) = 1.; 28 | dNdxi(3,1) = -1.; 29 | dNdxi(3,2) = -1.; 30 | elseif ( nelnodes == 6 ) 31 | xi3 = 1.-xi(1)-xi(2); 32 | dNdxi(1,1) = 4.*xi(1)-1.; 33 | dNdxi(2,2) = 4.*xi(2)-1.; 34 | dNdxi(3,1) = -(4.*xi3-1.); 35 | dNdxi(3,2) = -(4.*xi3-1.); 36 | dNdxi(4,1) = 4.*xi(2); 37 | dNdxi(4,2) = 4.*xi(1); 38 | dNdxi(5,1) = -4.*xi(2); 39 | dNdxi(5,2) = -4.*xi(1); 40 | dNdxi(6,1) = 4.*xi3 - 4.*xi(1); 41 | dNdxi(6,2) = 4.*xi3 - 4.*xi(2); 42 | % 43 | % Rectangular element 44 | % 45 | elseif ( nelnodes == 4 ) 46 | dNdxi(1,1) = -0.25*(1.-xi(2)); 47 | dNdxi(1,2) = -0.25*(1.-xi(1)); 48 | dNdxi(2,1) = 0.25*(1.-xi(2)); 49 | dNdxi(2,2) = -0.25*(1.+xi(1)); 50 | dNdxi(3,1) = 0.25*(1.+xi(2)); 51 | dNdxi(3,2) = 0.25*(1.+xi(1)); 52 | dNdxi(4,1) = -0.25*(1.+xi(2)); 53 | dNdxi(4,2) = 0.25*(1.-xi(1)); 54 | elseif (nelnodes == 8) 55 | dNdxi(1,1) = 0.25*(1.-xi(2))*(2.*xi(1)+xi(2)); 56 | dNdxi(1,2) = 0.25*(1.-xi(1))*(xi(1)+2.*xi(2)); 57 | dNdxi(2,1) = 0.25*(1.-xi(2))*(2.*xi(1)-xi(2)); 58 | dNdxi(2,2) = 0.25*(1.+xi(1))*(2.*xi(2)-xi(1)); 59 | dNdxi(3,1) = 0.25*(1.+xi(2))*(2.*xi(1)+xi(2)); 60 | dNdxi(3,2) = 0.25*(1.+xi(1))*(2.*xi(2)+xi(1)); 61 | dNdxi(4,1) = 0.25*(1.+xi(2))*(2.*xi(1)-xi(2)); 62 | dNdxi(4,2) = 0.25*(1.-xi(1))*(2.*xi(2)-xi(1)); 63 | dNdxi(5,1) = -xi(1)*(1.-xi(2)); 64 | dNdxi(5,2) = -0.5*(1.-xi(1)*xi(1)); 65 | dNdxi(6,1) = 0.5*(1.-xi(2)*xi(2)); 66 | dNdxi(6,2) = -(1.+xi(1))*xi(2); 67 | dNdxi(7,1) = -xi(1)*(1.+xi(2)); 68 | dNdxi(7,2) = 0.5*(1.-xi(1)*xi(1)); 69 | dNdxi(8,1) = -0.5*(1.-xi(2)*xi(2)); 70 | dNdxi(8,2) = -(1.-xi(1))*xi(2); 71 | end 72 | % 73 | % 3D elements 74 | % 75 | elseif (ncoord==3) 76 | 77 | if (nelnodes == 4) 78 | dNdxi(1,1) = 1.; 79 | dNdxi(2,2) = 1.; 80 | dNdxi(3,3) = 1.; 81 | dNdxi(4,1) = -1.; 82 | dNdxi(4,2) = -1.; 83 | dNdxi(4,3) = -1.; 84 | elseif (nelnodes == 10) 85 | xi4 = 1.-xi(1)-xi(2)-xi(3); 86 | dNdxi(1,1) = (4.*xi(1)-1.); 87 | dNdxi(2,2) = (4.*xi(2)-1.); 88 | dNdxi(3,3) = (4.*xi(3)-1.); 89 | dNdxi(4,1) = -(4.*xi4-1.); 90 | dNdxi(4,2) = -(4.*xi4-1.); 91 | dNdxi(4,3) = -(4.*xi4-1.); 92 | dNdxi(5,1) = 4.*xi(2); 93 | dNdxi(5,2) = 4.*xi(1); 94 | dNdxi(6,2) = 4.*xi(3); 95 | dNdxi(6,3) = 4.*xi(2); 96 | dNdxi(7,1) = 4.*xi(3); 97 | dNdxi(7,3) = 4.*xi(1); 98 | dNdxi(8,1) = 4.*(xi4-xi(1)); 99 | dNdxi(8,2) = -4.*xi(1); 100 | dNdxi(8,3) = -4.*xi(1); 101 | dNdxi(9,1) = -4.*xi(2); 102 | dNdxi(9,2) = 4.*(xi4-xi(2)); 103 | dNdxi(9,3) = -4.*xi(2); 104 | dNdxi(10,1) = -4.*xi(3)*xi4; 105 | dNdxi(10,2) = -4.*xi(3); 106 | dNdxi(10,3) = 4.*(xi4-xi(3)); 107 | elseif (nelnodes == 8) 108 | dNdxi(1,1) = -(1.-xi(2))*(1.-xi(3))/8.; 109 | dNdxi(1,2) = -(1.-xi(1))*(1.-xi(3))/8.; 110 | dNdxi(1,3) = -(1.-xi(1))*(1.-xi(2))/8.; 111 | dNdxi(2,1) = (1.-xi(2))*(1.-xi(3))/8.; 112 | dNdxi(2,2) = -(1.+xi(1))*(1.-xi(3))/8.; 113 | dNdxi(2,3) = -(1.+xi(1))*(1.-xi(2))/8.; 114 | dNdxi(3,1) = (1.+xi(2))*(1.-xi(3))/8.; 115 | dNdxi(3,2) = (1.+xi(1))*(1.-xi(3))/8.; 116 | dNdxi(3,3) = -(1.+xi(1))*(1.+xi(2))/8.; 117 | dNdxi(4,1) = -(1.+xi(2))*(1.-xi(3))/8.; 118 | dNdxi(4,2) = (1.-xi(1))*(1.-xi(3))/8.; 119 | dNdxi(4,3) = -(1.-xi(1))*(1.+xi(2))/8.; 120 | dNdxi(5,1) = -(1.-xi(2))*(1.+xi(3))/8.; 121 | dNdxi(5,2) = -(1.-xi(1))*(1.+xi(3))/8.; 122 | dNdxi(5,3) = (1.-xi(1))*(1.-xi(2))/8.; 123 | dNdxi(6,1) = (1.-xi(2))*(1.+xi(3))/8.; 124 | dNdxi(6,2) = -(1.+xi(1))*(1.+xi(3))/8.; 125 | dNdxi(6,3) = (1.+xi(1))*(1.-xi(2))/8.; 126 | dNdxi(7,1) = (1.+xi(2))*(1.+xi(3))/8.; 127 | dNdxi(7,2) = (1.+xi(1))*(1.+xi(3))/8.; 128 | dNdxi(7,3) = (1.+xi(1))*(1.+xi(2))/8.; 129 | dNdxi(8,1) = -(1.+xi(2))*(1.+xi(3))/8.; 130 | dNdxi(8,2) = (1.-xi(1))*(1.+xi(3))/8.; 131 | dNdxi(8,3) = (1.-xi(1))*(1.+xi(2))/8.; 132 | elseif (nelnodes == 20) 133 | dNdxi(1,1) = (-(1.-xi(2))*(1.-xi(3))*(-xi(1)-xi(2)-xi(3)-2.)-(1.-xi(1))*(1.-xi(2))*(1.-xi(3)))/8.; 134 | dNdxi(1,2) = (-(1.-xi(1))*(1.-xi(3))*(-xi(1)-xi(2)-xi(3)-2.)-(1.-xi(1))*(1.-xi(2))*(1.-xi(3)))/8.; 135 | dNdxi(1,3) = (-(1.-xi(1))*(1.-xi(2))*(-xi(1)-xi(2)-xi(3)-2.)-(1.-xi(1))*(1.-xi(2))*(1.-xi(3)))/8.; 136 | 137 | dNdxi(2,1) = ((1.-xi(2))*(1.-xi(3))*(xi(1)-xi(2)-xi(3)-2.)+(1.+xi(1))*(1.-xi(2))*(1.-xi(3)))/8.; 138 | dNdxi(2,2) = (-(1.+xi(1))*(1.-xi(3))*(xi(1)-xi(2)-xi(3)-2.)-(1.+xi(1))*(1.-xi(2))*(1.-xi(3)))/8.; 139 | dNdxi(2,3) = (-(1.+xi(1))*(1.-xi(2))*(xi(1)-xi(2)-xi(3)-2.)-(1.+xi(1))*(1.-xi(2))*(1.-xi(3)))/8.; 140 | 141 | dNdxi(3,1) = ((1.+xi(2))*(1.-xi(3))*(xi(1)+xi(2)-xi(3)-2.)+(1.+xi(1))*(1.+xi(2))*(1.-xi(3)))/8.; 142 | dNdxi(3,2) = ((1.+xi(1))*(1.-xi(3))*(xi(1)+xi(2)-xi(3)-2.)+(1.+xi(1))*(1.+xi(2))*(1.-xi(3)))/8.; 143 | dNdxi(3,3) = (-(1.+xi(1))*(1.+xi(2))*(xi(1)+xi(2)-xi(3)-2.)-(1.+xi(1))*(1.+xi(2))*(1.-xi(3)))/8.; 144 | 145 | dNdxi(4,1) = (-(1.+xi(2))*(1.-xi(3))*(-xi(1)+xi(2)-xi(3)-2.)-(1.-xi(1))*(1.+xi(2))*(1.-xi(3)))/8.; 146 | dNdxi(4,2) = ((1.-xi(1))*(1.-xi(3))*(-xi(1)+xi(2)-xi(3)-2.)+(1.-xi(1))*(1.+xi(2))*(1.-xi(3)))/8.; 147 | dNdxi(4,3) = (-(1.-xi(1))*(1.+xi(2))*(-xi(1)+xi(2)-xi(3)-2.)-(1.-xi(1))*(1.+xi(2))*(1.-xi(3)))/8.; 148 | dNdxi(5,1) = (-(1.-xi(2))*(1.+xi(3))*(-xi(1)-xi(2)+xi(3)-2.)-(1.-xi(1))*(1.-xi(2))*(1.+xi(3)))/8.; 149 | dNdxi(5,2) = (-(1.-xi(1))*(1.+xi(3))*(-xi(1)-xi(2)+xi(3)-2.)-(1.-xi(1))*(1.-xi(2))*(1.+xi(3)))/8.; 150 | dNdxi(5,3) = ((1.-xi(1))*(1.-xi(2))*(-xi(1)-xi(2)+xi(3)-2.)+(1.-xi(1))*(1.-xi(2))*(1.+xi(3)))/8.; 151 | dNdxi(6,1) = ((1.-xi(2))*(1.+xi(3))*(xi(1)-xi(2)+xi(3)-2.)+(1.+xi(1))*(1.-xi(2))*(1.+xi(3)))/8.; 152 | dNdxi(6,2) = (-(1.+xi(1))*(1.+xi(3))*(xi(1)-xi(2)+xi(3)-2.)-(1.+xi(1))*(1.-xi(2))*(1.+xi(3)))/8.; 153 | dNdxi(6,3) = ((1.+xi(1))*(1.-xi(2))*(xi(1)-xi(2)+xi(3)-2.)+(1.+xi(1))*(1.-xi(2))*(1.+xi(3)))/8.; 154 | dNdxi(7,1) = ((1.+xi(2))*(1.+xi(3))*(xi(1)+xi(2)+xi(3)-2.)+(1.+xi(1))*(1.+xi(2))*(1.+xi(3)))/8.; 155 | dNdxi(7,2) = ((1.+xi(1))*(1.+xi(3))*(xi(1)+xi(2)+xi(3)-2.)+(1.+xi(1))*(1.+xi(2))*(1.+xi(3)))/8.; 156 | dNdxi(7,3) = ((1.+xi(1))*(1.+xi(2))*(xi(1)+xi(2)+xi(3)-2.)+(1.+xi(1))*(1.+xi(2))*(1.+xi(3)))/8.; 157 | dNdxi(8,1) = (-(1.+xi(2))*(1.+xi(3))*(-xi(1)+xi(2)+xi(3)-2.)-(1.-xi(1))*(1.+xi(2))*(1.+xi(3)))/8.; 158 | dNdxi(8,2) = ((1.-xi(1))*(1.+xi(3))*(-xi(1)+xi(2)+xi(3)-2.)+(1.-xi(1))*(1.+xi(2))*(1.+xi(3)))/8.; 159 | dNdxi(8,3) = ((1.-xi(1))*(1.+xi(2))*(-xi(1)+xi(2)+xi(3)-2.)+(1.-xi(1))*(1.+xi(2))*(1.+xi(3)))/8.; 160 | dNdxi(9,1) = -2.*xi(1)*(1.-xi(2))*(1.-xi(3))/4.; 161 | dNdxi(9,2) = -(1.-xi(1)^2)*(1.-xi(3))/4.; 162 | dNdxi(9,3) = -(1.-xi(1)^2)*(1.-xi(2))/4.; 163 | dNdxi(10,1) = (1.-xi(2)^2)*(1.-xi(3))/4.; 164 | dNdxi(10,2) = -2.*xi(2)*(1.+xi(1))*(1.-xi(3))/4.; 165 | dNdxi(10,3) = -(1.-xi(2)^2)*(1.+xi(1))/4.; 166 | dNdxi(11,1) = -2.*xi(1)*(1.+xi(2))*(1.-xi(3))/4.; 167 | dNdxi(11,2) = (1.-xi(1)^2)*(1.-xi(3))/4.; 168 | dNdxi(11,3) = -(1.-xi(1)^2)*(1.+xi(2))/4.; 169 | dNdxi(12,1) = -(1.-xi(2)^2)*(1.-xi(3))/4.; 170 | dNdxi(12,2) = -2.*xi(2)*(1.-xi(1))*(1.-xi(3))/4.; 171 | dNdxi(12,3) = -(1.-xi(2)^2)*(1.-xi(1))/4.; 172 | dNdxi(13,1) = -2.*xi(1)*(1.-xi(2))*(1.+xi(3))/4.; 173 | dNdxi(13,2) = -(1.-xi(1)^2)*(1.+xi(3))/4.; 174 | dNdxi(13,3) = (1.-xi(1)^2)*(1.-xi(2))/4.; 175 | dNdxi(14,1) = (1.-xi(2)^2)*(1.+xi(3))/4.; 176 | dNdxi(14,2) = -2.*xi(2)*(1.+xi(1))*(1.+xi(3))/4.; 177 | dNdxi(14,3) = (1.-xi(2)^2)*(1.+xi(1))/4.; 178 | dNdxi(15,1) = -2.*xi(1)*(1.+xi(2))*(1.+xi(3))/4.; 179 | dNdxi(15,2) = (1.-xi(1)^2)*(1.+xi(3))/4.; 180 | dNdxi(15,3) = (1.-xi(1)^2)*(1.+xi(2))/4.; 181 | dNdxi(16,1) = -(1.-xi(2)^2)*(1.+xi(3))/4.; 182 | dNdxi(16,2) = -2.*xi(2)*(1.-xi(1))*(1.+xi(3))/4.; 183 | dNdxi(16,3) = (1.-xi(2)^2)*(1.-xi(1))/4.; 184 | dNdxi(17,1) = -(1.-xi(2))*(1.-xi(3)^2)/4.; 185 | dNdxi(17,2) = -(1.-xi(1))*(1.-xi(3)^2)/4.; 186 | dNdxi(17,3) = -xi(3)*(1.-xi(1))*(1.-xi(2))/2.; 187 | dNdxi(18,1) = (1.-xi(2))*(1.-xi(3)^2)/4.; 188 | dNdxi(18,2) = -(1.+xi(1))*(1.-xi(3)^2)/4.; 189 | dNdxi(18,3) = -xi(3)*(1.+xi(1))*(1.-xi(2))/2.; 190 | dNdxi(19,1) = (1.+xi(2))*(1.-xi(3)^2)/4.; 191 | dNdxi(19,2) = (1.+xi(1))*(1.-xi(3)^2)/4.; 192 | dNdxi(19,3) = -xi(3)*(1.+xi(1))*(1.+xi(2))/2.; 193 | dNdxi(20,1) = -(1.+xi(2))*(1.-xi(3)^2)/4.; 194 | dNdxi(20,2) = (1.-xi(1))*(1.-xi(3)^2)/4.; 195 | dNdxi(20,3) = -xi(3)*(1.-xi(1))*(1.+xi(2))/2.; 196 | end 197 | end 198 | 199 | end 200 | -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib/shapefunctions.m: -------------------------------------------------------------------------------- 1 | % 2 | %================= SHAPE FUNCTIONS ================================== 3 | % 4 | % Calculates shape functions for various element types 5 | % 6 | function N = shapefunctions(nelnodes,ncoord,elident,xi) 7 | 8 | 9 | N = zeros(nelnodes,1); 10 | % 11 | % 1D elements 12 | % 13 | if (ncoord == 1) 14 | if (nelnodes==2) 15 | N(1) = 0.5*(1.