├── FEM
    ├── 2-5
    │   ├── 2-5.png
    │   ├── count.txt
    │   ├── data.txt
    │   ├── load.txt
    │   ├── mat.txt
    │   ├── node.txt
    │   ├── pre.txt
    │   ├── unit.txt
    │   └── unit2.txt
    ├── Main.m
    ├── To_Bke.m
    ├── To_P.m
    └── data
    │   ├── 2-5x.jpg
    │   ├── 2-5x1.jpg
    │   ├── 2-5xy.jpg
    │   ├── 2-5xy1.jpg
    │   ├── 2-5y.jpg
    │   ├── 2-5y1.jpg
    │   ├── Readme.md
    │   ├── load.txt
    │   ├── mat.txt
    │   ├── node.txt
    │   ├── pre.txt
    │   └── unit.txt
└── README.md


/FEM/2-5/2-5.png:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/Ron-Wang/FEM-Matlab/5438235a09fcead03bc8565988bbc9360ee06fdc/FEM/2-5/2-5.png


--------------------------------------------------------------------------------
/FEM/2-5/count.txt:
--------------------------------------------------------------------------------
1 | 289
2 | 512
3 | 4
4 | 2


--------------------------------------------------------------------------------
/FEM/2-5/data.txt:
--------------------------------------------------------------------------------
1 | 
2 | 


--------------------------------------------------------------------------------
/FEM/2-5/load.txt:
--------------------------------------------------------------------------------
1 | 545 25
2 | 577 25


--------------------------------------------------------------------------------
/FEM/2-5/mat.txt:
--------------------------------------------------------------------------------
1 | 10000 0.15 10


