直梁的有限元分析

1、计算机辅助工程分析计算机辅助工程分析内容内容2 有限元法的直接刚度法有限元法的直接刚度法 2.1 直梁的有限元分析直梁的有限元分析要求要求 了解：了解：单元、节点单元、节点的概念的概念 理解：梁单元理解：梁单元节点内力、节点载荷节点内力、节点载荷的概念的概念 梁梁单元刚度矩阵单元刚度矩阵的概念的概念 掌握：梁单元刚度矩阵的建立办法掌握：梁单元刚度矩阵的建立办法 利用利用节点平衡节点平衡组装整体刚度组装整体刚度作业作业 超静定悬臂梁的有限元分析超静定悬臂梁的有限元分析上节回顾上节回顾整体离散单元组装上节回顾上节回顾本节提要一个例题：MDCBAZ212343ZM4321ZM4321M4321ijq

2、imiqjmj ,eTiijjpq m q m ,eTiijjffjfifjiijjqimiqjmjjfifjiij11121314212223243132333441424344iiijjiiijjjiijjjiijjqa faa famafaafaqa faafamafaafa11121314212223243132333441424344iiijjiiijjjiijjjiijjqa faa famafaafaqa faafamafaafa11121314212223243132333441424344iiiijjjjqfaaaamaaaaqfaaaamaaaa eeepKep eeK11

3、121314112122232421313233343141424344411000iijjqaaaaamaaaaaqaaaaamaaaaa 1,0,0,0iijjff1if 1if 11312iEIqal2126iEImal1i11121314122122232422313233343241424344420100iijjqaaaaamaaaaaqaaaaamaaaaa 0,1,0,0iijjff1226iEIqal224iEImal1i3232111213142221222324313233343232414243442212612664621261266264eEIEIEIEIlllla

4、aaaEIEIEIEIaaaallllKaaaaEIEIEIEIllllaaaaEIEIEIEIllll ,eTiijjff ,eTiijjpq m q m eeepK2q11m11q21m2113q22m22q32m3224q33m33q43m43311122111312222122126126646221261266264fllqllllmEIflllqllllm 22222222323322233126126646221261266264fllqllllmEIflllqllllm 3332233333442234412612664621261266264fllqllllmEIflllql

5、lllmM4321Z1M1m11q11Z4M4m43q43Z2M2m22q22q21m21Z3M3m33q33q32m32Z1M1m11q1100YM111112231221111223212612626462EIZqflfllEIMmlfllfll00YM1222211223223331222222112232222333212612621261262626426462EIZqqflfllEIflfllEIMmmlfllfllEIlfllfllZ2M2m22q22q21m21Z4M4m43q43Z3M3m33q33q32m32 11223344,TQZ M ZMZ MZM QK Q 1122

6、3344,Tffff K 222222322222212612600006462000012612 126 612600626 6 44620020012612 66 36300626 3 42300006363000033 2llllllllllllllllllEIKlllllllllllllllllll 对称，稀疏，奇异，主对角元恒正 QK122122222233222234412612600006462000012612 12661260062664462002000126126636300062634230000636300000ZllMllllZZllllMMllllllllEIZl

7、llllMllllllllZllM1122334224000332ffffllll122122222233222234412612600006462000012612 12661260062664462002000126126636300062634230000636300000ZllMllllZZllllMMllllllllEIZlllllMllllllllZllM1122334224000332ffffllll22223322232242401260086202012618330623600032fZlmlllEIfllllllllllll 对称，稀疏，非奇异，主对角元恒正 22223322232242401260086202012618330623600032fZlmlllEIfllllllllllll 11223344,Tffff本节课小结第一步，对直梁进行离散化，划分为有限个单元。第二步，对各结点和单元进行编码。第三步，