+xi(1)); 16 | N(2) = 0.5*(1.-xi(1)); 17 | elseif (nelnodes == 3) 18 | N(1) = -0.5*xi(1)*(1.-xi(1)); 19 | N(2) = 0.5*xi(1)*(1.+xi(1)); 20 | N(3) = (1.-xi(1))*(1.+xi(1)); 21 | end 22 | % 23 | % 2D elements 24 | % 25 | elseif (ncoord == 2) 26 | % 27 | % Triangular element 28 | % 29 | if ( nelnodes == 3 ) 30 | N(1) = xi(1); 31 | N(2) = xi(2); 32 | N(3) = 1.-xi(1)-xi(2); 33 | elseif ( nelnodes == 6 ) 34 | xi3 = 1.-xi(1)-xi(2); 35 | N(1) = (2.*xi(1)-1.)*xi(1); 36 | N(2) = (2.*xi(2)-1.)*xi(2); 37 | N(3) = (2.*xi3-1.)*xi3; 38 | N(4) = 4.*xi(1)*xi(2); 39 | N(5) = 4.*xi(2)*xi3; 40 | N(6) = 4.*xi3*xi(1); 41 | % 42 | % Rectangular element 43 | % 44 | elseif ( nelnodes == 4 ) 45 | N(1) = 0.25*(1.-xi(1))*(1.-xi(2)); 46 | N(2) = 0.25*(1.+xi(1))*(1.-xi(2)); 47 | N(3) = 0.25*(1.+xi(1))*(1.+xi(2)); 48 | N(4) = 0.25*(1.-xi(1))*(1.+xi(2)); 49 | elseif (nelnodes == 8) 50 | N(1) = -0.25*(1.-xi(1))*(1.-xi(2))*(1.+xi(1)+xi(2)); 51 | N(2) = 0.25*(1.+xi(1))*(1.-xi(2))*(xi(1)-xi(2)-1.); 52 | N(3) = 0.25*(1.+xi(1))*(1.+xi(2))*(xi(1)+xi(2)-1.); 53 | N(4) = 0.25*(1.-xi(1))*(1.+xi(2))*(xi(2)-xi(1)-1.); 54 | N(5) = 0.5*(1.-xi(1)*xi(1))*(1.-xi(2)); 55 | N(6) = 0.5*(1.+xi(1))*(1.-xi(2)*xi(2)); 56 | N(7) = 0.5*(1.-xi(1)*xi(1))*(1.+xi(2)); 57 | N(8) = 0.5*(1.-xi(1))*(1.-xi(2)*xi(2)); 58 | end 59 | % 60 | elseif (ncoord==3) 61 | 62 | if (nelnodes == 4) 63 | N(1) = xi(1); 64 | N(2) = xi(2); 65 | N(3) = xi(3); 66 | N(4) = 1.-xi(1)-xi(2)-xi(3); 67 | elseif (nelnodes == 10) 68 | xi4 = 1.-xi(1)-xi(2)-xi(3); 69 | N(1) = (2.*xi(1)-1.)*xi(1); 70 | N(2) = (2.*xi(2)-1.)*xi(2); 71 | N(3) = (2.*xi(3)-1.)*xi(3); 72 | N(4) = (2.*xi4-1.)*xi4; 73 | N(5) = 4.*xi(1)*xi(2); 74 | N(6) = 4.*xi(2)*xi(3); 75 | N(7) = 4.*xi(3)*xi(1); 76 | N(8) = 4.*xi(1)*xi4; 77 | N(9) = 4.*xi(2)*xi4; 78 | N(10) = 4.*xi(3)*xi4; 79 | elseif (nelnodes == 8) 80 | N(1) = (1.-xi(1))*(1.-xi(2))*(1.-xi(3))/8.; 81 | N(2) = (1.+xi(1))*(1.-xi(2))*(1.-xi(3))/8.; 82 | N(3) = (1.+xi(1))*(1.+xi(2))*(1.-xi(3))/8.; 83 | N(4) = (1.-xi(1))*(1.+xi(2))*(1.-xi(3))/8.; 84 | N(5) = (1.-xi(1))*(1.-xi(2))*(1.+xi(3))/8.; 85 | N(6) = (1.+xi(1))*(1.-xi(2))*(1.+xi(3))/8.; 86 | N(7) = (1.+xi(1))*(1.+xi(2))*(1.+xi(3))/8.; 87 | N(8) = (1.-xi(1))*(1.+xi(2))*(1.+xi(3))/8.; 88 | elseif (nelnodes == 20) 89 | N(1) = (1.-xi(1))*(1.-xi(2))*(1.-xi(3))*(-xi(1)-xi(2)-xi(3)-2.)/8.; 90 | N(2) = (1.+xi(1))*(1.-xi(2))*(1.-xi(3))*(xi(1)-xi(2)-xi(3)-2.)/8.; 91 | N(3) = (1.+xi(1))*(1.+xi(2))*(1.-xi(3))*(xi(1)+xi(2)-xi(3)-2.)/8.; 92 | N(4) = (1.-xi(1))*(1.+xi(2))*(1.-xi(3))*(-xi(1)+xi(2)-xi(3)-2.)/8.; 93 | N(5) = (1.-xi(1))*(1.-xi(2))*(1.+xi(3))*(-xi(1)-xi(2)+xi(3)-2.)/8.; 94 | N(6) = (1.+xi(1))*(1.-xi(2))*(1.+xi(3))*(xi(1)-xi(2)+xi(3)-2.)/8.; 95 | N(7) = (1.+xi(1))*(1.+xi(2))*(1.+xi(3))*(xi(1)+xi(2)+xi(3)-2.)/8.; 96 | N(8) = (1.-xi(1))*(1.+xi(2))*(1.+xi(3))*(-xi(1)+xi(2)+xi(3)-2.)/8.; 97 | N(9) = (1.-xi(1)^2)*(1.-xi(2))*(1.-xi(3))/4.; 98 | N(10) = (1.+xi(1))*(1.-xi(2)^2)*(1.-xi(3))/4.; 99 | N(11) = (1.-xi(1)^2)*(1.+xi(2))*(1.-xi(3))/4.; 100 | N(12) = (1.-xi(1))*(1.-xi(2)^2)*(1.-xi(3))/4.; 101 | N(13) = (1.-xi(1)^2)*(1.-xi(2))*(1.+xi(3))/4.; 102 | N(14) = (1.+xi(1))*(1.-xi(2)^2)*(1.+xi(3))/4.; 103 | N(15) = (1.-xi(1)^2)*(1.+xi(2))*(1.+xi(3))/4.; 104 | N(16) = (1.-xi(1))*(1.-xi(2)^2)*(1.+xi(3))/4.; 105 | N(17) = (1.-xi(1))*(1.-xi(2))*(1.-xi(3)^2)/4.; 106 | N(18) = (1.+xi(1))*(1.-xi(2))*(1.-xi(3)^2)/4.; 107 | N(19) = (1.+xi(1))*(1.+xi(2))*(1.-xi(3)^2)/4.; 108 | N(20) = (1.-xi(1))*(1.+xi(2))*(1.-xi(3)^2)/4.; 109 | end 110 | end 111 | 112 | end 113 | -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib/solution.m: -------------------------------------------------------------------------------- 1 | function [d, rf] = solution(K, R, debc, ebcVals) 2 | dof = length(R); 3 | df = setdiff(1:dof, debc); 4 | Kf = K(df, df); 5 | Rf = R(df) - K(df, debc)*ebcVals; 6 | dfVals = Kf\Rf; 7 | d = zeros(dof,1); 8 | d(debc) = ebcVals; 9 | d(df) = dfVals; 10 | rf = K(debc,:)*d - R(debc); 11 | -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib_io/inpFileReader.p: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/shahrokhx/FEM_Toolbox/8dda726b82d707d2e3404996893c95b8e2de3ef9/Source Code/PlaneStress PlaneStrain/lib_io/inpFileReader.p -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib_io/printResult.m: -------------------------------------------------------------------------------- 1 | function printResult(Solution,fid) 2 | 3 | if nargin < 2 4 | fid = 1; 5 | end 6 | BULLET_CHAR = char(15); 7 | 8 | fprintf(fid,'\n\n'); 9 | printDLine(fid) 10 | printCTitle(fid,'O U T P U T S U M M A R Y') 11 | printDLine(fid) 12 | 13 | if isfield(Solution,'info') 14 | fprintf(fid,'%c About: \n',BULLET_CHAR); 15 | fprintf(fid,'%s\n', Solution.info); 16 | end 17 | printLine(fid) 18 | 19 | 20 | if isfield(Solution, 'nodalDisplacements') 21 | u = Solution.nodalDisplacements; 22 | [nNode,nDof] = size(u); 23 | printCTitle(fid,'Nodal Displacements'); 24 | printSLine(fid); 25 | for i = 1 : nNode 26 | formatStr = repmat('%10.5f\t',1,nDof); 27 | fprintf(fid,['[%3d] ',formatStr,'\n'],i,u(i,:)); 28 | end 29 | end 30 | printLine(fid) 31 | if isfield(Solution, 'reactionForces') 32 | rf = Solution.reactionForces; 33 | [nNode,nDof] = size(rf); 34 | printCTitle(fid,'Reaction Forces'); 35 | printSLine(fid); 36 | for i = 1 : nNode 37 | formatStr = repmat('%10.5f\t',1,nDof); 38 | fprintf(fid,['[%3d] ',formatStr,'\n'],i,rf(i,:)); 39 | end 40 | end 41 | 42 | printDLine(fid); 43 | end 44 | 45 | 46 | % Helper Functions 47 | function printLine(fid,n) 48 | if nargin < 2 49 | n = 80; 50 | end 51 | if nargin < 1 52 | fid = 1; 53 | end 54 | fprintf(fid,'%s\n',repmat('_',1,n)); 55 | end 56 | 57 | function printDLine(fid,n) 58 | if nargin < 2 59 | n = 80; 60 | end 61 | if nargin < 1 62 | fid = 1; 63 | end 64 | fprintf(fid,'%s\n',repmat('=',1,n)); 65 | end 66 | 67 | function printSLine(fid,n) 68 | if nargin < 2 69 | n = 80; 70 | end 71 | if nargin < 1 72 | fid = 1; 73 | end 74 | fprintf(fid,'%s\n',repmat('-',1,n)); 75 | end 76 | % printing centered text title 77 | function printCTitle(fid,text,n) 78 | if nargin < 3 79 | n = 80; 80 | end 81 | if nargin < 2 82 | text =''; 83 | end 84 | if nargin < 1 85 | fid = 1; 86 | end 87 | tLen = length(text); 88 | space = floor((n-tLen)/2); 89 | fprintf(fid,'%s\n',[repmat(' ',1,space),text]); 90 | end 91 | -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/lib_io/printSummary.m: -------------------------------------------------------------------------------- 1 | function printSummary(Model,fid) 2 | % PURPOSE: reads input files and generates a structure including all data 3 | % 4 | % INPUT(S): 5 | % - Model: a structure including the following fields 6 | % - fid : file id to store 7 | % 8 | % OUTPUT(S): 9 | % 10 | % 11 | % USAGE: 12 | % >> printSummary(Model) print input details on command window 13 | % >> printSummary(Model,fid) print input details on a file with fid 14 | % identifier 15 | 16 | % DEVELOPMENT HISTORY: 17 | % [2018, Oct, 29] Shahrokh Shahi -- initial development 18 | % [2018, XXX, XX] Shahrokh Shahi -- 19 | 20 | if nargin < 2 21 | fid = 1; 22 | end 23 | BULLET_CHAR = char(15); 24 | 25 | printDLine(fid) 26 | tText = 'A S U M M A R Y O F T H E I N P U T M O D E L'; 27 | printCTitle(fid,tText) 28 | printDLine(fid) 29 | 30 | 31 | if isfield(Model,'info') 32 | fprintf(fid,'%c About: \n',BULLET_CHAR); 33 | fprintf(fid,'%s\n', Model.info); 34 | end 35 | if isfield(Model,'analysisType') 36 | fprintf(fid,'\n%c Structure Type: \n',BULLET_CHAR); 37 | fprintf(fid,'%s\n', Model.analysisType); 38 | end 39 | printLine(fid) 40 | 41 | 42 | fprintf(fid,'%c Control Variables: \n',BULLET_CHAR); 43 | fprintf(fid,' - Dimension: %dD\n' ,Model.nDim); 44 | fprintf(fid,' - Number of DOF(s): %d \n' ,Model.nDof); 45 | fprintf(fid,'\n'); 46 | fprintf(fid,' - Number of Nodes: %4d \n' ,Model.nNode); 47 | fprintf(fid,' - Number of Elements: %4d \n' ,Model.nElem); 48 | fprintf(fid,' - Nodes per Elements: %d\n',Model.nElemNode); 49 | fprintf(fid,'\n'); 50 | fprintf(fid,' - Number of Sections: %d \n',Model.nSection); 51 | printDLine(fid) 52 | 53 | 54 | printCTitle(fid,'N O D A L I N F O R M A T I O N') 55 | printLine(fid) 56 | headerTxt = ['Node Coordinates Nodal Loads ',... 