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Robust multiphase topology optimization accounting for manufacturing uncertainty via stochastic collocation

机译：通过随机搭配制造不确定性的鲁棒多相拓扑优化核算

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This paper presents a computational framework for multimaterial topology optimization under uncertainty. We combine stochastic collocation with design sensitivity analysis to facilitate robust design optimization. The presence of uncertainty is motivated by the induced scatter in the mechanical properties of candidate materials in the additive manufacturing process. The effective elastic modulus in each finite element is obtained by an interpolation scheme which is parameterized with three distinct elastic moduli corresponding to the available design materials. The parametrization enables the SIMP-style penalization of intermediate material properties, thus ensuring convergence to a discrete manufacturable design. We consider independent random variables for the elastic modulus of different materials and generate designs that minimize the variability in the performance, namely structural compliance. We use a newly developed quadrature rule, designed quadrature, to compute statistical moments with reduced computational cost. We show our approach on numerical benchmark problems of linear elastic continua where we demonstrate the improved performance of robust designs compared with deterministic designs. We provide the MATLAB implementation of our approach.
机译：本文介绍了不确定性下多国拓扑优化的计算框架。我们将随机搭配与设计敏感性分析相结合，以促进强大的设计优化。不确定性的存在是通过在添加剂制造过程中候选材料的机械性能的诱导散射来激发。每个有限元中的有效弹性模量通过插值方案获得，该内插方案用与可用设计材料对应的三种不同的弹性模量进行参数化。参数化能够实现中间材料特性的SIMP风格，从而确保了分立的可铺展设计的收敛性。我们考虑不同材料弹性模量的独立随机变量，并产生最小化性能变化，即结构顺应性的设计。我们使用新开发的正交规则设计正交，以计算计算成本降低的统计矩。我们展示了线性弹性连续型数值基准问题的方法，我们展示了与确定性设计相比强大设计的改进性能。我们提供了MATLAB的实现我们的方法。

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