考虑载荷不确定性的多材料结构稳健拓扑优化

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振动与冲击 ›› 2019, Vol. 38 ›› Issue (19) : 182-190.

论文

赵清海1,2,张洪信2,蒋荣超2,华青松1,2,袁林2

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Robust topology optimization design of a multi-material structure considering load uncertainty

ZHAO Qinghai1,2, ZHANG Hongxin2, JIANG Rongchao2, HUA Qingsong1,2, YUAN Lin2

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摘要

传统的拓扑优化设计通常基于单材料与确定性条件，往往难以兼顾结构性能的稳健性。针对实际工程中载荷不确定性问题，研究多材料结构稳健拓扑优化设计方法。基于有序各向同性微结构材料惩罚模型法（Ordered-Solid Isotropic Microstructures with Penalization, Ordered-SIMP），进行多材料插值模型表征。构建载荷概率分布条件下结构柔度均值与标准差的加权目标函数，辅以体积约束。针对载荷满足随机场分布时，采用Karhunen-Loève展开将载荷随机场变换为有限个不相关的载荷随机变量加权和，并借助稀疏网格数值积分方法，将多材料结构稳健拓扑优化转化为求解一组多工况加权多目标确定性拓扑优化设计问题。通过数值算例验证所提方法的有效性与优化结果的稳健性。结果表明：针对不同材料组合方案，均能有效获得良好的多材料拓扑构型；与确定性设计相比较，稳健设计具有不同的材料布局方案，且结构性能更加稳定。

Abstract

The traditional topology optimization design is generally based on single-material and deterministic conditions, it is difficult to consider the robustness of structural performance. Here, aiming at the load uncertainty in practical engineering, the robust topology optimization design methodwas studied. The multi-material interpolation model was characterized based on the ordered-solid isotropic microstructures with penalization (Ordered-SIMP). The weighted objective function forthe mean and standard deviation of structural flexibility under the load probability distribution was constructedand assisted by volume constraints. When load satisfied the random field distribution, the load random field was transformed into a weighted sum of finite uncorrelated load random variables using Karhunen-Loèveexpansion, and the sparse grid numerical integration method was employed to convert the robust topology optimization of multi-material structure into solving a set of multi-condition weighted multi-objective deterministic topology optimization design problems. The effectiveness of the proposed method and the robustness of optimization resultswere verified with numerical examples. The results demonstrated that good topological configurationscan be effectively achieved for combination schemes of different materials;compared with deterministic designs, robust designs can have different material layout schemes and more stable structural performance.

关键词

多材料 / 拓扑优化 / 稳健设计 / 稀疏网格 / 载荷不确定性

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赵清海1,2,张洪信2,蒋荣超2,华青松1,2,袁林2. 考虑载荷不确定性的多材料结构稳健拓扑优化[J]. 振动与冲击, 2019, 38(19): 182-190

ZHAO Qinghai1,2, ZHANG Hongxin2, JIANG Rongchao2, HUA Qingsong1,2, YUAN Lin2. Robust topology optimization design of a multi-material structure considering load uncertainty[J]. Journal of Vibration and Shock, 2019, 38(19): 182-190

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