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Robust topology optimization for multi-material structures under interval uncertainty

机译：区间不确定性下多材料结构的鲁棒拓扑优化

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摘要

In this paper, we propose an efficient method to design robust multi-material structures under interval loading uncertainty. The objective of this study is to minimize the structural compliance of linear elastic structures. First, the loading uncertainty can be decomposed into two unit forces in the horizontal and vertical directions based on the orthogonal decomposition, which separates the uncertainty into the calculation coefficients of structural compliance that are not related to the finite element analysis. In this manner, the time-consuming procedure, namely, the nested double-loop optimization, can be avoided. Second, the uncertainty problem can be transformed into an augmented deterministic problem by means of uniform sampling, which exploits the coefficients related to interval variables. Finally, an efficient sensitivity analysis method is explicitly developed. Thus, the robust topology optimization (RTO) problem considering interval uncertainty can be solved by combining orthogonal decomposition with uniform sampling (ODUS). In order to eliminate the influence of numerical units when comparing the optimal results to deterministic and RTO solutions, the relative uncertainty related to interval objective function is employed to characterize the structural robustness. Several multi-material structure optimization cases are provided to demonstrate the feasibility and efficiency of the proposed method, where the magnitude uncertainty, directional uncertainty, and combined uncertainty are investigated. (C) 2019 Elsevier Inc. All rights reserved.
机译：在本文中，我们提出了一种在间隔载荷不确定性下设计鲁棒多材料结构的有效方法。这项研究的目的是最小化线性弹性结构的结构柔度。首先，基于正交分解，可将载荷不确定性分解为水平和垂直方向上的两个单位力，从而将不确定性分为与有限元分析无关的结构柔韧性计算系数。以这种方式，可以避免耗时的过程，即嵌套的双循环优化。其次，不确定性问题可以通过统一采样转化为扩充确定性问题，该采样利用与区间变量相关的系数。最后，明确开发了一种有效的灵敏度分析方法。因此，可以通过将正交分解与均匀采样（ODUS）相结合来解决考虑区间不确定性的鲁棒拓扑优化（RTO）问题。为了在将最佳结果与确定性和RTO解进行比较时消除数值单元的影响，采用与区间目标函数相关的相对不确定性来表征结构的稳健性。提供了几种多材料结构优化案例，以证明该方法的可行性和有效性，其中研究了幅​​度不确定性，方向不确定性和组合不确定性。 （C）2019 Elsevier Inc.保留所有权利。

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