Abstract To date, both the stress-related and multi-material topology optimization problems have been extensively studied. However, there are few works addressing the stress-constrained multi-material topology optimization (SMMTO) problem. Hence, a novel solution to the SMMTO problem is proposed in this paper based on the ordered SIMP method. To be specific, description of the multi-material elastic model is achieved with the ordered SIMP interpolation. More importantly, a novel ordered SIMP-like interpolation function is proposed to realize the relaxed and scaled stress interpolation, so that only a unique set of density variables are required for the SMMTO problem. Scaling of the stress measure plays a vital role in properly addressing the different yield limits. The global stress constraint is established with the p-norm function combined with the stability transformation method to close the gap between the p-norm stress and the exact maximum local stress. The adjoint sensitivity analysis is performed and the optimization problem is solved using a MMA optimizer. Several benchmark numerical examples are investigated and discussed to illustrate the effectiveness of the proposed approach.

中文翻译：

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使用有序 SIMP 方法进行应力约束多材料拓扑优化

摘要 迄今为止，应力相关和多材料拓扑优化问题都得到了广泛的研究。然而，很少有工作解决应力约束多材料拓扑优化 (SMMTO) 问题。因此，本文提出了一种基于有序 SIMP 方法的 SMMTO 问题的新解决方案。具体来说，多材料弹性模型的描述是通过有序的 SIMP 插值实现的。更重要的是，提出了一种新颖的有序类 SIMP 插值函数来实现松弛和缩放的应力插值，因此 SMMTO 问题只需要一组唯一的密度变量。应力测量的缩放在正确解决不同屈服极限方面起着至关重要的作用。通过p范数函数结合稳定性变换方法建立全局应力约束，以缩小p范数应力与精确最大局部应力之间的差距。执行伴随敏感性分析并使用 MMA 优化器解决优化问题。研究和讨论了几个基准数值示例，以说明所提出方法的有效性。