第一篇:《有限元平面问题》
NODE X-COMP Y-COMP NODE X-COMP Y-COMP 1 2.99508E-04 2.83161E-28 51 1.63076E-04 7.38998E-04 2 2.82112E-04 5.60467E-28 52 1.81720E-04 8.85926E-04 3 2.67142E-04 6.32250E-28 53 2.05863E-04 1.06709E-03 4 2.55889E-04 7.13968E-28 54 2.37816E-04 1.28691E-03 5 2.49478E-04 8.10222E-28 55 2.79384E-04 1.55030E-03 6 2.48867E-04 9.26477E-28 56 1.67621E-04 3.95546E-04 7 2.54877E-04 1.06915E-27 57 1.34628E-04 4.12963E-04 8 2.68240E-04 1.24602E-27 58 1.18134E-04 4.42427E-04 9 2.89659E-04 10 3.19826E-04 11 3.59299E-04 12 2.84856E-04 13 2.65541E-04 14 2.49518E-04 15 2.38113E-04 16 2.32306E-04 17 2.32797E-04 18 2.40070E-04 19 2.54507E-04 20 2.76415E-04 21 3.05906E-04 22 3.42448E-04 23 2.58373E-04 24 2.33092E-04 25 2.14285E-04 26 2.02686E-04 27 1.98425E-04 28 2.01203E-04 29 2.10667E-04 30 2.26536E-04 31 2.48566E-04 32 2.76618E-04 33 3.11583E-04 34 2.27012E-04 35 1.95870E-04 36 1.76176E-04 37 1.66745E-04 38 1.65708E-04 39 1.71612E-04 40 1.83533E-04 41 2.00907E-04 42 2.23579E-04 43 2.52415E-04 1.46699E-27 1.74617E-27 9.85121E-28 1.19117E-04 1.31016E-04 1.43059E-04 1.56429E-04 1.72401E-04 1.92334E-04 2.17709E-04 2.50207E-04 2.91966E-04 3.46226E-04 4.19035E-04 2.20761E-04 2.40435E-04 2.61146E-04 2.85894E-04 3.17393E-04 3.58231E-04 4.10964E-04 4.78422E-04 5.64153E-04 6.72884E-04 8.10198E-04 2.97121E-04 3.20157E-04 3.47396E-04 3.83763E-04 4.32907E-04 4.97812E-04 5.81487E-04 6.87492E-04 8.20157E-04 9.84106E-04 59 1.11877E-04 60 1.12335E-04 61 1.17739E-04 62 1.27202E-04 63 1.40406E-04 64 1.57738E-04 65 1.80611E-04 66 2.10267E-04 67 1.25167E-04 68 9.76741E-05 69 8.46360E-05 70 7.94215E-05 71 7.89998E-05 72 8.20023E-05 73 8.77858E-05 74 9.61249E-05 75 1.07235E-04 76 1.21904E-04 77 1.41089E-04 78 6.85829E-05 79 5.16721E-05 80 4.43001E-05 81 4.13546E-05 82 4.09276E-05 83 4.22439E-05 84 4.49651E-05 85 4.89786E-05 86 5.43883E-05 87 6.15651E-05 88 7.09743E-05 89 4.86901E-28 90 6.94898E-28 91 6.75913E-28 92 7.13050E-28 93 7.83428E-28 4.89332E-04 5.55918E-04 6.44337E-04 7.57486E-04 8.99168E-04 1.07399E-03 1.28705E-03 1.54426E-03 4.42083E-04 4.50096E-04 4.74500E-04 5.17931E-04 5.81422E-04 6.66575E-04 7.75955E-04 9.13100E-04 1.08246E-03 1.28928E-03 1.53964E-03 4.80750E-04 4.78456E-04 4.98618E-04 5.39550E-04 6.00878E-04 6.83720E-04 7.90405E-04 9.24304E-04 1.08975E-03 1.29196E-03 1.53718E-03 5.03364E-04 4.89770E-04 5.07381E-04 5.47475E-04 6.08168E-04{1.63761E,19}.
