四边形八节点matlab.docx
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四边形八节点matlab.docx
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四边形八节点matlab
有限单元法作业
四边形八节点示例(自重作用下的位移分析)
定义材料性质:
划分单元网格
示意图如下
求形参
对形参求导
求雅克比矩阵
求单元刚度矩阵
求总刚
求荷载
引入边界条件
求解
结果如下:
工程实例:
牛腿受力计算,如图示:
定义材料参数
离散化
单元坐标
NODE=[195616
194756
481317
481513
5029
5072
3913
39381
596665
593666
636057
636160
674720
674647
424443
424144
684326
684243
346933
344069
316940
693033
313069
426828
682128
262168
466722
671822
201867
356636
666465
356466
403659
631262
606564
546435
645760
63812
314059
626163
486212
621716
586061
605565
555965
592731
545764
57863
114812
166162
615658
535856
481762
165661
564753
585560
415558
552759
534158
544957
545149
395254
49857
412755
403236
353954
504951
534441
501049
525154
474653
464553
454453
45239
55152
51650
234546
244445
254344
422941
3439
4552
5651
6750
91050
10849
111448
141548
192047
222346
232445
242544
252643
282942
292741
343240
353739
373839];
节点坐标:
COOR=[0.000000000000.00000000000
0.6000000000000.00000000000
0.1000000000000.00000000000
0.2000000000000.00000000000
0.3000000000000.00000000000
0.4000000000000.00000000000
0.5000000000000.00000000000
0.6000000000000.300000000000
0.6000000000000.100000000000
0.6000000000000.200000000000
1.200000000000.830000000000
0.9000000000000.565000000000
1.200000000001.10000000000
1.200000000000.920000000000
1.200000000001.01000000000
0.6000000000001.10000000000
0.9000000000001.10000000000
0.6000000000001.40000000000
0.6000000000001.20000000000
0.6000000000001.30000000000
0.000000000001.40000000000
0.5000000000001.40000000000
0.4000000000001.40000000000
0.3000000000001.40000000000
0.2000000000001.40000000000
0.1000000000001.40000000000
0.000000000001.10000000000
0.000000000001.30000000000
0.000000000001.20000000000
-0.6000000000001.10000000000
-0.3000000000001.10000000000
-0.6000000000000.830000000000
-0.6000000000001.01000000000
-0.6000000000000.920000000000
0.000000000000.300000000000
-0.3000000000000.565000000000
0.000000000000.200000000000
0.000000000000.100000000000
0.1159376540270.150000000000
-0.4032303696290.876234924455
0.1414213562371.15000000000
0.935269118376E-011.27036541094
0.1376990442021.34262247197
0.2168022175441.29104549929
0.3371839179311.32364125770
0.4292877937771.31766605561
0.4940647565941.24596904004
1.025715749420.965000000000
0.4542108618930.240132709409
0.5028686110050.935929145200E-01
0.3658694151430.115017692231
0.2479486369590.107078360362
0.3429565703041.20959814379
0.2579361156250.270374109581
0.1202769982950.939989503139
0.4712367608691.11681030424
0.3981851387270.457322100165
0.3154013233351.01529247286
-0.1142390678900.841409546731
0.3113963793370.752586420750
0.5051198749650.922770465237
0.7510790581220.885894350169
0.5776300751920.647262222720
0.1792596132230.521562494628
0.917388160693E-010.736058406596
-0.286481277195E-010.592806089591
0.5246705100741.33272701913
0.652388530423E-011.33852449439
-0.5006460739261.00124698489];
网格显示:
显示结果如下:
初始化
形参
单元刚度矩阵
体力
集中荷载
引入边界条件
求解
结果如下:
ans=
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-2.5179e-6
-2.658e-6
4.3222e-6
-1.355e-6
-6.5653e-6
1.8075e-6
9.0003e-6
-6.4186e-6
6.7654e-6
-0.000021457
-0.000018249
-7.8807e-6
0.000024898
9.4667e-6
-8.9103e-6
-0.000013477
-0.000010047
0.000072777
-0.000032123
0.00013444
0
-55.9
-0.000015178
-0.000040611
-6.2254e-7
0.00001808
0
-49.672
0
0
0
0
0
0
0
0
0
0
-8.6097e-6
1.8748e-6
-3.5153e-8
7.7191e-7
9.6856e-7
-1.7328e-6
-0.000012788
0.00002064
-0.000019666
0.000062352
6.4663e-6
8.6302e-6
-8.6761e-6
0.000013339
6.7897e-7
-0.000011903
-0.000029059
1.2631e-6
8.0712e-6
0.000025956
-0.000025311
-0.000057477
-0.000035149
0.00013154
-0.000014439
0.000050496
2.6262e-6
-0.000030881
-3.7732e-6
2.7239e-6
2.9753e-7
-8.2062e-7
-1.4597e-7
1.9484e-7
-5.0318e-7
2.3168e-7
-3.4713e-7
-1.3173e-7
-1.4993e-6
2.1689e-7
-8.1358e-6
-2.8565e-6
9.8974e-6
-0.000062791
-0.000012565
7.5908e-6
4.2532e-6
-3.5373e-6
1.4444e-6
-2.1787e-6
-1.9704e-6
4.5535e-6
-3.9993e-6
1.1964e-6
-0.000023971
0.000018131
-2.2593e-6
-4.8703e-6
1.6204e-6
0.000010678
1.7695e-6
-5.3775e-6
-1.1273e-6
-8.3521e-7
-5.7721e-6
-0.000019108
5.5301e-6
-4.3693e-6
-3.4188e-6
-0.000019993
3.1499e-6
-0.000044307
9.4287e-6
2.1447e-6
6.3059e-6
-6.8809e-6
9.1488e-7
-5.4441e-6
9.2092e-6
6.1594e-6
-1.4782e-6
1.615e-6
-2.8617e-7
4.8944e-7
-8.0106e-6
-3.9688e-6
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