--------------------------------------------------------------------------------
/FEM/2-5/node.txt:
--------------------------------------------------------------------------------
  1 | 0 0
  2 | 0.5 0
  3 | 1 0
  4 | 1.5 0
  5 | 2 0
  6 | 2.5 0
  7 | 3 0
  8 | 3.5 0
  9 | 4 0
 10 | 4.5 0
 11 | 5 0
 12 | 5.5 0
 13 | 6 0
 14 | 6.5 0
 15 | 7 0
 16 | 7.5 0
 17 | 8 0
 18 | 0 0.5
 19 | 0.5 0.5
 20 | 1 0.5
 21 | 1.5 0.5
 22 | 2 0.5
 23 | 2.5 0.5
 24 | 3 0.5
 25 | 3.5 0.5
 26 | 4 0.5
 27 | 4.5 0.5
 28 | 5 0.5
 29 | 5.5 0.5
 30 | 6 0.5
 31 | 6.5 0.5
 32 | 7 0.5
 33 | 7.5 0.5
 34 | 8 0.5
 35 | 0 1
 36 | 0.5 1
 37 | 1 1
 38 | 1.5 1
 39 | 2 1
 40 | 2.5 1
 41 | 3 1
 42 | 3.5 1
 43 | 4 1
 44 | 4.5 1
 45 | 5 1
 46 | 5.5 1
 47 | 6 1
 48 | 6.5 1
 49 | 7 1
 50 | 7.5 1
 51 | 8 1
 52 | 0 1.5
 53 | 0.5 1.5
 54 | 1 1.5
 55 | 1.5 1.5
 56 | 2 1.5
 57 | 2.5 1.5
 58 | 3 1.5
 59 | 3.5 1.5
 60 | 4 1.5
 61 | 4.5 1.5
 62 | 5 1.5
 63 | 5.5 1.5
 64 | 6 1.5
 65 | 6.5 1.5
 66 | 7 1.5
 67 | 7.5 1.5
 68 | 8 1.5
 69 | 0 2
 70 | 0.5 2
 71 | 1 2
 72 | 1.5 2
 73 | 2 2
 74 | 2.5 2
 75 | 3 2
 76 | 3.5 2
 77 | 4 2
 78 | 4.5 2
 79 | 5 2
 80 | 5.5 2
 81 | 6 2
 82 | 6.5 2
 83 | 7 2
 84 | 7.5 2
 85 | 8 2
 86 | 0 2.5
 87 | 0.5 2.5
 88 | 1 2.5
 89 | 1.5 2.5
 90 | 2 2.5
 91 | 2.5 2.5
 92 | 3 2.5
 93 | 3.5 2.5
 94 | 4 2.5
 95 | 4.5 2.5
 96 | 5 2.5
 97 | 5.5 2.5
 98 | 6 2.5
 99 | 6.5 2.5
100 | 7 2.5
101 | 7.5 2.5
102 | 8 2.5
103 | 0 3
104 | 0.5 3
105 | 1 3
106 | 1.5 3
107 | 2 3
108 | 2.5 3
109 | 3 3
110 | 3.5 3
111 | 4 3
112 | 4.5 3
113 | 5 3
114 | 5.5 3
115 | 6 3
116 | 6.5 3
117 | 7 3
118 | 7.5 3
119 | 8 3
120 | 0 3.5
121 | 0.5 3.5
122 | 1 3.5
123 | 1.5 3.5
124 | 2 3.5
125 | 2.5 3.5
126 | 3 3.5
127 | 3.5 3.5
128 | 4 3.5
129 | 4.5 3.5
130 | 5 3.5
131 | 5.5 3.5
132 | 6 3.5
133 | 6.5 3.5
134 | 7 3.5
135 | 7.5 3.5
136 | 8 3.5
137 | 0 4
138 | 0.5 4
139 | 1 4
140 | 1.5 4
141 | 2 4
142 | 2.5 4
143 | 3 4
144 | 3.5 4
145 | 4 4
146 | 4.5 4
147 | 5 4
148 | 5.5 4
149 | 6 4
150 | 6.5 4
151 | 7 4
152 | 7.5 4
153 | 8 4
154 | 0 4.5
155 | 0.5 4.5
156 | 1 4.5
157 | 1.5 4.5
158 | 2 4.5
159 | 2.5 4.5
160 | 3 4.5
161 | 3.5 4.5
162 | 4 4.5
163 | 4.5 4.5
164 | 5 4.5
165 | 5.5 4.5
166 | 6 4.5
167 | 6.5 4.5
168 | 7 4.5
169 | 7.5 4.5
170 | 8 4.5
171 | 0 5
172 | 0.5 5
173 | 1 5
174 | 1.5 5
175 | 2 5
176 | 2.5 5
177 | 3 5
178 | 3.5 5
179 | 4 5
180 | 4.5 5
181 | 5 5
182 | 5.5 5
183 | 6 5
184 | 6.5 5
185 | 7 5
186 | 7.5 5
187 | 8 5
188 | 0 5.5
189 | 0.5 5.5
190 | 1 5.5
191 | 1.5 5.5
192 | 2 5.5
193 | 2.5 5.5
194 | 3 5.5
195 | 3.5 5.5
196 | 4 5.5
197 | 4.5 5.5
198 | 5 5.5
199 | 5.5 5.5
200 | 6 5.5
201 | 6.5 5.5
202 | 7 5.5
203 | 7.5 5.5
204 | 8 5.5
205 | 0 6
206 | 0.5 6
207 | 1 6
208 | 1.5 6
209 | 2 6
210 | 2.5 6
211 | 3 6
212 | 3.5 6
213 | 4 6
214 | 4.5 6
215 | 5 6
216 | 5.5 6
217 | 6 6
218 | 6.5 6
219 | 7 6
220 | 7.5 6
221 | 8 6
222 | 0 6.5
223 | 0.5 6.5
224 | 1 6.5
225 | 1.5 6.5
226 | 2 6.5
227 | 2.5 6.5
228 | 3 6.5
229 | 3.5 6.5
230 | 4 6.5
231 | 4.5 6.5
232 | 5 6.5
233 | 5.5 6.5
234 | 6 6.5
235 | 6.5 6.5
236 | 7 6.5
237 | 7.5 6.5
238 | 8 6.5
239 | 0 7
240 | 0.5 7
241 | 1 7
242 | 1.5 7
243 | 2 7
244 | 2.5 7
245 | 3 7
246 | 3.5 7
247 | 4 7
248 | 4.5 7
249 | 5 7
250 | 5.5 7
251 | 6 7
252 | 6.5 7
253 | 7 7
254 | 7.5 7
255 | 8 7
256 | 0 7.5
257 | 0.5 7.5
258 | 1 7.5
259 | 1.5 7.5
260 | 2 7.5
261 | 2.5 7.5
262 | 3 7.5
263 | 3.5 7.5
264 | 4 7.5
265 | 4.5 7.5
266 | 5 7.5
267 | 5.5 7.5
268 | 6 7.5
269 | 6.5 7.5
270 | 7 7.5
271 | 7.5 7.5
272 | 8 7.5
273 | 0 8
274 | 0.5 8
275 | 1 8
276 | 1.5 8
277 | 2 8
278 | 2.5 8
279 | 3 8
280 | 3.5 8
281 | 4 8
282 | 4.5 8
283 | 5 8
284 | 5.5 8
285 | 6 8
286 | 6.5 8
287 | 7 8
288 | 7.5 8
289 | 8 8
290 | 


--------------------------------------------------------------------------------
/FEM/2-5/pre.txt:
--------------------------------------------------------------------------------
1 | 0 0
2 | 33 0
3 | 32 0
4 | 1 0