44 2.90617E-04 1.18201E-03 94 8.81682E-28 6.90264E-04 45 1.96913E-04 3.49379E-04 95 1.00767E-27 7.96004E-04 46 1.61878E-04 3.74459E-04 96 1.16369E-27 9.28702E-04 47 1.44164E-04 4.08957E-04 97 1.35450E-27 1.09263E-03 48 1.38295E-04 4.59561E-04 98 1.58801E-27 1.29296E-03 49 1.40654E-04 5.29539E-04 99 8.50264E-28 1.53573E-03 50 1.49265E-04 6.21589E-04
NODAL REACTIONS
NODE X-COMP Y-COMP NODE X-COMP Y-COMP 1 0.0 -2.83161 89 -4.86901 0.0 2 0.0 -5.60467 90 -6.94898 0.0 3 0.0 -6.3225 91 -6.75913 0.0 4 0.0 -7.13968 92 -7.1305 0.0 5 0.0 -8.10222 93 -7.83428 0.0 6 0.0 -9.26477 94 -8.81682 0.0 7 0.0 -10.69146 95 -10.07665 0.0 8 0.0 -12.46017 96 -11.63689 0.0 9 0.0 -14.6699 97 -13.54497 0.0 10 0.0 -17.46171 98 -15.88009 0.0 11 0.0 -9.85121 99 -8.50264 0.0
ELEMENT STRESSES
IEL SIG XX SIG YY TAU XY IEL SIG XX SIG YY TAU XY 1 0.2802 9.40426 -0.50892 81 4.58932 6.24679 -4.15107 2 0.20145 8.50994 -1.05488 82 3.3539 5.53969 -2.86679 3 0.89848 8.83604 -0.45051 83 4.81847 5.65334 -2.41878 4 0.92284 8.00302 -0.97832 84 3.77605 5.24738 -1.79273 5 1.471 8.25979 -0.38162 85 4.49774 5.55101 -1.40793 6 1.57591 7.55408 -0.84507 86 3.83351 5.34118 -1.10094 7 1.97052 7.73786 -0.31019 87 4.18421 5.60886 -0.85314 8 2.11722 7.1764 -0.69148 88 3.77657 5.501 -0.68692 9 2.38479 7.29935 -0.24347 89 3.95237 5.69226 -0.53617 10 2.53824 6.87386 -0.54133 90 3.69331 5.63579 -0.43606 11 2.71381 6.95247 -0.18634 91 3.78476 5.76366 -0.34408 12 2.84914 6.64427 -0.40784 92 3.60807 5.7332 -0.27712 13 2.96565 6.694 -0.14129 93 3.65662 5.81298 -0.21839 14 3.07063 6.48311 -0.29624 94 3.52763 5.79679 -0.16906 15 3.15273 6.51568 -0.10865 95 3.55105 5.83454 -0.12611 16 3.22386 6.38709 -0.205 96 3.45926 5.82799 -0.08913 17 3.28799 6.41043 -0.08769 97 3.46398 5.82481 -0.05104 18 3.32527 6.36014 -0.12656 98 3.41475 5.82438 -0.02951 19 3.38171 6.37932 -0.07784 99 3.40994 5.80444 -0.00225 20 3.38591 6.42607 -0.04445 100 3.39006 5.80125 0.00101{1.63761E,19}.{1.63761E,19}.
65 3.82553 6.01735 -1.58462 145 5.53823 4.58722 -0.16361 66 3.74817 5.69087 -1.29184 146 4.49467 4.32655 67 3.71388 5.79727 -1.01736 147 4.80622 5.06 68 3.78734 5.76209 -0.83069 148 4.17207 4.89165 69 3.63333 5.76341 -0.66087 149 4.35661 5.34996
-0.36283 -0.09201 -0.22101 -0.05734
70 3.74326 5.8235 -0.54013 150 3.94529 5.24184 -0.14242 71 3.57043 5.78958 -0.43186 151 4.05931 5.53673 -0.03644 72 3.67263 5.86836 -0.35253 152 3.77769 5.46518 -0.09474 73 3.51208 5.82606 -0.27741 153 3.85004 5.65851 -0.02217 74 3.59503 5.89385 -0.22357 154 3.64895 5.60999 -0.0634 75 3.45147 5.85173 -0.16394 155 3.69471 5.73561 -0.01149 76 3.51897 5.89069 -0.12461 156 3.54926 5.70313 -0.04066 77 3.39499 5.85224 -0.07269 157 3.57629 5.77903 -0.00293 78 3.45535 5.84715 -0.0427 158 3.47581 5.75954 -0.02214 79 3.37516 5.82117 -0.012 159 3.48808 5.79472 0.00421 80 3.41703 5.79491 0.00405 160 3.42481 5.78816 -0.00571 ********************** THE END ********************** 五、分析讨论： 1、正确性验证
a.水平外边界上的单元号分别是20,40,60,80他们的水平应力分别是3.38591, 3.44523, 3.44953, 3.41703单位都是MPa和水平分布荷载3.4MPa相比较误差小于0.5MPa
b.竖直外边界上的单元号分别是100,120,140,160他们的竖向应力分别是5.80125, 5.80617, 5.7994, 5.78816单位都是MPa和竖向分布荷载5.8MPa相比较误差小于0.5MPa
c.计算模型竖向约束反力分别是-2.83161,-5.60467,-6.3225,-7.13968,-8.10222,-9.26477, -10.69146,-12.46017,-14.6699,-17.46171,-9.85121之和为-104.4。而作用模型上表面的竖向{1.63761E,19}.
荷载为6×3×5.8=104.4,因此误差小于0.005MN
d.计算模型水平约束反力分别是-4.86901,-6.94898,-6.75913,-7.1305,-7.83428 -8.81682,-10.07665,-11.63689,-13.54497,-15.88009,-8.50264之和为-102。而作用模型右表面的水平荷载为6×5×5.8=102，因此误差小于0.005MN 因此验算之后计算正确
2、分析应力、位移分布：
a、邻近水平轴各单元水平应力与竖向应力和单元横向坐标的关系曲线图 1
2{1.63761E,19}.{1.63761E,19}.
b、邻近竖直轴各单元水平应力与竖向应力和单元竖向坐标的关系曲线图
1）邻近竖直轴各单元水平应力与竖向坐标的关系曲线数据准备如下：