Considering structural strength and castability in topology optimization is very attractive from the perspective of theory and application. This article introduces stress considerations into casting-oriented topology optimization to explore structural optimization methods that simultaneously consider the above two vital design indicators. Two stress-related topology optimization formulations for castable design are proposed and assessed systematically, namely, a compliance minimization with stress and casting constraints and a stress minimization with casting constraint. An effective optimization algorithm is developed to overcome various numerical difficulties caused by stress and castability issues in the solution. Particularly, a nonuniform threshold scheme along with the corresponding implementation algorithm is proposed to improve the casting constraint on irregular structures without appreciably increased computational effort. Benchmark examples are presented to discuss the numerical characteristics of the achieved designs and demonstrate the effectiveness of the introduced algorithms. This research illustrates the necessity and feasibility of stress considerations in casting-oriented topology optimization. The results show that it is more appropriate to treat stress as a constraint rather than an optimization objective in the casting-constrained topology optimization. The proposed formulations and algorithms allow designers to effectively achieve high-performance castable designs with required structural strength requirements.

中文翻译：

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用于浇注料设计的应力相关拓扑优化

在拓扑优化中考虑结构强度和可铸性从理论和应用的角度来看是非常有吸引力的。本文将应力考虑引入面向铸件的拓扑优化中，探索同时考虑上述两个重要设计指标的结构优化方法。提出并系统地评估了两种与应力相关的浇注料设计拓扑优化公式，即具有应力和铸造约束的柔度最小化以及具有铸造约束的应力最小化。开发了一种有效的优化算法，以克服解决方案中由应力和可铸性问题引起的各种数值困难。特别，提出了一种非均匀阈值方案以及相应的实现算法，以在不明显增加计算量的情况下改善对不规则结构的铸造约束。提供了基准示例来讨论所实现设计的数值特性并证明所引入算法的有效性。本研究说明了在面向铸造的拓扑优化中考虑应力的必要性和可行性。结果表明，在铸造约束拓扑优化中，将应力视为约束而不是优化目标更为合适。所提出的公式和算法使设计人员能够有效地实现具有所需结构强度要求的高性能浇注料设计。