静动载约束桁架结构拓扑优化的微分演化算法

Differential Evolution Algorithm for the Topology Optimization of Truss Structure with Static and Dynamic Constraints

结构在使用期内严重的动载激励下,频率影响变得非常重要且不能被忽视。为了获得全局最优解和解决固有频率、应力、位移、屈曲以及动态失稳等静动荷载约束耦合给优化问题带来的困难,将微分演化算法(differential evolution, DE)应用于桁架结构的拓扑优化问题中。以结构重量极小化为目标函数,采用同时考虑桁架尺寸和拓扑变量的一阶段分析法,建立了多工况荷载作用的桁架拓扑优化数学模型,该模型能较好地解决奇异最优解和不必要分析的问题。算例结果表明:所提的分析方法能够有效、方便地对桁架结构进行拓扑优化设计。

When the structure is under severe dynamic excitation during the service life,the effect of frequencies becomes momentous and cannot be ignored.Differential Evolution Algorithm(DEA)is introduced in the topology optimization of truss structures to get the global optimal solution and overcome the difficulties of natural frequency,stress,displacement,buckling and dynamic instability brought by the coupling of static and dynamic constraints.This paper takes the structural weight minimization as the objective function,and adopts single stage method which considers truss size and topology variables simultaneously to formulate a mathematical model for truss topology optimization with multiple loading conditions.The model can effectively solve singular optimization solution and problems that are unnecessary to analyze.Several examples demonstrate that the proposed method can effectively and conveniently optimize the topology design of truss structure.