随机位移法解小挠度薄板弯曲问题

RANDOM DISPLANCEMEMT METHOD ON ANALYSING BENDING PLATE

应用一种新的力学计算方法——随机位移法来分析小挠度薄板弯曲问题 .计算时先借用有限元法的离散技术 ,将薄板结构离散成若干个单元和节点 ,以节点位移为基本未知量并给其以一定范围内的随机初值 ,由分片插值方法求出各单元位移 ,并由此获得各单元的应变能和结构的总势能 .根据最小势能原理 ,当结构的总势能最小时 ,所给的节点位移为真实位移 .这时若以总势能为目标函数 ,利用遗传算法求其最优解 。

A new mechanical method,random displacement method,was used to analyse bending plates.In analysing,a plate was discreted into elements and nodes,and then the nodal displacements were chosen to be study variables and used to form the potential energy of the plate.The mechanical problem was transformed into a minimum optimal problem by using the minimum potential energy principle.The genetic alogrithm was applied to solve the optimal problem.By this means the nodal displacements were worked out.Numerical computing results show that the new method is feasible and effective in analying bending plates.