Lattice-like structures can provide a combination of high stiffness with light weight that is useful in many applications, but a resolved finite element mesh of such structures results in a computationally expensive discretization. This computational expense may be particularly burdensome in many-query applications, such as optimization. We develop a stress-constrained topology optimization method for lattice-like structures that uses component-wise reduced order models as a cheap surrogate, providing accurate computation of stress fields while greatly reducing run time relative to a full order model. We demonstrate the ability of our method to produce large reductions in mass while respecting a constraint on the maximum stress in a pair of test problems. The ROM methodology provides a speedup of about 150x in forward solves compared to full order static condensation and provides a relative error of less than 5% in the relaxed stress.

翻译：高硬度和轻重结构可以提供在许多应用中有用的高硬度和轻重组合,但这种结构的固定的有限元素组合导致计算成本昂贵的离散。这种计算成本在诸如优化等许多细小应用中可能特别繁琐。我们开发了一种压力限制的顶层优化方法,用于以低压减序模型作为廉价替代器的衬垫结构,提供准确的应力场计算,同时大大缩短运行时间相对于全序模型的比重。我们展示了我们的方法能够大量减少质量,同时尊重对一对测试问题的最大压力的限制。ROM方法提供了与全顺序静凝聚相比的大约150x的前方溶液加速度,并在放松压力中提供了不到5%的相对错误。