57 | ' Nodal Restraints \n']; 58 | fprintf(fid,headerTxt); 59 | printSLine(fid) 60 | switch Model.nDim 61 | case 1 62 | headerTxt1 =' ID X '; 63 | headerTxt2 =' Fx '; 64 | headerTxt3 =' ux \n'; 65 | 66 | case 2 67 | headerTxt1 =' ID X Y '; 68 | headerTxt2 =' Fx Fy '; 69 | headerTxt3 =' ux uy \n'; 70 | 71 | case 3 72 | headerTxt1 =' ID X Y Z '; 73 | headerTxt2 =' Fx Fy Fz '; 74 | headerTxt3 =' ux uy uz \n'; 75 | end 76 | fprintf(fid,[headerTxt1,headerTxt2,headerTxt3]); 77 | printLine(fid) 78 | 79 | % nodal forces to displaying 80 | F = zeros(Model.nNode,Model.nDim); 81 | for i = 1 : Model.nNodalForce 82 | node = Model.loading.nodalForces(i,1); 83 | F(node, 1:Model.nDim) = Model.loading.nodalForces(i,2:end); 84 | end 85 | 86 | % printing table contents 87 | for i = 1 : Model.nNode 88 | coord = Model.geometry.coordinates(i,:); 89 | fprintf(fid,'%2d ',i); 90 | for j = 1 : length(coord) 91 | fprintf(fid,'%7.2f ',coord(j)); 92 | end 93 | fprintf(fid,'\t'); 94 | for j = 1 : size(F,2) 95 | fprintf(fid,'%10.2f ',F(i,j)); 96 | end 97 | 98 | fprintf(fid,'\t'); 99 | index = find(Model.boundary(:,1)==i); 100 | dx='-';dy='-';dz='-';bc=''; 101 | 102 | if ~isempty(index) 103 | for k = 1 : length(index) 104 | if Model.boundary(index(k),2)==1 105 | dx=num2str(Model.boundary(index(k),3)); 106 | elseif Model.boundary(index(k),2)==2 107 | dy=num2str(Model.boundary(index(k),3)); 108 | elseif Model.boundary(index(k),2)==3 109 | dz=num2str(Model.boundary(index(k),3)); 110 | end 111 | end 112 | if length(index)==1 113 | bc = 'Roller '; 114 | elseif length(index)==2 115 | bc = 'Pin'; 116 | elseif length(index)==3 117 | bc = 'Fixed'; 118 | end 119 | end 120 | presc = [dx, dy, dz]; %prescribed values 121 | for j = 1 : Model.nDof 122 | fprintf(fid,' %s',presc(j)); 123 | end 124 | fprintf(fid,' %s\n',bc); 125 | end 126 | printDLine(fid); 127 | 128 | printCTitle(fid,'E L E M E N T S I N F O R M A T I O N') 129 | printLine(fid) 130 | fprintf(fid,' ID\t '); 131 | for i = 1 : Model.nElemNode 132 | fprintf(fid,'Node%d\t',i); 133 | end 134 | fprintf(fid,' Section No. Material Properties\n'); 135 | printLine(fid); 136 | 137 | for i = 1 : Model.nElem 138 | fprintf(fid,'%2d\t ',i); 139 | for j = 1 : Model.nElemNode 140 | fprintf(fid,'%2d\t\t',Model.geometry.elements(i,j)); 141 | end 142 | fprintf(fid,'\t'); 143 | fprintf(fid,'\t%2d\t\t\t[',Model.elemSectId(i)); 144 | for j = 1 : Model.nMaterialProp 145 | fprintf(fid,'%g\t\t',Model.sections(Model.elemSectId(i),j)); 146 | end 147 | fprintf(fid,']\n'); 148 | end 149 | 150 | printDLine(fid); 151 | 152 | end 153 | 154 | 155 | % Helper Functions 156 | function printLine(fid,n) 157 | if nargin < 2 158 | n = 80; 159 | end 160 | if nargin < 1 161 | fid = 1; 162 | end 163 | fprintf(fid,'%s\n',repmat('_',1,n)); 164 | end 165 | 166 | function printDLine(fid,n) 167 | if nargin < 2 168 | n = 80; 169 | end 170 | if nargin < 1 171 | fid = 1; 172 | end 173 | fprintf(fid,'%s\n',repmat('=',1,n)); 174 | end 175 | 176 | function printSLine(fid,n) 177 | if nargin < 2 178 | n = 80; 179 | end 180 | if nargin < 1 181 | fid = 1; 182 | end 183 | fprintf(fid,'%s\n',repmat('-',1,n)); 184 | end 185 | % printing centered text title 186 | function printCTitle(fid,text,n) 187 | if nargin < 3 188 | n = 80; 189 | end 190 | if nargin < 2 191 | text =''; 192 | end 193 | if nargin < 1 194 | fid = 1; 195 | end 196 | tLen = length(text); 197 | space = floor((n-tLen)/2); 198 | fprintf(fid,'%s\n',[repmat(' ',1,space),text]); 199 | end -------------------------------------------------------------------------------- /Source Code/PlaneStress PlaneStrain/main.m: -------------------------------------------------------------------------------- 1 | %% M A I N F U N C T I O N 2 | %__________________________________________________________________________ 3 | % 4 | % Finite Element Methods 5 | % Developed by SHAHROKH SHAHI 6 | % (www.sshahi.com) 7 | % 8 | % Georgia Institute of Technology 9 | %__________________________________________________________________________ 10 | % 11 | % This file is the main function to handle the PLANE STRESS/STRAIN analysis 12 | % by employing the functions in the folder "lib" 13 | 14 | 15 | % DEVELOPMENT HISTORY: 16 | % [2018, Oct, 28] Shahrokh Shahi -- initial development 17 | % [2018, XXX, XX] Shahrokh Shahi -- 18 | 19 | %% Initial Setup ( You do NOT need to change this section) 20 | clc 21 | clear 22 | close all 23 | 24 | format short g 25 | format compact 26 | 27 | % adding "lib" folder to the path 28 | path = mfilename('fullpath'); 29 | path(end-length(mfilename):end)=[]; 30 | addpath(fullfile(path,'lib')) 31 | addpath(fullfile(path,'lib_io')) 32 | 33 | %% Reading the Input File 34 | 35 | % input file name: 36 | 37 | % input1.txt: 2D triangular element 38 | % input2.txt: 2D quad element 39 | % input3.txt: 3D 8nodes-brick element 40 | inpFileName = 'input2.txt'; 41 | 42 | %-------------------------------------------------------------------------- 43 | % E X T R A C T M O D E L F R O M I N P U T F I L E 44 | %-------------------------------------------------------------------------- 45 | Model = inpFileReader(inpFileName); 46 | 47 | %-------------------------------------------------------------------------- 48 | % P R I N T I N P U T S U M M A R Y 49 | %-------------------------------------------------------------------------- 50 | printSummary(Model) 51 | 52 | %-------------------------------------------------------------------------- 53 | % S I M P L E P L O T 54 | %-------------------------------------------------------------------------- 55 | plotmesh(Model,'b'); 56 | 57 | %% Run The Analysis 58 | Solution = femGeneral(Model); 59 | 60 | 61 | -------------------------------------------------------------------------------- /Source Code/PlaneTruss/input1.txt: -------------------------------------------------------------------------------- 1 | 2 | 3 | * INFO 4 | SOURCE: EXAMPLE 3.5 (Logan, D. (2012). A first course in the finite element 5 | method (5th ed.)) 6 | 7 | 8 | * ANALYSIS TYPE 9 | Truss 10 | 11 | 12 | * COORDINATES 13 | 1 0.0 0.0 14 | 2 0.0 120.0 15 | 3 120.0 0.0 16 | 4 120.0 120.0 17 | 18 | * ELEMENTS 19 | 1 1 1 2 20 | 2 1 1 3 21 | 3 1 1 4 22 | 23 | 24 | * SECTIONS 25 | 1 30e6 2 26 | 27 | * NODAL FORCES 28 | 1 0 -1e4 29 | 30 | * BOUNDARY 31 | 2 1 0.0 32 | 2 2 0.0 33 | 3 1 0.0 34 | 3 2 0.0 35 | 4 1 0.0 36 | 4 2 0.0 37 | 38 | 39 | -------------------------------------------------------------------------------- /Source Code/PlaneTruss/input2.txt: -------------------------------------------------------------------------------- 1 | * INFO 2 | A truss example with distributed axial force 3 | [Ref] Logan, Problem 3.58 (page 162) 4 | 5 | * ANALYSIS TYPE 6 | Truss 7 | 8 | * COORDINATES 9 | 1 0.0 0.0 10 | 2 10.0 0.0 11 | 12 | 13 | * ELEMENTS 14 | 1 1 1 2 15 | 16 | 17 | # in this example we don't need SECTIONS 18 | * SECTIONS 19 | 1 210e3 10 20 | 21 | 22 | 23 | * TRACTION FORCES 24 | 1 1 100+5*x 0 25 | 26 | * BOUNDARY 27 | 1 1 0.0 28 | 1 2 0.0 29 | 2 2 0.0 30 | 31 | 32 | 33 | -------------------------------------------------------------------------------- /Source Code/PlaneTruss/input3.txt: -------------------------------------------------------------------------------- 1 | 2 | 3 | * INFO 4 | SOURCE: EXAMPLE 3.5 (Logan, D. (2012). A first course in the finite element 5 | method (5th ed.)) 6 | 7 | 8 | * ANALYSIS TYPE 9 | Truss 10 | 11 | 12 | * COORDINATES 13 | 1 0.0 0.0 14 | 2 0.0 120.0 15 | 3 120.0 0.0 16 | 4 120.0 120.0 17 | 18 | * ELEMENTS 19 | 1 1 1 2 20 | 2 1 1 3 21 | 3 1 1 4 22 | 23 | 24 | * SECTIONS 25 | 1 30e6 2 26 | 27 | * NODAL FORCES 28 | 1 0 -1e4 29 | 30 | * BOUNDARY 31 | 2 1 0.0 32 | 2 2 0.0 33 | 3 1 0.0 34 | 3 2 0.0 35 | 4 1 0.0 36 | 4 2 0.0 37 | 38 | 39 | -------------------------------------------------------------------------------- /Source Code/PlaneTruss/lib/shapefunctionderivs.m: -------------------------------------------------------------------------------- 1 | %================= SHAPE FUNCTION DERIVATIVES ====================== 2 | % 3 | function dNdxi = shapefunctionderivs(nDim,nElemNode,xi) 4 | 5 | dNdxi = zeros(nElemNode,nDim); 6 | % 7 | % 1D elements 8 | % 9 | if (nDim == 1) 10 | if (nElemNode==2) 11 | dNdxi(1,1) = 0.5; 12 | dNdxi(2,1) = -0.5; 13 | elseif (nElemNode == 3) 14 | dNdxi(1,1) = -0.5+xi(1); 15 | dNdxi(2,1) = 0.5+xi(1); 16 | dNdxi(3,1) = -2.*xi(1); 17 | end 18 | % 19 | % 2D elements 20 | % 21 | elseif (nDim == 2) 22 | % 23 | % Triangular element 24 | % 25 | if ( nElemNode == 3 ) 26 | dNdxi(1,1) = 1.; 27 | dNdxi(2,2) = 1.; 28 | dNdxi(3,1) = -1.; 29 | dNdxi(3,2) = -1.; 30 | elseif ( nElemNode == 6 ) 31 | xi3 = 1.-xi(1)-xi(2); 32 | dNdxi(1,1) = 4.*xi(1)-1.; 33 | dNdxi(2,2) = 4.*xi(2)-1.; 34 | dNdxi(3,1) = -(4.*xi3-1.); 35 | dNdxi(3,2) = -(4.