基于功能度量法的刚性结构可靠性拓扑优化

相对尺寸优化和形状优化，结构拓扑优化可以更大程度上节约材料和改善设计；实际工程中必然存在着各种不确定性因素，从而考虑不确定性的可靠性拓扑优化逐渐成为研究热点。本文考虑载荷和材料参数的不确定性，采用功能度量法进行可靠性评估，基于变密度法开展了刚性结构的可靠性拓扑优化设计。通过四角支撑平面板、L型梁和二维三维悬臂梁算例，分析拓扑构型与体积分数随目标可靠指标、随机变量个数以及变异系数的变化情况，结果表明，可靠性拓扑优化设计能得到既符合最优传力路径又满足可靠性要求的刚性结构。

Reliability-based topology optimization of rigid structures using performance measure approach

Compared with size optimization and shape optimization, structural topology optimization can save materials and improve the design to a greater extent.There must be various uncertain factors in practical engineering, so reliability-based topology optimization (RBTO) considering uncertainty has gradually become a research hotspot.Considering the uncertainty of load and material parameters and using performance measure approach for reliability evaluation, this paper has carries out RBTO of rigid structures based on variable density method.Through examples of a four-corner-supported flat panel, an L-shaped beam and a 2-D and a 3-D cantilever beams, the effects of target reliability index, and the number and coefficient of variation of random variables on the topological configuration and volume fraction are analyzed.The results show that RBTO can obtain a rigid structure that meets both the optimal force-transferring-path and the reliability requirements.