考虑载荷随机性的可行域调整的结构拓扑优化设计

Feasible Domain Adjustment Topology Optimization Designs of Structures under 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,结构体积为约束函数,研究稳健结构拓扑优化方法。首先给出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,而后改进可行域调整方案,提出具有收敛特征的稳健结构拓扑优化设计方法,探讨结构柔顺度期望和方差的权重因子以及随机量的方差对拓扑构型的影响。给出的算例表明,不论是确定载荷拓扑优化还是随机载荷拓扑优化,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 the weighted sum minimizing problem of the expected value of the compliance and its variance with a volume constraint, is proposed. Firstly, explicit approximate expressions of the compliance expected value, its variance and their derivatives are derived. Secondly, an improved feasible domain adjustment scheme and a set of algorithms for robust structural topology optimization designs are given. The effects of the weighted coefficients of the objective function and the variance of the perturbations on the optimized solutions, are investigated. Given simulation examples show that no matter determine load topology optimization or random load topology optimization,the proposed method is feasible and effective, and can be adopted to obtain a series of clear topology configurations and a robust optimal topology.