*xi3-1.); 36 | dNdxi(4,1) = 4.*xi(2); 37 | dNdxi(4,2) = 4.*xi(1); 38 | dNdxi(5,1) = -4.*xi(2); 39 | dNdxi(5,2) = -4.*xi(1); 40 | dNdxi(6,1) = 4.*xi3 - 4.*xi(1); 41 | dNdxi(6,2) = 4.*xi3 - 4.*xi(2); 42 | % 43 | % Rectangular element 44 | % 45 | elseif ( nElemNode == 4 ) 46 | dNdxi(1,1) = -0.25*(1.-xi(2)); 47 | dNdxi(1,2) = -0.25*(1.-xi(1)); 48 | dNdxi(2,1) = 0.25*(1.-xi(2)); 49 | dNdxi(2,2) = -0.25*(1.+xi(1)); 50 | dNdxi(3,1) = 0.25*(1.+xi(2)); 51 | dNdxi(3,2) = 0.25*(1.+xi(1)); 52 | dNdxi(4,1) = -0.25*(1.+xi(2)); 53 | dNdxi(4,2) = 0.25*(1.-xi(1)); 54 | elseif (nElemNode == 8) 55 | dNdxi(1,1) = 0.25*(1.-xi(2))*(2.*xi(1)+xi(2)); 56 | dNdxi(1,2) = 0.25*(1.-xi(1))*(xi(1)+2.*xi(2)); 57 | dNdxi(2,1) = 0.25*(1.-xi(2))*(2.*xi(1)-xi(2)); 58 | dNdxi(2,2) = 0.25*(1.+xi(1))*(2.*xi(2)-xi(1)); 59 | dNdxi(3,1) = 0.25*(1.+xi(2))*(2.*xi(1)+xi(2)); 60 | dNdxi(3,2) = 0.25*(1.+xi(1))*(2.*xi(2)+xi(1)); 61 | dNdxi(4,1) = 0.25*(1.+xi(2))*(2.*xi(1)-xi(2)); 62 | dNdxi(4,2) = 0.25*(1.-xi(1))*(2.*xi(2)-xi(1)); 63 | dNdxi(5,1) = -xi(1)*(1.-xi(2)); 64 | dNdxi(5,2) = -0.5*(1.-xi(1)*xi(1)); 65 | dNdxi(6,1) = 0.5*(1.-xi(2)*xi(2)); 66 | dNdxi(6,2) = -(1.+xi(1))*xi(2); 67 | dNdxi(7,1) = -xi(1)*(1.+xi(2)); 68 | dNdxi(7,2) = 0.5*(1.-xi(1)*xi(1)); 69 | dNdxi(8,1) = -0.5*(1.-xi(2)*xi(2)); 70 | dNdxi(8,2) = -(1.-xi(1))*xi(2); 71 | end 72 | % 73 | % 3D elements 74 | % 75 | elseif (nDim==3) 76 | 77 | if (nElemNode == 4) 78 | dNdxi(1,1) = 1.; 79 | dNdxi(2,2) = 1.; 80 | dNdxi(3,3) = 1.; 81 | dNdxi(4,1) = -1.; 82 | dNdxi(4,2) = -1.; 83 | dNdxi(4,3) = -1.; 84 | elseif (nElemNode == 10) 85 | xi4 = 1.-xi(1)-xi(2)-xi(3); 86 | dNdxi(1,1) = (4.*xi(1)-1.); 87 | dNdxi(2,2) = (4.*xi(2)-1.); 88 | dNdxi(3,3) = (4.*xi(3)-1.); 89 | dNdxi(4,1) = -(4.*xi4-1.); 90 | dNdxi(4,2) = -(4.*xi4-1.); 91 | dNdxi(4,3) = -(4.*xi4-1.); 92 | dNdxi(5,1) = 4.*xi(2); 93 | dNdxi(5,2) = 4.*xi(1); 94 | dNdxi(6,2) = 4.*xi(3); 95 | dNdxi(6,3) = 4.*xi(2); 96 | dNdxi(7,1) = 4.*xi(3); 97 | dNdxi(7,3) = 4.*xi(1); 98 | dNdxi(8,1) = 4.*(xi4-xi(1)); 99 | dNdxi(8,2) = -4.*xi(1); 100 | dNdxi(8,3) = -4.*xi(1); 101 | dNdxi(9,1) = -4.*xi(2); 102 | dNdxi(9,2) = 4.*(xi4-xi(2)); 103 | dNdxi(9,3) = -4.*xi(2); 104 | dNdxi(10,1) = -4.*xi(3)*xi4; 105 | dNdxi(10,2) = -4.*xi(3); 106 | dNdxi(10,3) = 4.*(xi4-xi(3)); 107 | elseif (nElemNode == 8) 108 | dNdxi(1,1) = -(1.-xi(2))*(1.-xi(3))/8.; 109 | dNdxi(1,2) = -(1.-xi(1))*(1.-xi(3))/8.; 110 | dNdxi(1,3) = -(1.-xi(1))*(1.-xi(2))/8.; 111 | dNdxi(2,1) = (1.-xi(2))*(1.-xi(3))/8.; 112 | dNdxi(2,2) = -(1.+xi(1))*(1.-xi(3))/8.; 113 | dNdxi(2,3) = -(1.+xi(1))*(1.-xi(2))/8.; 114 | dNdxi(3,1) = (1.+xi(2))*(1.-xi(3))/8.; 115 | dNdxi(3,2) = (1.+xi(1))*(1.-xi(3))/8.; 116 | dNdxi(3,3) = -(1.+xi(1))*(1.+xi(2))/8.; 117 | dNdxi(4,1) = -(1.+xi(2))*(1.-xi(3))/8.; 118 | dNdxi(4,2) = (1.-xi(1))*(1.-xi(3))/8.; 119 | dNdxi(4,3) = -(1.-xi(1))*(1.+xi(2))/8.; 120 | dNdxi(5,1) = -(1.-xi(2))*(1.+xi(3))/8.; 121 | dNdxi(5,2) = -(1.-xi(1))*(1.+xi(3))/8.; 122 | dNdxi(5,3) = (1.-xi(1))*(1.-xi(2))/8.; 123 | dNdxi(6,1) = (1.-xi(2))*(1.+xi(3))/8.; 124 | dNdxi(6,2) = -(1.+xi(1))*(1.+xi(3))/8.; 125 | dNdxi(6,3) = (1.+xi(1))*(1.-xi(2))/8.; 126 | dNdxi(7,1) = (1.+xi(2))*(1.+xi(3))/8.; 127 | dNdxi(7,2) = (1.+xi(1))*(1.+xi(3))/8.; 128 | dNdxi(7,3) = (1.+xi(1))*(1.+xi(2))/8.; 129 | dNdxi(8,1) = -(1.+xi(2))*(1.+xi(3))/8.; 130 | dNdxi(8,2) = (1.-xi(1))*(1.+xi(3))/8.; 131 | dNdxi(8,3) = (1.-xi(1))*(1.+xi(2))/8.; 132 | elseif (nElemNode == 20) 133 | dNdxi(1,1) = (-(1.-xi(2))*(1.-xi(3))*(-xi(1)-xi(2)-xi(3)-2.)-(1.-xi(1))*(1.-xi(2))*(1.-xi(3)))/8.; 134 | dNdxi(1,2) = (-(1.-xi(1))*(1.-xi(3))*(-xi(1)-xi(2)-xi(3)-2.)-(1.-xi(1))*(1.-xi(2))*(1.-xi(3)))/8.; 135 | dNdxi(1,3) = (-(1.-xi(1))*(1.-xi(2))*(-xi(1)-xi(2)-xi(3)-2.)-(1.-xi(1))*(1.-xi(2))*(1.-xi(3)))/8.; 136 | 137 | dNdxi(2,1) = ((1.-xi(2))*(1.-xi(3))*(xi(1)-xi(2)-xi(3)-2.)+(1.+xi(1))*(1.-xi(2))*(1.-xi(3)))/8.; 138 | dNdxi(2,2) = (-(1.+xi(1))*(1.-xi(3))*(xi(1)-xi(2)-xi(3)-2.)-(1.+xi(1))*(1.-xi(2))*(1.-xi(3)))/8.; 139 | dNdxi(2,3) = (-(1.+xi(1))*(1.-xi(2))*(xi(1)-xi(2)-xi(3)-2.)-(1.+xi(1))*(1.-xi(2))*(1.-xi(3)))/8.; 140 | 141 | dNdxi(3,1) = ((1.+xi(2))*(1.-xi(3))*(xi(1)+xi(2)-xi(3)-2.)+(1.+xi(1))*(1.+xi(2))*(1.-xi(3)))/8.; 142 | dNdxi(3,2) = ((1.+xi(1))*(1.-xi(3))*(xi(1)+xi(2)-xi(3)-2.)+(1.+xi(1))*(1.+xi(2))*(1.-xi(3)))/8.; 143 | dNdxi(3,3) = (-(1.+xi(1))*(1.+xi(2))*(xi(1)+xi(2)-xi(3)-2.)-(1.+xi(1))*(1.+xi(2))*(1.-xi(3)))/8.; 144 | 145 | dNdxi(4,1) = (-(1.+xi(2))*(1.-xi(3))*(-xi(1)+xi(2)-xi(3)-2.)-(1.-xi(1))*(1.+xi(2))*(1.-xi(3)))/8.; 146 | dNdxi(4,2) = ((1.-xi(1))*(1.-xi(3))*(-xi(1)+xi(2)-xi(3)-2.)+(1.-xi(1))*(1.+xi(2))*(1.-xi(3)))/8.; 147 | dNdxi(4,3) = (-(1.-xi(1))*(1.+xi(2))*(-xi(1)+xi(2)-xi(3)-2.)-(1.-xi(1))*(1.+xi(2))*(1.-xi(3)))/8.; 148 | dNdxi(5,1) = (-(1.-xi(2))*(1.+xi(3))*(-xi(1)-xi(2)+xi(3)-2.)-(1.-xi(1))*(1.-xi(2))*(1.+xi(3)))/8.; 149 | dNdxi(5,2) = (-(1.-xi(1))*(1.+xi(3))*(-xi(1)-xi(2)+xi(3)-2.)-(1.-xi(1))*(1.-xi(2))*(1.+xi(3)))/8.; 150 | dNdxi(5,3) = ((1.-xi(1))*(1.-xi(2))*(-xi(1)-xi(2)+xi(3)-2.)+(1.-xi(1))*(1.-xi(2))*(1.+xi(3)))/8.; 151 | dNdxi(6,1) = ((1.-xi(2))*(1.+xi(3))*(xi(1)-xi(2)+xi(3)-2.)+(1.+xi(1))*(1.-xi(2))*(1.+xi(3)))/8.; 152 | dNdxi(6,2) = (-(1.+xi(1))*(1.+xi(3))*(xi(1)-xi(2)+xi(3)-2.)-(1.+xi(1))*(1.-xi(2))*(1.+xi(3)))/8.; 153 | dNdxi(6,3) = ((1.+xi(1))*(1.-xi(2))*(xi(1)-xi(2)+xi(3)-2.)+(1.+xi(1))*(1.-xi(2))*(1.+xi(3)))/8.; 154 | dNdxi(7,1) = ((1.+xi(2))*(1.+xi(3))*(xi(1)+xi(2)+xi(3)-2.)+(1.+xi(1))*(1.+xi(2))*(1.+xi(3)))/8.; 155 | dNdxi(7,2) = ((1.+xi(1))*(1.+xi(3))*(xi(1)+xi(2)+xi(3)-2.)+(1.+xi(1))*(1.+xi(2))*(1.+xi(3)))/8.; 156 | dNdxi(7,3) = ((1.+xi(1))*(1.+xi(2))*(xi(1)+xi(2)+xi(3)-2.)+(1.+xi(1))*(1.+xi(2))*(1.+xi(3)))/8.; 157 | dNdxi(8,1) = (-(1.+xi(2))*(1.+xi(3))*(-xi(1)+xi(2)+xi(3)-2.)-(1.-xi(1))*(1.+xi(2))*(1.+xi(3)))/8.; 158 | dNdxi(8,2) = ((1.-xi(1))*(1.+xi(3))*(-xi(1)+xi(2)+xi(3)-2.)+(1.-xi(1))*(1.+xi(2))*(1.+xi(3)))/8.; 159 | dNdxi(8,3) = ((1.-xi(1))*(1.+xi(2))*(-xi(1)+xi(2)+xi(3)-2.)+(1.-xi(1))*(1.+xi(2))*(1.+xi(3)))/8.; 160 | dNdxi(9,1) = -2.*xi(1)*(1.-xi(2))*(1.-xi(3))/4.; 161 | dNdxi(9,2) = -(1.-xi(1)^2)*(1.-xi(3))/4.; 162 | dNdxi(9,3) = -(1.-xi(1)^2)*(1.-xi(2))/4.; 163 | dNdxi(10,1) = (1.-xi(2)^2)*(1.-xi(3))/4.; 164 | dNdxi(10,2) = -2.*xi(2)*(1.+xi(1))*(1.-xi(3))/4.; 165 | dNdxi(10,3) = -(1.-xi(2)^2)*(1.+xi(1))/4.; 166 | dNdxi(11,1) = -2.*xi(1)*(1.+xi(2))*(1.-xi(3))/4.; 167 | dNdxi(11,2) = (1.-xi(1)^2)*(1.-xi(3))/4.; 168 | dNdxi(11,3) = -(1.-xi(1)^2)*(1.+xi(2))/4.; 169 | dNdxi(12,1) = -(1.-xi(2)^2)*(1.-xi(3))/4.; 170 | dNdxi(12,2) = -2.*xi(2)*(1.-xi(1))*(1.-xi(3))/4.; 171 | dNdxi(12,3) = -(1.-xi(2)^2)*(1.-xi(1))/4.; 172 | dNdxi(13,1) = -2.*xi(1)*(1.-xi(2))*(1.+xi(3))/4.; 173 | dNdxi(13,2) = -(1.-xi(1)^2)*(1.+xi(3))/4.; 174 | dNdxi(13,3) = (1.-xi(1)^2)*(1.-xi(2))/4.; 175 | dNdxi(14,1) = (1.-xi(2)^2)*(1.+xi(3))/4.; 176 | dNdxi(14,2) = -2.*xi(2)*(1.+xi(1))*(1.+xi(3))/4.; 177 | dNdxi(14,3) = (1.-xi(2)^2)*(1.+xi(1))/4.; 178 | dNdxi(15,1) = -2.*xi(1)*(1.+xi(2))*(1.+xi(3))/4.; 179 | dNdxi(15,2) = (1.-xi(1)^2)*(1.+xi(3))/4.; 180 | dNdxi(15,3) = (1.-xi(1)^2)*(1.+xi(2))/4.; 181 | dNdxi(16,1) = -(1.-xi(2)^2)*(1.+xi(3))/4.; 182 | dNdxi(16,2) = -2.*xi(2)*(1.-xi(1))*(1.+xi(3))/4.; 183 | dNdxi(16,3) = (1.-xi(2)^2)*(1.-xi(1))/4.; 184 | dNdxi(17,1) = -(1.-xi(2))*(1.-xi(3)^2)/4.; 185 | dNdxi(17,2) = -(1.-xi(1))*(1.-xi(3)^2)/4.; 186 | dNdxi(17,3) = -xi(3)*(1.-xi(1))*(1.-xi(2))/2.; 187 | dNdxi(18,1) = (1.-xi(2))*(1.-xi(3)^2)/4.; 188 | dNdxi(18,2) = -(1.+xi(1))*(1.-xi(3)^2)/4.; 189 | dNdxi(18,3) = -xi(3)*(1.+xi(1))*(1.-xi(2))/2.; 190 | dNdxi(19,1) = (1.+xi(2))*(1.-xi(3)^2)/4.; 191 | dNdxi(19,2) = (1.+xi(1))*(1.-xi(3)^2)/4.; 192 | dNdxi(19,3) = -xi(3)*(1.+xi(1))*(1.+xi(2))/2.; 193 | dNdxi(20,1) = -(1.+xi(2))*(1.-xi(3)^2)/4.; 194 | dNdxi(20,2) = (1.-xi(1))*(1.-xi(3)^2)/4.; 195 | dNdxi(20,3) = -xi(3)*(1.-xi(1))*(1.+xi(2))/2.; 196 | end 197 | end 198 | 199 | end 200 | -------------------------------------------------------------------------------- /Source Code/PlaneTruss/lib/shapefunctions.m: -------------------------------------------------------------------------------- 1 | % 2 | %================= SHAPE FUNCTIONS ================================== 3 | % 4 | % Calculates shape functions for various element types 5 | % 6 | function N = shapefunctions(nDim,nElemNode,xi) 7 | 8 | 9 | N = zeros(nElemNode,1); 10 | % 11 | % 1D elements 12 | % 13 | if (nDim == 1) 14 | if (nElemNode==2) 15 | N(1) = 0.5*(1.+xi(1)); 16 | N(2) = 0.5*(1.-xi(1)); 17 | elseif (nElemNode == 3) 18 | N(1) = -0.5*xi(1)*(1.-xi(1)); 19 | N(2) = 0.5*xi(1)*(1.+xi(1)); 20 | N(3) = (1.-xi(1))*(1.