--------------------------------------------------------------------------------
/FEM/2-5/unit.txt:
--------------------------------------------------------------------------------
  1 | 0 1 17
  2 | 1 18 17
  3 | 1 2 18
  4 | 2 19 18
  5 | 2 3 19
  6 | 3 20 19
  7 | 3 4 20
  8 | 4 21 20
  9 | 4 5 21
 10 | 5 22 21
 11 | 5 6 22
 12 | 6 23 22
 13 | 6 7 23
 14 | 7 24 23
 15 | 7 8 24
 16 | 8 25 24
 17 | 8 9 25
 18 | 9 26 25
 19 | 9 10 26
 20 | 10 27 26
 21 | 10 11 27
 22 | 11 28 27
 23 | 11 12 28
 24 | 12 29 28
 25 | 12 13 29
 26 | 13 30 29
 27 | 13 14 30
 28 | 14 31 30
 29 | 14 15 31
 30 | 15 32 31
 31 | 15 16 32
 32 | 16 33 32
 33 | 17 18 34
 34 | 18 35 34
 35 | 18 19 35
 36 | 19 36 35
 37 | 19 20 36
 38 | 20 37 36
 39 | 20 21 37
 40 | 21 38 37
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 42 | 22 39 38
 43 | 22 23 39
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 46 | 24 41 40
 47 | 24 25 41
 48 | 25 42 41
 49 | 25 26 42
 50 | 26 43 42
 51 | 26 27 43
 52 | 27 44 43
 53 | 27 28 44
 54 | 28 45 44
 55 | 28 29 45
 56 | 29 46 45
 57 | 29 30 46
 58 | 30 47 46
 59 | 30 31 47
 60 | 31 48 47
 61 | 31 32 48
 62 | 32 49 48
 63 | 32 33 49
 64 | 33 50 49
 65 | 34 35 51
 66 | 35 52 51
 67 | 35 36 52
 68 | 36 53 52
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 70 | 37 54 53
 71 | 37 38 54
 72 | 38 55 54
 73 | 38 39 55
 74 | 39 56 55
 75 | 39 40 56
 76 | 40 57 56
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 79 | 41 42 58
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 82 | 43 60 59
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 84 | 44 61 60
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 89 | 46 47 63
 90 | 47 64 63
 91 | 47 48 64
 92 | 48 65 64
 93 | 48 49 65
 94 | 49 66 65
 95 | 49 50 66
 96 | 50 67 66
 97 | 51 52 68
 98 | 52 69 68
 99 | 52 53 69
100 | 53 70 69
101 | 53 54 70
102 | 54 71 70
103 | 54 55 71
104 | 55 72 71
105 | 55 56 72
106 | 56 73 72
107 | 56 57 73
108 | 57 74 73
109 | 57 58 74
110 | 58 75 74
111 | 58 59 75
112 | 59 76 75
113 | 59 60 76
114 | 60 77 76
115 | 60 61 77
116 | 61 78 77
117 | 61 62 78
118 | 62 79 78
119 | 62 63 79
120 | 63 80 79
121 | 63 64 80
122 | 64 81 80
123 | 64 65 81
124 | 65 82 81
125 | 65 66 82
126 | 66 83 82
127 | 66 67 83
128 | 67 84 83
129 | 68 69 85
130 | 69 86 85
131 | 69 70 86
132 | 70 87 86
133 | 70 71 87
134 | 71 88 87
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159 | 83 84 100
160 | 84 101 100
161 | 85 86 102
162 | 86 103 102
163 | 86 87 103
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172 | 91 108 107
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261 | 138 139 155
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284 | 150 167 166
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296 | 157 174 173
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299 | 158 159 175
300 | 159 176 175
301 | 159 160 176
302 | 160 177 176
303 | 160 161 177
304 | 161 178 177
305 | 161 162 178
306 | 162 179 178
307 | 162 163 179
308 | 163 180 179
309 | 163 164 180
310 | 164 181 180
311 | 164 165 181
312 | 165 182 181
313 | 165 166 182
314 | 166 183 182
315 | 166 167 183
316 | 167 184 183
317 | 167 168 184
318 | 168 185 184
319 | 168 169 185
320 | 169 186 185
321 | 170 171 187
322 | 171 188 187
323 | 171 172 188
324 | 172 189 188
325 | 172 173 189
326 | 173 190 189
327 | 173 174 190
328 | 174 191 190
329 | 174 175 191
330 | 175 192 191
331 | 175 176 192
