基于可靠性的结构动态拓扑优化方法

摘要

Actual engineering structures are often designed using deterministic parameters,which may lead to high failure probability.This paper proposed a reliability-based structural dynamic topology method,in which structural reliability analysis was incorporated into the topology optimization procedure.The geometry dimensions and material volume were considered as uncertain parameters,and it was assumed that they obey a Gaussian distribution.It is a two-nested optimization problem when the structural reliability analysis is considered as constraints into the topology optimization,which results in low efficiency and cannot be used in practice.To this end,a new decouple strategy was proposed to decouple the reliability analysis from the topology optimization procedure.In this case,structure reliability analysis and dynamic topology optimization become two independent optimization cycles,and the computational efficiency is improved enormously.The design problem was then constructed so as to maximize the first eigenfrequency and to meet the volume and reliability requirement.SIMP and MMA were combined to successfully solve the design problem.The proposed method can produce various topologies that satisfy different reliability requirement,and its validity is demonstrated by one benchmark example.%实际工程结构设计往往在确定性范畴内进行,所得结构存在较大失效可能性.基于此,提出一种基于可靠性的连续体动态拓扑优化方法,将结构可靠性分析方法嵌套到连续体拓扑优化中.考虑了结构几何尺寸和材料体积的不确定性,并用高斯分布来度量.将结构可靠度作为约束嵌套到连续体拓扑优化中,属于二次嵌套优化问题,但计算效率低下,不适于工程应用.提出一种解耦策略将结构可靠性分析从连续体拓扑优化中解耦出来,使结构可靠性分析与动态拓扑优化为两个独立的优化循环,大大提高了计算效率,建立以结构基频最大为优化目标,满足一定体积约束和可靠度要求的优化问题,利用各向同性材料惩罚模型(SIMP)和移动渐进方法(MMA)求解该优化问题.所提方法可以得到满足不同可靠度要求的一系列最优结构,并用标准算例验证其有效性.