+xi(1)); 21 | end 22 | % 23 | % 2D elements 24 | % 25 | elseif (nDim == 2) 26 | % 27 | % Triangular element 28 | % 29 | if ( nElemNode == 3 ) 30 | N(1) = xi(1); 31 | N(2) = xi(2); 32 | N(3) = 1.-xi(1)-xi(2); 33 | elseif ( nElemNode == 6 ) 34 | xi3 = 1.-xi(1)-xi(2); 35 | N(1) = (2.*xi(1)-1.)*xi(1); 36 | N(2) = (2.*xi(2)-1.)*xi(2); 37 | N(3) = (2.*xi3-1.)*xi3; 38 | N(4) = 4.*xi(1)*xi(2); 39 | N(5) = 4.*xi(2)*xi3; 40 | N(6) = 4.*xi3*xi(1); 41 | % 42 | % Rectangular element 43 | % 44 | elseif ( nElemNode == 4 ) 45 | N(1) = 0.25*(1.-xi(1))*(1.-xi(2)); 46 | N(2) = 0.25*(1.+xi(1))*(1.-xi(2)); 47 | N(3) = 0.25*(1.+xi(1))*(1.+xi(2)); 48 | N(4) = 0.25*(1.-xi(1))*(1.+xi(2)); 49 | elseif (nElemNode == 8) 50 | N(1) = -0.25*(1.-xi(1))*(1.-xi(2))*(1.+xi(1)+xi(2)); 51 | N(2) = 0.25*(1.+xi(1))*(1.-xi(2))*(xi(1)-xi(2)-1.); 52 | N(3) = 0.25*(1.+xi(1))*(1.+xi(2))*(xi(1)+xi(2)-1.); 53 | N(4) = 0.25*(1.-xi(1))*(1.+xi(2))*(xi(2)-xi(1)-1.); 54 | N(5) = 0.5*(1.-xi(1)*xi(1))*(1.-xi(2)); 55 | N(6) = 0.5*(1.+xi(1))*(1.-xi(2)*xi(2)); 56 | N(7) = 0.5*(1.-xi(1)*xi(1))*(1.+xi(2)); 57 | N(8) = 0.5*(1.-xi(1))*(1.-xi(2)*xi(2)); 58 | end 59 | % 60 | elseif (nDim==3) 61 | 62 | if (nElemNode == 4) 63 | N(1) = xi(1); 64 | N(2) = xi(2); 65 | N(3) = xi(3); 66 | N(4) = 1.-xi(1)-xi(2)-xi(3); 67 | elseif (nElemNode == 10) 68 | xi4 = 1.-xi(1)-xi(2)-xi(3); 69 | N(1) = (2.*xi(1)-1.)*xi(1); 70 | N(2) = (2.*xi(2)-1.)*xi(2); 71 | N(3) = (2.*xi(3)-1.)*xi(3); 72 | N(4) = (2.*xi4-1.)*xi4; 73 | N(5) = 4.*xi(1)*xi(2); 74 | N(6) = 4.*xi(2)*xi(3); 75 | N(7) = 4.*xi(3)*xi(1); 76 | N(8) = 4.*xi(1)*xi4; 77 | N(9) = 4.*xi(2)*xi4; 78 | N(10) = 4.*xi(3)*xi4; 79 | elseif (nElemNode == 8) 80 | N(1) = (1.-xi(1))*(1.-xi(2))*(1.-xi(3))/8.; 81 | N(2) = (1.+xi(1))*(1.-xi(2))*(1.-xi(3))/8.; 82 | N(3) = (1.+xi(1))*(1.+xi(2))*(1.-xi(3))/8.; 83 | N(4) = (1.-xi(1))*(1.+xi(2))*(1.-xi(3))/8.; 84 | N(5) = (1.-xi(1))*(1.-xi(2))*(1.+xi(3))/8.; 85 | N(6) = (1.+xi(1))*(1.-xi(2))*(1.+xi(3))/8.; 86 | N(7) = (1.+xi(1))*(1.+xi(2))*(1.+xi(3))/8.; 87 | N(8) = (1.-xi(1))*(1.+xi(2))*(1.+xi(3))/8.; 88 | elseif (nElemNode == 20) 89 | N(1) = (1.-xi(1))*(1.-xi(2))*(1.-xi(3))*(-xi(1)-xi(2)-xi(3)-2.)/8.; 90 | N(2) = (1.+xi(1))*(1.-xi(2))*(1.-xi(3))*(xi(1)-xi(2)-xi(3)-2.)/8.; 91 | N(3) = (1.+xi(1))*(1.+xi(2))*(1.-xi(3))*(xi(1)+xi(2)-xi(3)-2.)/8.; 92 | N(4) = (1.-xi(1))*(1.+xi(2))*(1.-xi(3))*(-xi(1)+xi(2)-xi(3)-2.)/8.; 93 | N(5) = (1.-xi(1))*(1.-xi(2))*(1.+xi(3))*(-xi(1)-xi(2)+xi(3)-2.)/8.; 94 | N(6) = (1.+xi(1))*(1.-xi(2))*(1.+xi(3))*(xi(1)-xi(2)+xi(3)-2.)/8.; 95 | N(7) = (1.+xi(1))*(1.+xi(2))*(1.+xi(3))*(xi(1)+xi(2)+xi(3)-2.)/8.; 96 | N(8) = (1.-xi(1))*(1.+xi(2))*(1.+xi(3))*(-xi(1)+xi(2)+xi(3)-2.)/8.; 97 | N(9) = (1.-xi(1)^2)*(1.-xi(2))*(1.-xi(3))/4.; 98 | N(10) = (1.+xi(1))*(1.-xi(2)^2)*(1.-xi(3))/4.; 99 | N(11) = (1.-xi(1)^2)*(1.+xi(2))*(1.-xi(3))/4.; 100 | N(12) = (1.-xi(1))*(1.-xi(2)^2)*(1.-xi(3))/4.; 101 | N(13) = (1.-xi(1)^2)*(1.-xi(2))*(1.+xi(3))/4.; 102 | N(14) = (1.+xi(1))*(1.-xi(2)^2)*(1.+xi(3))/4.; 103 | N(15) = (1.-xi(1)^2)*(1.+xi(2))*(1.+xi(3))/4.; 104 | N(16) = (1.-xi(1))*(1.-xi(2)^2)*(1.+xi(3))/4.; 105 | N(17) = (1.-xi(1))*(1.-xi(2))*(1.-xi(3)^2)/4.; 106 | N(18) = (1.+xi(1))*(1.-xi(2))*(1.-xi(3)^2)/4.; 107 | N(19) = (1.+xi(1))*(1.+xi(2))*(1.-xi(3)^2)/4.; 108 | N(20) = (1.-xi(1))*(1.+xi(2))*(1.-xi(3)^2)/4.; 109 | end 110 | end 111 | 112 | end 113 | -------------------------------------------------------------------------------- /Source Code/PlaneTruss/lib/trussAnalysisExplicit.m: -------------------------------------------------------------------------------- 1 | function Solution = trussAnalysisExplicit(Model) 2 | % PURPOSE: Analysing trusses with explicit stiffness matrices 3 | % 4 | % INPUT(S): 5 | % - Model: a structure including the model data 6 | % 7 | % OUTPUT(S): 8 | % - Solution: a structure including the solution of the analysis 9 | 10 | % storing information in Solution structs 11 | time = clock; 12 | Solution.info = sprintf(['Solution obtained on %s %d:%d:%d',... 13 | '\nExplicit Stiffness Matrices' ],... 14 | date,time(4),time(5),floor(time(6))); 15 | % Pre-processing 16 | %-------------------------------------------------------------------------- 17 | % I N P U T D A T A 18 | %-------------------------------------------------------------------------- 19 | 20 | % control variables 21 | 22 | nNode = Model.nNode; 23 | nElem = Model.nElem; 24 | nDof = Model.nDof; 25 | 26 | %nodal coordinates 27 | coordinates = Model.geometry.coordinates; 28 | 29 | % nodal forces 30 | F = zeros(size(coordinates)); 31 | for i = 1 : Model.nNodalForce 32 | node = Model.loading.nodalForces(i,1); 33 | F(node, 1:Model.nDim) = Model.loading.nodalForces(i,2:end); 34 | end 35 | 36 | % reshape to vector form 37 | Feq=reshape(F',1,nDof*nNode)'; 38 | 39 | % elements connectivity 40 | elements = Model.geometry.elements; 41 | 42 | % section/materaial properties 43 | A = zeros(1, Model.nElem); 44 | E = zeros(1, Model.nElem); 45 | for i = 1 : Model.nElem 46 | E(i) = Model.sections(Model.elemSectId(i), 1); 47 | A(i) = Model.sections(Model.elemSectId(i), 2); 48 | end 49 | 50 | % boundary condition 51 | boundary = Model.boundary'; 52 | 53 | 54 | %-------------------------------------------------------------------------- 55 | % P R O C E S S I N G 56 | %-------------------------------------------------------------------------- 57 | % initializing the loop variables 58 | K = zeros(nDof*nNode); 59 | k(:,:,nElem) = zeros(2 * nDof); 60 | L = zeros(1,nElem); 61 | 62 | % loop over elements 63 | for i = 1 : nElem 64 | a = coordinates(elements(i,1),1:2); % start node coordinates 65 | b = coordinates(elements(i,2),1:2); % end node coordinates 66 | 67 | % calculating length 68 | L(i) = sqrt((a(1)-b(1)).^2 + (a(2)-b(2)).^2); 69 | 70 | % sin and cos 71 | c = (b(1) - a(1))/L(i); % cos(t) = (x2 - x1)/L 72 | s = (b(2) - a(2))/L(i); % sin(t) = (y2 - y1)/L 73 | 74 | % TODO: this only works for 2D 75 | lambda = [c*c c*s; c*s s*s]; 76 | T = [lambda -lambda; -lambda lambda]; 77 | 78 | k(:,:,i) = E(i)*A(i)/L(i) * T; 79 | 80 | % TODO : this only works for 2D 81 | T_sigma(:,:,i) = [c s 0 0; 0 0 c s]; 82 | 83 | % node i --------> dof ndof*i - ndof + 1 : ndof*i 84 | % e.g. node 1 --> dof 1 : 2 85 | % node 3 --> dof 5 : 6 86 | inode = elements(i,1); 87 | jnode = elements(i,2); 88 | 89 | index = [nDof*(inode-1)+1:nDof*inode,nDof*(jnode-1)+1:nDof*jnode]; 90 | K(index,index) = K(index,index) + k(:,:,i); 91 | end 92 | Solution.data.elementStiff = k; 93 | Solution.data.globalStiff = K; 94 | Solution.data.globalForce = Feq; 95 | 96 | % imposing displacement boundary conditions 97 | debc = double(nDof) .* (boundary(1,:) - 1) + boundary(2,:); 98 | ebcVals = boundary(3,:)'; 99 | [dofs, rf] = solution(K, Feq, debc, ebcVals); 100 | Solution.nodalDisplacements = reshape(dofs,Model.nDim,Model.nNode)'; 101 | 102 | Solution.reactionForces = zeros(Model.nNode, Model.nDim); 103 | for i = 1 : size(boundary,2) 104 | node = boundary(1,i); 105 | dof = boundary(2,i); 106 | Solution.reactionForces(node,dof) = rf(i); 107 | end 108 | 109 | %-------------------------------------------------------------------------- 110 | % P O S T - P R O C E S S I N G 111 | %-------------------------------------------------------------------------- 112 | % calculating element stresses 113 | 114 | Solution.elementStresses.sigma11 = zeros(nElem,1); 115 | Solution.internalForces.axial = zeros(nElem,1); 116 | 117 | for i = 1 : nElem 118 | 119 | inode = elements(i,1); 120 | jnode = elements(i,2); 121 | 122 | index = [nDof*(inode-1)+1:nDof*inode,nDof*(jnode-1)+1:nDof*jnode]; 123 | 124 | sigma = E(i) * [-1/L(i), 1/L(i)] * T_sigma(:,:,i) * dofs(index); 125 | 126 | Solution.elementStresses.sigma11(i) = sigma; 127 | Solution.internalForces.axial(i,1) = sigma * A(i); 128 | end 129 | 130 | %-------------------------------------------------------------------------- 131 | % this part will be moved in the future 132 | if isfield(Model,'analysis') 133 | if Model.analysis.showResults 134 | printResult(Solution,1) 135 | end 136 | if Model.analysis.showDetails 137 | % print stiffness matrices 138 | printStiff(Solution,1) 139 | end 140 | if Model.analysis.saveToFile 141 | outFile = fopen(Model.analysis.outputFileName, 'w'); 142 | printSummary(Model,outFile); 143 | printResult(Solution,outFile); 144 | 145 | fclose(outFile); 146 | end 147 | end 148 | %-------------------------------------------------------------------------- 149 | end 150 | 151 | function [d, rf] = solution(K, R, debc, ebcVals) 152 | dof = length(R); 153 | df = setdiff(1:dof, debc); 154 | Kf = K(df, df); 155 | Rf = R(df) - K(df, debc)*ebcVals; 156 | dfVals = Kf\Rf; 157 | d = zeros(dof,1); 158 | d(debc) = ebcVals; 159 | d(df) = dfVals; 160 | rf = K(debc,:)*d - R(debc); 161 | end -------------------------------------------------------------------------------- /Source Code/PlaneTruss/lib/trussAnalysisNumerical.m: -------------------------------------------------------------------------------- 1 | function Solution = trussAnalysisNumerical(Model) 2 | % PURPOSE: Analysing trusses with numerical integration stiffness matrices 3 | % 4 | % INPUT(S): 5 | % - Model: a structure including the model data 6 | % 7 | % OUTPUT(S): 8 | % - Solution: a structure including the solution of the analysis 9 | 10 | % DEVELOPMENT HISTORY: 11 | % [2018, Oct, 23] Shahrokh Shahi -- development (function mode) 12 | % [2018, Nov, 13] Shahrokh Shahi -- Handlig traction (distributed axial) 13 | 14 | time = clock; 15 | Solution.info = sprintf(['Solution obtained on %s %d:%d:%d',... 