332 | 176 193 192
333 | 176 177 193
334 | 177 194 193
335 | 177 178 194
336 | 178 195 194
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338 | 179 196 195
339 | 179 180 196
340 | 180 197 196
341 | 180 181 197
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344 | 182 199 198
345 | 182 183 199
346 | 183 200 199
347 | 183 184 200
348 | 184 201 200
349 | 184 185 201
350 | 185 202 201
351 | 185 186 202
352 | 186 203 202
353 | 187 188 204
354 | 188 205 204
355 | 188 189 205
356 | 189 206 205
357 | 189 190 206
358 | 190 207 206
359 | 190 191 207
360 | 191 208 207
361 | 191 192 208
362 | 192 209 208
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364 | 193 210 209
365 | 193 194 210
366 | 194 211 210
367 | 194 195 211
368 | 195 212 211
369 | 195 196 212
370 | 196 213 212
371 | 196 197 213
372 | 197 214 213
373 | 197 198 214
374 | 198 215 214
375 | 198 199 215
376 | 199 216 215
377 | 199 200 216
378 | 200 217 216
379 | 200 201 217
380 | 201 218 217
381 | 201 202 218
382 | 202 219 218
383 | 202 203 219
384 | 203 220 219
385 | 204 205 221
386 | 205 222 221
387 | 205 206 222
388 | 206 223 222
389 | 206 207 223
390 | 207 224 223
391 | 207 208 224
392 | 208 225 224
393 | 208 209 225
394 | 209 226 225
395 | 209 210 226
396 | 210 227 226
397 | 210 211 227
398 | 211 228 227
399 | 211 212 228
400 | 212 229 228
401 | 212 213 229
402 | 213 230 229
403 | 213 214 230
404 | 214 231 230
405 | 214 215 231
406 | 215 232 231
407 | 215 216 232
408 | 216 233 232
409 | 216 217 233
410 | 217 234 233
411 | 217 218 234
412 | 218 235 234
413 | 218 219 235
414 | 219 236 235
415 | 219 220 236
416 | 220 237 236
417 | 221 222 238
418 | 222 239 238
419 | 222 223 239
420 | 223 240 239
421 | 223 224 240
422 | 224 241 240
423 | 224 225 241
424 | 225 242 241
425 | 225 226 242
426 | 226 243 242
427 | 226 227 243
428 | 227 244 243
429 | 227 228 244
430 | 228 245 244
431 | 228 229 245
432 | 229 246 245
433 | 229 230 246
434 | 230 247 246
435 | 230 231 247
436 | 231 248 247
437 | 231 232 248
438 | 232 249 248
439 | 232 233 249
440 | 233 250 249
441 | 233 234 250
442 | 234 251 250
443 | 234 235 251
444 | 235 252 251
445 | 235 236 252
446 | 236 253 252
447 | 236 237 253
448 | 237 254 253
449 | 238 239 255
450 | 239 256 255
451 | 239 240 256
452 | 240 257 256
453 | 240 241 257
454 | 241 258 257
455 | 241 242 258
456 | 242 259 258
457 | 242 243 259
458 | 243 260 259
459 | 243 244 260
460 | 244 261 260
461 | 244 245 261
462 | 245 262 261
463 | 245 246 262
464 | 246 263 262
465 | 246 247 263
466 | 247 264 263
467 | 247 248 264
468 | 248 265 264
469 | 248 249 265
470 | 249 266 265
471 | 249 250 266
472 | 250 267 266
473 | 250 251 267
474 | 251 268 267
475 | 251 252 268
476 | 252 269 268
477 | 252 253 269
478 | 253 270 269
479 | 253 254 270
480 | 254 271 270
481 | 255 256 272
482 | 256 273 272
483 | 256 257 273
484 | 257 274 273
485 | 257 258 274
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488 | 259 276 275
489 | 259 260 276
490 | 260 277 276
491 | 260 261 277
492 | 261 278 277
493 | 261 262 278
494 | 262 279 278
495 | 262 263 279
496 | 263 280 279
497 | 263 264 280
498 | 264 281 280
499 | 264 265 281
500 | 265 282 281
501 | 265 266 282
502 | 266 283 282
503 | 266 267 283
504 | 267 284 283
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506 | 268 285 284
507 | 268 269 285
508 | 269 286 285
509 | 269 270 286
510 | 270 287 286
511 | 270 271 287
512 | 271 288 287
513 | 


