应力和位移约束下桁架拓扑优化的有无复合体方法

EXIST-NULL COMBINATION METHOD FOR THE TOPOLOGICAL OPTIMIZATION OF TRUSS WITH STRESS AND DISPLACEMENT CONSTRAINT

按照独立连续拓扑变量的思想 ,将有无复合体模型由构造应力约束问题发展为应力与位移约束问题 ,用于桁架结构拓扑优化 .基于该文提出的位移约束与拓扑变量关系的近似显式 ,建立了具有应力、位移约束下桁架结构拓扑优化的有无复合体模型 ,用序列二次规划算法求解 .数值结果令人满意 .这一工作表明独立连续拓扑变量的提出对于结构拓扑优化的研究是有价值的 .

In terms of the idea of independent and continuous topological variables, the exist-null combined model which was proposed by the authors is generalized in this paper through considering the topological optimization of truss structures. With stress and displacements constrains based on the explicit formulation between topological variables and displacement constraints presented in this paper, the mathematical model of the truss topological optimization with stress and displacement constraints is establised. The sequential algorithm of the quadratic programming is used to solve the problem. Numerical results are given. It is shown that the introduction of the dependent and continuous topological variables is valuable to the research of structural topology optimization.