16 | '\nNumerical Integration Stiffness Matrices' ],... 17 | date,time(4),time(5),floor(time(6))); 18 | % Pre-processing 19 | %-------------------------------------------------------------------------- 20 | % I N P U T D A T A 21 | %-------------------------------------------------------------------------- 22 | 23 | % control variables 24 | 25 | nNode = Model.nNode; 26 | nElem = Model.nElem; 27 | nDof = Model.nDof; 28 | nElemNode = Model.nElemNode; 29 | nDim = Model.nDim; 30 | 31 | %nodal coordinates 32 | coordinates = Model.geometry.coordinates; 33 | 34 | % nodal forces 35 | F = zeros(size(coordinates)); 36 | for i = 1 : Model.nNodalForce 37 | node = Model.loading.nodalForces(i,1); 38 | F(node, 1:Model.nDim) = Model.loading.nodalForces(i,2:end); 39 | end 40 | 41 | % reshape to vector form 42 | Feq=reshape(F',1,nDof*nNode)'; 43 | 44 | % elements connectivity 45 | elements = Model.geometry.elements; 46 | 47 | % section/materaial properties 48 | A = zeros(1, Model.nElem); 49 | E = zeros(1, Model.nElem); 50 | for i = 1 : Model.nElem 51 | E(i) = Model.sections(Model.elemSectId(i), 1); 52 | A(i) = Model.sections(Model.elemSectId(i), 2); 53 | end 54 | 55 | % boundary condition 56 | boundary = Model.boundary'; 57 | 58 | 59 | %-------------------------------------------------------------------------- 60 | % P R O C E S S I N G 61 | %-------------------------------------------------------------------------- 62 | % initializing the loop variables 63 | K = zeros(nDof*nNode); 64 | k(:,:,nElem) = zeros(2 * nDof); 65 | L = zeros(1,nElem); 66 | 67 | % loop over elements 68 | for i = 1 : nElem 69 | 70 | a = coordinates(elements(i,1),1:2); % start node coordinates 71 | b = coordinates(elements(i,2),1:2); % end node coordinates 72 | 73 | % calculating length 74 | L(i) = sqrt((a(1)-b(1)).^2 + (a(2)-b(2)).^2); 75 | 76 | % sin and cos 77 | c = (b(1) - a(1))/L(i); % cos(t) = (x2 - x1)/L 78 | s = (b(2) - a(2))/L(i); % sin(t) = (y2 - y1)/L 79 | 80 | % TODO: this only works for 2D 81 | T = [[c s; -s c] zeros(2) ; 82 | zeros(2) [c s; -s c]]; 83 | T_sigma(:,:,i) = [c s 0 0; 0 0 c s]; 84 | T_rot (:,:,i) = T; 85 | 86 | k(:,:,i) = T' * elstif(nDof,[a;b]',E(i),A(i)) * T; 87 | 88 | % node i --------> dof ndof*i - ndof + 1 : ndof*i 89 | % e.g. node 1 --> dof 1 : 2 90 | % node 3 --> dof 5 : 6 91 | inode = elements(i,1); 92 | jnode = elements(i,2); 93 | 94 | index = [nDof*(inode-1)+1:nDof*inode,nDof*(jnode-1)+1:nDof*jnode]; 95 | K(index,index) = K(index,index) + k(:,:,i); 96 | end 97 | Solution.data.elementStiff = k; 98 | Solution.data.globalStiff = K; 99 | 100 | % handling distributed axial force 101 | F_dist = zeros(size(coordinates)); 102 | if Model.nTractionForce > 0 103 | NPOINTS = 3; 104 | traction = Model.loading.tractionForces; 105 | 106 | for iLoad = 1 : length(traction) 107 | element = traction(iLoad).element; 108 | face = traction(iLoad).face; 109 | loadEq = traction(iLoad).eq; 110 | 111 | nodeIdList = facenodes(nDim,nElemNode,face); 112 | nElemReduc = length(nodeIdList); 113 | 114 | elemId = Model.geometry.elements(element,nodeIdList); 115 | faceCoord = Model.geometry.coordinates(elemId,:)'; 116 | L = norm(diff(faceCoord')); 117 | 118 | [xiList, wList] = intQuad(NPOINTS); 119 | fel = zeros(nElemNode*nDof , 1); 120 | for intpt = 1 : length(xiList) 121 | xi = xiList(:,intpt)'; 122 | w = wList (intpt) ; 123 | 124 | % shape functions and derivatives at local integration points 125 | N = shapefunctions (nDim-1,nElemReduc,xi); 126 | dNdxi = shapefunctionderivs(nDim-1,nElemReduc,xi); 127 | 128 | % Jacobian matrix 129 | J = faceCoord * dNdxi; 130 | 131 | % inverse and determinent of the Jacobian matrix 132 | if size(J) == [2,1] 133 | detJ = norm(J); 134 | else 135 | detJ = abs(det(J)); 136 | end 137 | detJ; % detJ=L/2 138 | 139 | load = zeros(length(loadEq),1); 140 | 141 | % coordinate transform to calculate loads at integration point 142 | x = (1+xi)/2 * L; 143 | for i = 1 : length(load) 144 | load(i,1) = loadEq{i}(x); 145 | end 146 | load; 147 | 148 | fel = fel + ... 149 | [N(1) * eye(2); ... 150 | N(2) * eye(2)] * load * detJ * w ; 151 | end 152 | fel_global = T_rot(:,:,element)' * fel; 153 | fel_global = reshape(fel_global,nDof,length(nodeIdList))'; 154 | F_dist(elemId,:) = F_dist(elemId,:) + fel_global; 155 | end 156 | end 157 | Feq_dist = reshape(F_dist',1,nDof*nNode)'; 158 | Feq = Feq + Feq_dist; 159 | Solution.data.globalForce = Feq; 160 | 161 | % imposing displacement boundary conditions 162 | debc = double(nDof) .* (boundary(1,:) - 1) + boundary(2,:); 163 | ebcVals = boundary(3,:)'; 164 | [dofs, rf] = solution(K, Feq, debc, ebcVals); 165 | Solution.nodalDisplacements = reshape(dofs,Model.nDim,Model.nNode)'; 166 | 167 | Solution.reactionForces = zeros(Model.nNode, Model.nDim); 168 | for i = 1 : size(boundary,2) 169 | node = boundary(1,i); 170 | dof = boundary(2,i); 171 | Solution.reactionForces(node,dof) = rf(i); 172 | end 173 | 174 | %-------------------------------------------------------------------------- 175 | % P O S T - P R O C E S S I N G 176 | %-------------------------------------------------------------------------- 177 | % calculating element stresses 178 | 179 | Solution.elementStresses.sigma11 = zeros(nElem,1); 180 | Solution.internalForces.axial = zeros(nElem,1); 181 | 182 | for i = 1 : nElem 183 | 184 | inode = elements(i,1); 185 | jnode = elements(i,2); 186 | 187 | index = [nDof*(inode-1)+1:nDof*inode,nDof*(jnode-1)+1:nDof*jnode]; 188 | 189 | sigma = E(i) * [-1/L(i), 1/L(i)] * T_sigma(:,:,i) * dofs(index); 190 | 191 | Solution.elementStresses.sigma11(i) = sigma; 192 | Solution.internalForces.axial(i,1) = sigma * A(i); 193 | end 194 | %-------------------------------------------------------------------------- 195 | % this part will be moved in the future 196 | if isfield(Model,'analysis') 197 | if Model.analysis.showResults 198 | printResult(Solution,1) 199 | end 200 | if Model.analysis.showDetails 201 | % print stiffness matrices 202 | printStiff(Solution,1) 203 | end 204 | if Model.analysis.saveToFile 205 | outFile = fopen(Model.analysis.outputFileName, 'w'); 206 | printSummary(Model,outFile); 207 | printResult(Solution,outFile); 208 | fclose(outFile); 209 | end 210 | end 211 | %-------------------------------------------------------------------------- 212 | end 213 | 214 | %-------------------------------------------------------------------------- 215 | function [d, rf] = solution(K, R, debc, ebcVals) 216 | dof = length(R); 217 | df = setdiff(1:dof, debc); 218 | Kf = K(df, df); 219 | Rf = R(df) - K(df, debc)*ebcVals; 220 | dfVals = Kf\Rf; 221 | d = zeros(dof,1); 222 | d(debc) = ebcVals; 223 | d(df) = dfVals; 224 | rf = K(debc,:)*d - R(debc); 225 | end 226 | 227 | %-------------------------------------------------------------------------- 228 | function k = elstif(nDof,coordinates,E,A) 229 | 230 | xiList = [-0.5773502692, 0.5773502692]; 231 | wList = [1.0 , 1.0 ]; 232 | nElemNode = 2; %hard-coded for trusses 233 | nDim = size(coordinates,1); 234 | 235 | dCoord = diff(coordinates'); 236 | L = norm(dCoord); 237 | coordinates = [0 L]; % in 1D view 238 | 239 | k2 = zeros(nDof); 240 | 241 | for intpt = 1 : length(xiList) 242 | 243 | xi = xiList(intpt); % local corrdinate 244 | w = wList (intpt); 245 | % shape functions and derivatives at local integration points 246 | N = shapefunctions (nDim-1,nElemNode,xi); 247 | dNdxi = shapefunctionderivs(nDim-1,nElemNode,xi); 248 | 249 | % Jacobian matrix 250 | J = coordinates * dNdxi; 251 | 252 | % inverse and determinent of the Jacobian matrix 253 | invJ = inv(J); 254 | detJ = abs(det(J)); 255 | 256 | % derivatives of the shape functions in the global coordinate 257 | dNdx = dNdxi * invJ; 258 | 259 | % B matrix 260 | B = dNdx'; 261 | 262 | % numerical summation 263 | k2 = k2 + B'*E*B * detJ * A * w; 264 | 265 | end 266 | k = zeros(nElemNode * nDof); 267 | k([1,3],[1,3]) = k2; 268 | end 269 | 270 | %-------------------------------------------------------------------------- 271 | % Gauss-Quadrature Numerical Integration Points 272 | function [xi, w] = intQuad(npoints) 273 | % xi: integration points (xi) 274 | % w : associated weights 275 | switch npoints 276 | case 1 277 | xi = 0.0; 278 | w = 2.0; 279 | case 2 280 | xi = [-1/sqrt(3), 1/sqrt(3)]; 281 | w = [1.0 ,1.0]; 282 | case 3 283 | xi = [-sqrt(3/5), 0.0, sqrt(3/5)]; 284 | w = [5/9, 8/9, 5/9]; 285 | case 4 286 | xi1= sqrt(3/7 - (2/7)*sqrt(6/5)); 287 | xi2= sqrt(3/7 + (2/7)*sqrt(6/5)); 288 | xi = [-xi2, -xi1, xi1, xi2]; 289 | w1 = (18 + sqrt(30)) / 36; 290 | w2 = (18 - sqrt(30)) / 36; 291 | w = [w2, w1, w1, w2]; 292 | case 5 293 | xi1 = (1/3)*sqrt(5-2*sqrt(10/7)); 294 | xi2 = (1/3)*sqrt(5+2*sqrt(10/7)); 295 | xi = [-xi2, -xi1, 0, xi1, xi2]; 296 | w1 = (322 + 13*sqrt(70))/900; 297 | w2 = (322 - 13*sqrt(70))/900; 298 | w = [w2, w1, 128/225, w1, w2]; 299 | end 300 | end 301 | %-------------------------------------------------------------------------- -------------------------------------------------------------------------------- /Source Code/PlaneTruss/lib_io/inpFileReader.p: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/shahrokhx/FEM_Toolbox/8dda726b82d707d2e3404996893c95b8e2de3ef9/Source Code/PlaneTruss/lib_io/inpFileReader.p -------------------------------------------------------------------------------- /Source Code/PlaneTruss/lib_io/plotModel.p: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/shahrokhx/FEM_Toolbox/8dda726b82d707d2e3404996893c95b8e2de3ef9/Source Code/PlaneTruss/lib_io/plotModel.p -------------------------------------------------------------------------------- /Source Code/PlaneTruss/lib_io/printResult.m: -------------------------------------------------------------------------------- 1 | function printResult(Solution,fid) 2 | 3 | if nargin < 2 4 | fid = 1; 5 | end 6 | 7 | BULLET_CHAR = char(15); 8 | 9 | fprintf(fid,'\n\n'); 10 | printDLine(fid) 11 | printCTitle(fid,'O U T P U T S U M M A R Y') 12 | printDLine(fid) 13 | 14 | if isfield(Solution,'info') 15 | fprintf(fid,'%c About: \n',BULLET_CHAR); 16 | fprintf(fid,'%s\n', Solution.info); 17 | end 18 | printLine(fid) 19 | 20 | 21 | if isfield(Solution, 'nodalDisplacements') 22 | u = Solution.nodalDisplacements; 23 | [nNode,nDof] = size(u); 24 | printCTitle(fid,'Nodal Displacements'); 25 | printSLine(fid); 26 | for i = 1 : nNode 27 | formatStr = repmat('%10.5f\t',1,nDof); 28 | fprintf(fid,['[%3d] ',formatStr,'\n'],i,u(i,:)); 29 | end 30 | end 31 | printLine(fid) 32 | if isfield(Solution, 'reactionForces') 33 | rf = Solution.reactionForces; 34 | [nNode,nDof] = size(rf); 35 | printCTitle(fid,'Reaction Forces'); 36 | printSLine(fid); 37 | for i = 1 : nNode 38 | formatStr = repmat('%10.5f\t',1,nDof); 39 | fprintf(fid,['[%3d] ',formatStr,'\n'],i,rf(i,:)); 40 | end 41 | end 42 | printLine(fid) 43 | if isfield(Solution, 'elementStresses') 44 | stress = Solution.elementStresses.sigma11; 45 | [nElem,nComponenet] = size(stress); 46 | printCTitle(fid,'Stresses'); 47 | printSLine(fid); 48 | for i = 1 : nElem 49 | formatStr = repmat('%10.5f\t',1,nComponenet); 50 | fprintf(fid,['[%3d] ',formatStr,'\n'],i,stress(i,:)); 51 | end 52 | end 53 | printLine(fid) 54 | if isfield(Solution, 'internalForces') 55 | internalForces = Solution.internalForces.axial; 56 | [nElem,nComponenet] = size(internalForces); 57 | printCTitle(fid,'Internal Forces (Axial)'); 58 | printSLine(fid); 59 | for i = 1 : nElem 60 | formatStr = repmat('%10.5f\t',1,nComponenet); 61 | fprintf(fid,['[%3d] ',formatStr,'\n'],i,internalForces(i,:)); 62 | end 63 | end 64 | printDLine(fid); 65 | end 66 | 67 | %-------------------------------------------------------------------------- 68 | % Helper Functions 69 | function printLine(fid,n) 70 | if nargin < 2 71 | n = 80; 72 | end 73 | if nargin < 1 74 | fid = 1; 75 | end 76 | fprintf(fid,'%s\n',repmat('_',1,n)); 77 | end 78 | 79 | %-------------------------------------------------------------------------- 80 | function printDLine(fid,n) 81 | if nargin < 2 82 | n = 80; 83 | end 84 | if nargin < 1 85 | fid = 1; 86 | end 87 | fprintf(fid,'%s\n',repmat('=',1,n)); 88 | end 89 | 90 | %-------------------------------------------------------------------------- 91 | function printSLine(fid,n) 92 | if nargin < 2 93 | n = 80; 94 | end 95 | if nargin < 1 96 | fid = 1; 97 | end 98 | fprintf(fid,'%s\n',repmat('-',1,n)); 99 | end 100 | 101 | %-------------------------------------------------------------------------- 102 | % printing centered text title 103 | function printCTitle(fid,text,n) 104 | if nargin < 3 105 | n = 80; 106 | end 107 | if nargin < 2 108 | text =''; 109 | end 110 | if nargin < 1 111 | fid = 1; 112 | end 113 | tLen = length(text); 114 | space = floor((n-tLen)/2); 115 | fprintf(fid,'%s\n',[repmat(' ',1,space),text]); 116 | end 117 | %-------------------------------------------------------------------------- -------------------------------------------------------------------------------- /Source Code/PlaneTruss/lib_io/printStiff.m: -------------------------------------------------------------------------------- 1 | function printStiff(Solution,fid) 2 | 3 | if nargin < 2 4 | fid = 1; 5 | end 6 | 7 | if isfield(Solution,'data') 8 | % element stiffness 9 | if isfield(Solution.data,'elementStiff') 10 | printCTitle(fid,'S T I F F N E S S M A T R I C E S') 11 | printLine(fid); 12 | 13 | [n,m,nElem] = size(Solution.data.elementStiff); 14 | for iElem = 1 : nElem 15 | stif = Solution.data.elementStiff(:,:,iElem); 16 | fprintf(fid, 'Element No. [%2d]\n',iElem); 17 | printSLine(fid); 18 | for i = 1 : n 19 | for j = 1 : m 20 | fprintf(fid,'%14.3e\t',stif(i,j)); 21 | end 22 | fprintf(fid,'\n'); 23 | end 24 | end 25 | end 26 | printLine(fid); 27 | 28 | % global stiffness 29 | if isfield(Solution.data,'globalStiff') 30 | fprintf(fid, 'Global Stiffness Matrix\n'); 31 | stif = Solution.data.globalStiff; 32 | [n,m] = size(stif); 33 | for i = 1 : n 34 | for j = 1 : m 35 | fprintf(fid,'%14.3e\t',stif(i,j)); 36 | end 37 | fprintf(fid,'\n'); 38 | end 39 | end 40 | printLine(fid); 41 | 42 | % global forces 43 | if isfield(Solution.data,'globalForce') 44 | fprintf(fid, 'Global Nodal Forces\n'); 45 | F = Solution.data.globalForce; 46 | [n,m] = size(F); 47 | for i = 1 : n 48 | fprintf(fid,'[%3d] \t',i); 49 | for j = 1 : m 50 | fprintf(fid,'%14.3e\t',F(i,j)); 51 | end 52 | fprintf(fid,'\n'); 53 | end 54 | end 55 | 56 | printDLine(fid); 57 | end 58 | end 59 | 60 | 61 | % Helper Functions 62 | function printLine(fid,n) 63 | if nargin < 2 64 | n = 80; 65 | end 66 | if nargin < 1 67 | fid = 1; 68 | end 69 | fprintf(fid,'%s\n',repmat('_',1,n)); 70 | end 71 | 72 | function printDLine(fid,n) 73 | if nargin < 2 74 | n = 80; 75 | end 76 | if nargin < 1 77 | fid = 1; 78 | end 79 | fprintf(fid,'%s\n',repmat('=',1,n)); 80 | end 81 | 82 | function printSLine(fid,n) 83 | if nargin < 2 84 | n = 80; 85 | end 86 | if nargin < 1 87 | fid = 1; 88 | end 89 | fprintf(fid,'%s\n',repmat('-',1,n)); 90 | end 91 | % printing centered text title 92 | function printCTitle(fid,text,n) 93 | if nargin < 3 94 | n = 80; 95 | end 96 | if nargin < 2 97 | text =''; 98 | end 99 | if nargin < 1 100 | fid = 1; 101 | end 102 | tLen = length(text); 103 | space = floor((n-tLen)/2); 104 | fprintf(fid,'%s\n',[repmat(' ',1,space),text]); 105 | end 106 | -------------------------------------------------------------------------------- /Source Code/PlaneTruss/lib_io/printSummary.m: -------------------------------------------------------------------------------- 1 | function printSummary(Model,fid) 2 | % PURPOSE: reads input files and generates a structure including all data 3 | % 4 | % INPUT(S): 5 | % - Model: a structure including the following fields 6 | % - fid : file id to store 7 | % 8 | % OUTPUT(S): 9 | % 10 | % 11 | % USAGE: 12 | % >> printSummary(Model) print input details on command window 13 | % >> printSummary(Model,fid) print input details on a file with fid 14 | % identifier 15 | 16 | % DEVELOPMENT HISTORY: 17 | % [2018, Oct, 29] Shahrokh Shahi -- initial development 18 | % [2018, XXX, XX] Shahrokh Shahi -- 19 | 20 | if nargin < 2 21 | fid = 1; 22 | end 23 | BULLET_CHAR = char(15); 24 | 25 | printDLine(fid) 26 | tText = 'A S U M M A R Y O F T H E I N P U T M O D E L'; 27 | printCTitle(fid,tText) 28 | printDLine(fid) 29 | 30 | 31 | if isfield(Model,'info') 32 | fprintf(fid,'%c About: \n',BULLET_CHAR); 33 | fprintf(fid,'%s\n', Model.info); 34 | end 35 | if isfield(Model,'analysisType') 36 | fprintf(fid,'\n%c Structure Type: \n',BULLET_CHAR); 37 | fprintf(fid,'%s\n', Model.analysisType); 38 | end 39 | printLine(fid) 40 | 41 | 42 | fprintf(fid,'%c Control Variables: \n',BULLET_CHAR); 43 | fprintf(fid,' - Dimension: %dD\n' ,Model.nDim); 44 | fprintf(fid,' - Number of DOF(s): %d \n' ,Model.nDof); 45 | fprintf(fid,'\n'); 46 | fprintf(fid,' - Number of Nodes: %4d \n' ,Model.nNode); 47 | fprintf(fid,' - Number of Elements: %4d \n' ,Model.nElem); 48 | fprintf(fid,' - Nodes per Elements: %d\n',Model.nElemNode); 49 | fprintf(fid,'\n'); 50 | fprintf(fid,' - Number of Sections: %d \n',Model.nSection); 51 | printDLine(fid) 52 | 53 | 54 | printCTitle(fid,'N O D A L I N F O R M A T I O N') 55 | printLine(fid) 56 | headerTxt = ['Node Coordinates Nodal Loads ',... 