--------------------------------------------------------------------------------
/FEM/2-5/unit2.txt:
--------------------------------------------------------------------------------
  1 | 0,1,18
  2 | 0,18,17
  3 | 1,2,19
  4 | 1,19,18
  5 | 2,3,20
  6 | 2,20,19
  7 | 3,4,21
  8 | 3,21,20
  9 | 4,5,22
 10 | 4,22,21
 11 | 5,6,23
 12 | 5,23,22
 13 | 6,7,24
 14 | 6,24,23
 15 | 7,8,25
 16 | 7,25,24
 17 | 8,9,26
 18 | 8,26,25
 19 | 9,10,27
 20 | 9,27,26
 21 | 10,11,28
 22 | 10,28,27
 23 | 11,12,29
 24 | 11,29,28
 25 | 12,13,30
 26 | 12,30,29
 27 | 13,14,31
 28 | 13,31,30
 29 | 14,15,32
 30 | 14,32,31
 31 | 15,16,33
 32 | 15,33,32
 33 | 17,18,35
 34 | 17,35,34
 35 | 18,19,36
 36 | 18,36,35
 37 | 19,20,37
 38 | 19,37,36
 39 | 20,21,38
 40 | 20,38,37
 41 | 21,22,39
 42 | 21,39,38
 43 | 22,23,40
 44 | 22,40,39
 45 | 23,24,41
 46 | 23,41,40
 47 | 24,25,42
 48 | 24,42,41
 49 | 25,26,43
 50 | 25,43,42
 51 | 26,27,44
 52 | 26,44,43
 53 | 27,28,45
 54 | 27,45,44
 55 | 28,29,46
 56 | 28,46,45
 57 | 29,30,47
 58 | 29,47,46
 59 | 30,31,48
 60 | 30,48,47
 61 | 31,32,49
 62 | 31,49,48
 63 | 32,33,50
 64 | 32,50,49
 65 | 34,35,52
 66 | 34,52,51
 67 | 35,36,53
 68 | 35,53,52
 69 | 36,37,54
 70 | 36,54,53
 71 | 37,38,55
 72 | 37,55,54
 73 | 38,39,56
 74 | 38,56,55
 75 | 39,40,57
 76 | 39,57,56
 77 | 40,41,58
 78 | 40,58,57
 79 | 41,42,59
 80 | 41,59,58
 81 | 42,43,60
 82 | 42,60,59
 83 | 43,44,61
 84 | 43,61,60
 85 | 44,45,62
 86 | 44,62,61
 87 | 45,46,63
 88 | 45,63,62
 89 | 46,47,64
 90 | 46,64,63
 91 | 47,48,65
 92 | 47,65,64
 93 | 48,49,66
 94 | 48,66,65
 95 | 49,50,67
 96 | 49,67,66
 97 | 51,52,69
 98 | 51,69,68
 99 | 52,53,70
100 | 52,70,69
101 | 53,54,71
102 | 53,71,70
103 | 54,55,72
104 | 54,72,71
105 | 55,56,73
106 | 55,73,72
107 | 56,57,74
108 | 56,74,73
109 | 57,58,75
110 | 57,75,74
111 | 58,59,76
112 | 58,76,75
113 | 59,60,77
114 | 59,77,76
115 | 60,61,78
116 | 60,78,77
117 | 61,62,79
118 | 61,79,78
119 | 62,63,80
120 | 62,80,79
121 | 63,64,81
122 | 63,81,80
123 | 64,65,82
124 | 64,82,81
125 | 65,66,83
126 | 65,83,82
127 | 66,67,84
128 | 66,84,83
129 | 68,69,86
130 | 68,86,85
131 | 69,70,87
132 | 69,87,86
133 | 70,71,88
134 | 70,88,87
135 | 71,72,89
136 | 71,89,88
137 | 72,73,90
138 | 72,90,89
139 | 73,74,91
140 | 73,91,90
141 | 74,75,92
142 | 74,92,91
143 | 75,76,93
144 | 75,93,92
145 | 76,77,94
146 | 76,94,93
147 | 77,78,95
148 | 77,95,94
149 | 78,79,96
150 | 78,96,95
151 | 79,80,97
152 | 79,97,96
153 | 80,81,98
154 | 80,98,97
155 | 81,82,99
156 | 81,99,98
157 | 82,83,100
158 | 82,100,99
159 | 83,84,101
160 | 83,101,100
161 | 85,86,103
162 | 85,103,102
163 | 86,87,104
164 | 86,104,103
165 | 87,88,105
166 | 87,105,104
167 | 88,89,106
168 | 88,106,105
169 | 89,90,107
170 | 89,107,106
171 | 90,91,108
172 | 90,108,107
173 | 91,92,109
174 | 91,109,108
175 | 92,93,110
176 | 92,110,109
177 | 93,94,111
178 | 93,111,110
179 | 94,95,112
180 | 94,112,111
181 | 95,96,113
182 | 95,113,112
183 | 96,97,114
184 | 96,114,113
185 | 97,98,115
186 | 97,115,114
187 | 98,99,116
188 | 98,116,115
189 | 99,100,117
190 | 99,117,116
191 | 100,101,118
192 | 100,118,117
193 | 102,103,120
194 | 102,120,119
195 | 103,104,121
196 | 103,121,120
197 | 104,105,122
198 | 104,122,121
199 | 105,106,123
200 | 105,123,122
201 | 106,107,124
202 | 106,124,123
203 | 107,108,125
204 | 107,125,124
205 | 108,109,126
206 | 108,126,125
207 | 109,110,127
208 | 109,127,126
209 | 110,111,128
210 | 110,128,127
211 | 111,112,129
212 | 111,129,128
213 | 112,113,130
214 | 112,130,129
215 | 113,114,131
216 | 113,131,130
217 | 114,115,132
218 | 114,132,131
219 | 115,116,133
220 | 115,133,132
221 | 116,117,134
222 | 116,134,133
223 | 117,118,135
224 | 117,135,134
225 | 119,120,137
226 | 119,137,136
227 | 120,121,138
228 | 120,138,137
229 | 121,122,139
230 | 121,139,138
231 | 122,123,140
232 | 122,140,139
233 | 123,124,141
234 | 123,141,140
235 | 124,125,142
236 | 124,142,141
237 | 125,126,143
238 | 125,143,142
239 | 126,127,144
240 | 126,144,143
241 | 127,128,145
242 | 127,145,144
243 | 128,129,146
244 | 128,146,145
245 | 129,130,147
246 | 129,147,146
247 | 130,131,148
248 | 130,148,147
249 | 131,132,149
250 | 131,149,148
251 | 132,133,150
252 | 132,150,149
253 | 133,134,151
254 | 133,151,150
255 | 134,135,152
256 | 134,152,151
257 | 136,137,154
258 | 136,154,153
259 | 137,138,155
260 | 137,155,154
261 | 138,139,156
262 | 138,156,155
263 | 139,140,157
264 | 139,157,156
265 | 140,141,158
266 | 140,158,157
