随机位移法解桁架结构的非线性弹性问题

Random Displacement Method on Analysing Truss Nonlinear Elastic Structure

尝试用一种新的力学计算方法——随机位移法来分析桁架的非线性弹性问题．其基本思想是借用有限元法的离散技术，将一个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，由分片插值方法未出各单元位移，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．从而将一个力学问题转化为一个优化问题，然后利用遗传算法求其最优解，即得各节点位移．由各书点位移和单元的几何、物理方程可求出各单元的应变和应力，算例表明，该方法是简便而又可行的．

A new mechanics method, random displacement method, wsas used to analyse nonlinoor elastic structure. For analysing, a structure was discreted into elements and nodes, then the nodal displacements were chosen to study variables and used to form the total portential energy of the structure. The mechanics problem was transformed into a minimum optimal problem by using the minimum potential energy principle. The genetic algorithm was applied to solve the optimal problem. By means of this method,the nodal displacements were worked out. Numerical computing results show that the new method was feasible and effective in analying nonlinear elastic structure.