57 | ' Nodal Restraints \n']; 58 | fprintf(fid,headerTxt); 59 | printSLine(fid) 60 | switch Model.nDim 61 | case 1 62 | headerTxt1 =' ID X '; 63 | headerTxt2 =' Fx '; 64 | headerTxt3 =' ux \n'; 65 | 66 | case 2 67 | headerTxt1 =' ID X Y '; 68 | headerTxt2 =' Fx Fy '; 69 | headerTxt3 =' ux uy \n'; 70 | 71 | case 3 72 | headerTxt1 =' ID X Y Z '; 73 | headerTxt2 =' Fx Fy Fz '; 74 | headerTxt3 =' ux uy uz \n'; 75 | end 76 | fprintf(fid,[headerTxt1,headerTxt2,headerTxt3]); 77 | printLine(fid) 78 | 79 | % nodal forces to displaying 80 | F = zeros(Model.nNode,Model.nDof); 81 | for i = 1 : Model.nNodalForce 82 | node = Model.loading.nodalForces(i,1); 83 | F(node, 1:Model.nDof) = Model.loading.nodalForces(i,2:end); 84 | end 85 | 86 | % printing table contents 87 | for i = 1 : Model.nNode 88 | coord = Model.geometry.coordinates(i,:); 89 | fprintf(fid,'%2d ',i); 90 | for j = 1 : length(coord) 91 | fprintf(fid,'%7.2f ',coord(j)); 92 | end 93 | fprintf(fid,'\t'); 94 | for j = 1 : size(F,2) 95 | fprintf(fid,'%10.2f ',F(i,j)); 96 | end 97 | 98 | fprintf(fid,'\t'); 99 | index = find(Model.boundary(:,1)==i); 100 | dx='-';dy='-';dz='-';bc=''; 101 | 102 | if ~isempty(index) 103 | for k = 1 : length(index) 104 | if Model.boundary(index(k),2)==1 105 | dx=num2str(Model.boundary(index(k),3)); 106 | elseif Model.boundary(index(k),2)==2 107 | dy=num2str(Model.boundary(index(k),3)); 108 | elseif Model.boundary(index(k),2)==3 109 | dz=num2str(Model.boundary(index(k),3)); 110 | end 111 | end 112 | if length(index)==1 113 | bc = 'Roller '; 114 | elseif length(index)==2 115 | bc = 'Pin'; 116 | elseif length(index)==3 117 | bc = 'Fixed'; 118 | end 119 | end 120 | presc = [dx, dy, dz]; %prescribed values 121 | for j = 1 : Model.nDof 122 | fprintf(fid,' %s',presc(j)); 123 | end 124 | fprintf(fid,' %s\n',bc); 125 | end 126 | printDLine(fid); 127 | 128 | printCTitle(fid,'E L E M E N T S I N F O R M A T I O N') 129 | printLine(fid) 130 | fprintf(fid,' ID\t '); 131 | for i = 1 : Model.nElemNode 132 | fprintf(fid,'Node%d\t',i); 133 | end 134 | fprintf(fid,' Section No. Material Properties\n'); 135 | printLine(fid); 136 | 137 | for i = 1 : Model.nElem 138 | fprintf(fid,'%2d\t ',i); 139 | for j = 1 : Model.nElemNode 140 | fprintf(fid,'%2d\t\t',Model.geometry.elements(i,j)); 141 | end 142 | fprintf(fid,'\t'); 143 | fprintf(fid,'\t%2d\t\t\t[',Model.elemSectId(i)); 144 | for j = 1 : Model.nMaterialProp 145 | fprintf(fid,'%g\t\t',Model.sections(Model.elemSectId(i),j)); 146 | end 147 | fprintf(fid,']\n'); 148 | end 149 | 150 | printDLine(fid); 151 | 152 | end 153 | 154 | 155 | % Helper Functions 156 | function printLine(fid,n) 157 | if nargin < 2 158 | n = 80; 159 | end 160 | if nargin < 1 161 | fid = 1; 162 | end 163 | fprintf(fid,'%s\n',repmat('_',1,n)); 164 | end 165 | 166 | function printDLine(fid,n) 167 | if nargin < 2 168 | n = 80; 169 | end 170 | if nargin < 1 171 | fid = 1; 172 | end 173 | fprintf(fid,'%s\n',repmat('=',1,n)); 174 | end 175 | 176 | function printSLine(fid,n) 177 | if nargin < 2 178 | n = 80; 179 | end 180 | if nargin < 1 181 | fid = 1; 182 | end 183 | fprintf(fid,'%s\n',repmat('-',1,n)); 184 | end 185 | % printing centered text title 186 | function printCTitle(fid,text,n) 187 | if nargin < 3 188 | n = 80; 189 | end 190 | if nargin < 2 191 | text =''; 192 | end 193 | if nargin < 1 194 | fid = 1; 195 | end 196 | tLen = length(text); 197 | space = floor((n-tLen)/2); 198 | fprintf(fid,'%s\n',[repmat(' ',1,space),text]); 199 | end -------------------------------------------------------------------------------- /Source Code/PlaneTruss/main.m: -------------------------------------------------------------------------------- 1 | %% M A I N F U N C T I O N 2 | %__________________________________________________________________________ 3 | % 4 | % Finite Element Methods 5 | % Developed by SHAHROKH SHAHI 6 | % (www.sshahi.com) 7 | % 8 | % Georgia Institute of Technology 9 | %__________________________________________________________________________ 10 | % 11 | % This file is the main function to handle the analysis by employing the 12 | % functions in the folder "lib" 13 | 14 | 15 | % DEVELOPMENT HISTORY: 16 | % [2018, Oct, 12] Shahrokh Shahi -- initial development 17 | % [2018, Nov, 15] Shahrokh Shahi -- Upgrading the libraries setup 18 | 19 | %% Initial Setup ( You do NOT need to change this section) 20 | clc 21 | clear 22 | close all 23 | 24 | format short g 25 | format compact 26 | 27 | % adding "lib" folder to the path 28 | path = mfilename('fullpath'); 29 | path(end-length(mfilename):end)=[]; 30 | addpath(fullfile(path,'lib')) 31 | addpath(fullfile(path,'lib_io')) 32 | 33 | %% Reading the Input File 34 | 35 | % input file name 36 | % inpFileName = 'input2.txt'; 37 | inpFileName = 'input1.txt'; 38 | 39 | %-------------------------------------------------------------------------- 40 | % E X T R A C T M O D E L F R O M I N P U T F I L E 41 | %-------------------------------------------------------------------------- 42 | Model = inpFileReader(inpFileName); 43 | 44 | %-------------------------------------------------------------------------- 45 | % P R I N T I N P U T S U M M A R Y 46 | %-------------------------------------------------------------------------- 47 | printSummary(Model) 48 | 49 | %-------------------------------------------------------------------------- 50 | % S I M P L E P L O T 51 | %-------------------------------------------------------------------------- 52 | plotModel(Model,1); 53 | 54 | %% Run The Analysis 55 | 56 | Solution1 = trussAnalysisExplicit(Model); 57 | printResult(Solution1) 58 | 59 | Solution2 = trussAnalysisNumerical(Model); 60 | printResult(Solution2) 61 | -------------------------------------------------------------------------------- /Source Code/fem.m: -------------------------------------------------------------------------------- 1 | %% P A C K A G E S T A R T E R 2 | %__________________________________________________________________________ 3 | % 4 | % Finite Element Package 5 | % developed by 6 | % SHAHROKH SHAHI 7 | % Georgia Institute of Technology 8 | % Spring 2019 9 | %__________________________________________________________________________ 10 | % 11 | % Homepage: www.sshahi.com 12 | % Email: shahi@gatech.edu 13 | %__________________________________________________________________________ 14 | function fem() 15 | %% Initialization 16 | clc 17 | clear 18 | close all 19 | 20 | format compact 21 | 22 | path (pathdef) 23 | 24 | %% Cleaning 25 | delete *.mat 26 | 27 | %% Add to path 28 | pathThis = mfilename('fullpath'); 29 | pathThis(end-length(mfilename):end)=[]; 30 | % addpath(fullfile(path,'PlaneTruss' ,'lib')) 31 | % addpath(fullfile(path,'PlaneFrame' ,'lib')) 32 | % addpath(fullfile(path,'PlaneStress PlaneStrain','lib')) 33 | addpath(fullfile(pathThis,'GUI')); 34 | 35 | %% Run GUI 36 | FiniteElementGUI() -------------------------------------------------------------------------------- /Toolbox Installation File/FEM Package.mltbx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/shahrokhx/FEM_Toolbox/8dda726b82d707d2e3404996893c95b8e2de3ef9/Toolbox Installation File/FEM Package.mltbx --------------------------------------------------------------------------------