267 | 141,142,159
268 | 141,159,158
269 | 142,143,160
270 | 142,160,159
271 | 143,144,161
272 | 143,161,160
273 | 144,145,162
274 | 144,162,161
275 | 145,146,163
276 | 145,163,162
277 | 146,147,164
278 | 146,164,163
279 | 147,148,165
280 | 147,165,164
281 | 148,149,166
282 | 148,166,165
283 | 149,150,167
284 | 149,167,166
285 | 150,151,168
286 | 150,168,167
287 | 151,152,169
288 | 151,169,168
289 | 153,154,171
290 | 153,171,170
291 | 154,155,172
292 | 154,172,171
293 | 155,156,173
294 | 155,173,172
295 | 156,157,174
296 | 156,174,173
297 | 157,158,175
298 | 157,175,174
299 | 158,159,176
300 | 158,176,175
301 | 159,160,177
302 | 159,177,176
303 | 160,161,178
304 | 160,178,177
305 | 161,162,179
306 | 161,179,178
307 | 162,163,180
308 | 162,180,179
309 | 163,164,181
310 | 163,181,180
311 | 164,165,182
312 | 164,182,181
313 | 165,166,183
314 | 165,183,182
315 | 166,167,184
316 | 166,184,183
317 | 167,168,185
318 | 167,185,184
319 | 168,169,186
320 | 168,186,185
321 | 170,171,188
322 | 170,188,187
323 | 171,172,189
324 | 171,189,188
325 | 172,173,190
326 | 172,190,189
327 | 173,174,191
328 | 173,191,190
329 | 174,175,192
330 | 174,192,191
331 | 175,176,193
332 | 175,193,192
333 | 176,177,194
334 | 176,194,193
335 | 177,178,195
336 | 177,195,194
337 | 178,179,196
338 | 178,196,195
339 | 179,180,197
340 | 179,197,196
341 | 180,181,198
342 | 180,198,197
343 | 181,182,199
344 | 181,199,198
345 | 182,183,200
346 | 182,200,199
347 | 183,184,201
348 | 183,201,200
349 | 184,185,202
350 | 184,202,201
351 | 185,186,203
352 | 185,203,202
353 | 187,188,205
354 | 187,205,204
355 | 188,189,206
356 | 188,206,205
357 | 189,190,207
358 | 189,207,206
359 | 190,191,208
360 | 190,208,207
361 | 191,192,209
362 | 191,209,208
363 | 192,193,210
364 | 192,210,209
365 | 193,194,211
366 | 193,211,210
367 | 194,195,212
368 | 194,212,211
369 | 195,196,213
370 | 195,213,212
371 | 196,197,214
372 | 196,214,213
373 | 197,198,215
374 | 197,215,214
375 | 198,199,216
376 | 198,216,215
377 | 199,200,217
378 | 199,217,216
379 | 200,201,218
380 | 200,218,217
381 | 201,202,219
382 | 201,219,218
383 | 202,203,220
384 | 202,220,219
385 | 204,205,222
386 | 204,222,221
387 | 205,206,223
388 | 205,223,222
389 | 206,207,224
390 | 206,224,223
391 | 207,208,225
392 | 207,225,224
393 | 208,209,226
394 | 208,226,225
395 | 209,210,227
396 | 209,227,226
397 | 210,211,228
398 | 210,228,227
399 | 211,212,229
400 | 211,229,228
401 | 212,213,230
402 | 212,230,229
403 | 213,214,231
404 | 213,231,230
405 | 214,215,232
406 | 214,232,231
407 | 215,216,233
408 | 215,233,232
409 | 216,217,234
410 | 216,234,233
411 | 217,218,235
412 | 217,235,234
413 | 218,219,236
414 | 218,236,235
415 | 219,220,237
416 | 219,237,236
417 | 221,222,239
418 | 221,239,238
419 | 222,223,240
420 | 222,240,239
421 | 223,224,241
422 | 223,241,240
423 | 224,225,242
424 | 224,242,241
425 | 225,226,243
426 | 225,243,242
427 | 226,227,244
428 | 226,244,243
429 | 227,228,245
430 | 227,245,244
431 | 228,229,246
432 | 228,246,245
433 | 229,230,247
434 | 229,247,246
435 | 230,231,248
436 | 230,248,247
437 | 231,232,249
438 | 231,249,248
439 | 232,233,250
440 | 232,250,249
441 | 233,234,251
442 | 233,251,250
443 | 234,235,252
444 | 234,252,251
445 | 235,236,253
446 | 235,253,252
447 | 236,237,254
448 | 236,254,253
449 | 238,239,256
450 | 238,256,255
451 | 239,240,257
452 | 239,257,256
453 | 240,241,258
454 | 240,258,257
455 | 241,242,259
456 | 241,259,258
457 | 242,243,260
458 | 242,260,259
459 | 243,244,261
460 | 243,261,260
461 | 244,245,262
462 | 244,262,261
463 | 245,246,263
464 | 245,263,262
465 | 246,247,264
466 | 246,264,263
467 | 247,248,265
468 | 247,265,264
469 | 248,249,266
470 | 248,266,265
471 | 249,250,267
472 | 249,267,266
473 | 250,251,268
474 | 250,268,267
475 | 251,252,269
476 | 251,269,268
477 | 252,253,270
478 | 252,270,269
479 | 253,254,271
480 | 253,271,270
481 | 255,256,273
482 | 255,273,272
483 | 256,257,274
484 | 256,274,273
485 | 257,258,275
486 | 257,275,274
487 | 258,259,276
488 | 258,276,275
489 | 259,260,277
490 | 259,277,276
491 | 260,261,278
492 | 260,278,277
493 | 261,262,279
494 | 261,279,278
495 | 262,263,280
496 | 262,280,279
497 | 263,264,281
498 | 263,281,280
499 | 264,265,282
500 | 264,282,281
501 | 265,266,283
502 | 265,283,282
503 | 266,267,284
504 | 266,284,283
505 | 267,268,285
506 | 267,285,284
507 | 268,269,286
508 | 268,286,285
509 | 269,270,287
510 | 269,287,286
511 | 270,271,288
512 | 270,288,287
513 | 


