考虑多约束和载荷随机性的稳健结构拓扑优化设计
Robust Topology Optimization Designs of Structures under Multiple Constraints Stochastic Loads

考虑载荷大小和方向的不确定性，以结构柔顺度的期望和方差的加权和为目标函数，结构体积及多个结构位移为约束函数，研究可获得清晰优化拓扑的稳健结构多约束拓扑优化方法。给出了载荷大小和方向不确定情况下结构柔顺度期望和方差及其导数的显式近似式。结合可行域调整方案，提出具有收敛特征的结构体积和多位移约束的稳健结构柔顺度拓扑优化设计方法。研究了结构柔顺度期望和方差的权重因子对拓扑构型的影响，探讨了位移约束对结构稳健性的影响规律。算例表明，方法是可行和有效的，且可获得一系列清晰的拓扑构型和稳健的优化拓扑。
Considering stochastic cases of load values and directions, a robust structural topology optimization method for weighted sum minimizing problem of the expected value of the compliance and its variance with a volume constraint and multiple displacement constraints is proposed to obtain a clear optimal topology. Firstly, the explicit approximate expressions of the compliance expected value, its variance and their derivatives are derived. Secondly, the set of algorithms for robust structural topology optimization designs with multiple constraints are given, being integrated with an feasible domain adjustment scheme. The effects of the weighted coefficients of the expected value and variance of the compliance on the optimized solutions, and the effects of the multiple displacement constraints on the robustness of the optimal topology are investigated. The simulation examples show that the present method is feasible and effective, and can be adopted to obtain a series of clear topology configurations and a robust optimal topology