--------------------------------------------------------------------------------
/FEM/Main.m:
--------------------------------------------------------------------------------
 1 | node = load('.\data\node.txt');
 2 | unit = load('.\data\unit.txt');
 3 | mat = load('.\data\mat.txt');
 4 | pre = load('.\data\pre.txt');
 5 | load = load('.\data\load.txt');
 6 | [node_num,~] = size(node);
 7 | [unit_num,~] = size(unit);
 8 | [pre_num,~] = size(pre);
 9 | [load_num,~] = size(load);
10 | D = mat(1)/(1-mat(2)^2)*[1,mat(2),0;mat(2),1,0;0,0,(1-mat(2))*0.5];
11 | B = zeros(3,6,unit_num);
12 | ke = zeros(6,6,unit_num);
13 | K = zeros(2*node_num);
14 | for i = 1:unit_num
15 |     [B(:,:,i),ke(:,:,i)] = To_Bke([node(unit(i,1)+1,1);node(unit(i,2)+1,1);node(unit(i,3)+1,1)],[node(unit(i,1)+1,2);node(unit(i,2)+1,2);node(unit(i,3)+1,2)],D,mat(3));
16 |     for j = 1:3
17 |          for k = 1:3
18 |              K(2*unit(i,j)+1,2*unit(i,k)+1) = K(2*unit(i,j)+1,2*unit(i,k)+1) + ke(2*j-1,2*k-1);
19 |              K(2*unit(i,j)+1,2*unit(i,k)+2) = K(2*unit(i,j)+1,2*unit(i,k)+2) + ke(2*j-1,2*k);
20 |              K(2*unit(i,j)+2,2*unit(i,k)+1) = K(2*unit(i,j)+2,2*unit(i,k)+1) + ke(2*j,2*k-1);
21 |              K(2*unit(i,j)+2,2*unit(i,k)+2) = K(2*unit(i,j)+2,2*unit(i,k)+2) + ke(2*j,2*k);
22 |          end
23 |     end
24 | end
25 | P = To_P(node_num,load_num,load);
26 | [pre,~] = sort(pre,1,'descend');
27 | for i = 1:pre_num
28 |     K(pre(i,1)+1,:)=[];
29 |     P(pre(i,1)+1)=[];
30 | end
31 | for i = 1:pre_num
32 |     K(:,pre(i,1)+1)=[];
33 | end
34 | clear mat node unit load pre;
35 | u = K\P;
36 | 


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/FEM/To_Bke.m:
--------------------------------------------------------------------------------
 1 | function [B,ke] = To_Bke(X,Y,D,t)
 2 | bi = Y(2)-Y(3);
 3 | ci = X(3)-X(2);
 4 | bj = Y(3)-Y(1);
 5 | cj = X(1)-X(3);
 6 | bm = Y(1)-Y(2);
 7 | cm = X(2)-X(1);
 8 | A = 0.5*(bj*cm - bm*cj);
 9 | B = 0.5 / A * [bi,0,bj,0,bm,0;
10 |                0,ci,0,cj,0,cm;
11 |                ci,bi,cj,bj,cm,bm];
12 | ke = B'*D*B*t*A;
13 | end


--------------------------------------------------------------------------------
/FEM/To_P.m:
--------------------------------------------------------------------------------
1 | function P = To_P(node_num,load_num,load)
2 | P = zeros(2*node_num,1);
3 | for i = 1:load_num
4 |     P(load(i,1)+1) = load(i,2);
5 | end
6 | end


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/FEM/data/2-5x.jpg:
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https://raw.githubusercontent.com/Ron-Wang/FEM-Matlab/5438235a09fcead03bc8565988bbc9360ee06fdc/FEM/data/2-5x.jpg


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/FEM/data/2-5x1.jpg:
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https://raw.githubusercontent.com/Ron-Wang/FEM-Matlab/5438235a09fcead03bc8565988bbc9360ee06fdc/FEM/data/2-5x1.jpg


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/FEM/data/2-5xy.jpg:
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https://raw.githubusercontent.com/Ron-Wang/FEM-Matlab/5438235a09fcead03bc8565988bbc9360ee06fdc/FEM/data/2-5xy.jpg


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/FEM/data/2-5xy1.jpg:
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https://raw.githubusercontent.com/Ron-Wang/FEM-Matlab/5438235a09fcead03bc8565988bbc9360ee06fdc/FEM/data/2-5xy1.jpg


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/FEM/data/2-5y.jpg:
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https://raw.githubusercontent.com/Ron-Wang/FEM-Matlab/5438235a09fcead03bc8565988bbc9360ee06fdc/FEM/data/2-5y.jpg


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/FEM/data/2-5y1.jpg:
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https://raw.githubusercontent.com/Ron-Wang/FEM-Matlab/5438235a09fcead03bc8565988bbc9360ee06fdc/FEM/data/2-5y1.jpg


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/FEM/data/Readme.md:
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1 | # 测试数据
2 | 


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/FEM/data/load.txt:
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1 | 25,25
2 | 27,50
3 | 29,25


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/FEM/data/mat.txt:
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1 | 200000,0.15,5


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/FEM/data/node.txt:
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 1 | 0,0
 2 | 5,0
 3 | 10,0
 4 | 0,5
 5 | 5,5
 6 | 10,5
 7 | 0,10
 8 | 5,10
 9 | 10,10
10 | 0,15
11 | 5,15
12 | 10,15
13 | 0,20
14 | 5,20
15 | 10,20


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/FEM/data/pre.txt:
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1 | 1,0
2 | 3,0
3 | 5,0
4 | 2,0


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/FEM/data/unit.txt:
--------------------------------------------------------------------------------
 1 | 4,3,0
 2 | 0,1,4
 3 | 5,4,1
 4 | 1,2,5
 5 | 7,6,3
 6 | 3,4,7
 7 | 8,7,4
 8 | 4,5,8
 9 | 10,9,6
10 | 6,7,10
11 | 11,10,7
12 | 7,8,11
13 | 13,12,9
14 | 9,10,13
15 | 14,13,10
16 | 10,11,14


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/README.md:
--------------------------------------------------------------------------------
 1 | # Finite-Element-Method (FEM)
 2 | 
 3 | 利用MATLAB编程，实现平面（应变）三角形单元的有限元静力学求解。  
 4 | 
 5 | ## 数据说明
 6 | *仅处理平面三角形单元*  
 7 | 
 8 | * node.txt  节点信息：x坐标，y坐标;  
 9 | * unit.txt  单元信息：节点号1，节点号2，节点号3;  
10 | * pre.txt  约束信息：自由度编号，约束条件(0表示位移为零);  
11 | * met.txt  材料信息：弹性模量E，泊松比ν，厚度t;  
12 | * load.txt  荷载信息（不计自重）：自由度编号，荷载大小;  
13 | 
14 | *其中节点编号、自由度编号均从0开始*  
15 | 
16 | ## 不同单元划分
17 | 
18 | ![image](https://github.com/Ron-Wang/FEM-Matlab/blob/master/FEM/2-5/2-5.png)  
19 | *另一单元划分为镜像*  
20 | 
21 | ## 计算结果 </br>
22 | * x方向（水平力）：  
23 | ![image](https://github.com/Ron-Wang/FEM-Matlab/blob/master/FEM/data/2-5x.jpg)  
24 | ![image](https://github.com/Ron-Wang/FEM-Matlab/blob/master/FEM/data/2-5x1.jpg)  
25 | 
26 | * y方向（竖直力）：  
27 | ![image](https://github.com/Ron-Wang/FEM-Matlab/blob/master/FEM/data/2-5y.jpg)  
28 | ![image](https://github.com/Ron-Wang/FEM-Matlab/blob/master/FEM/data/2-5y1.jpg)  
29 | 
30 | * xy方向（剪力）：  
31 | ![image](https://github.com/Ron-Wang/FEM-Matlab/blob/master/FEM/data/2-5xy.jpg)  
32 | ![image](https://github.com/Ron-Wang/FEM-Matlab/blob/master/FEM/data/2-5xy1.jpg)  
33 | 
34 | 


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