Structural optimization software that can produce high-resolution designs optimized for arbitrary cost and constraint functions is essential to solve real-world engineering problems. Such requirements are not easily met due to the large-scale simulations and software engineering they entail. In this paper, we present a large-scale topology optimization framework with adaptive mesh refinement (AMR) applied to stress-constrained problems. AMR allows us to save computational resources by refining regions of the domain to increase the design resolution and simulation accuracy, leaving void regions coarse. We discuss the challenges necessary to resolve such large-scale problems with AMR, namely, the need for a regularization method that works across different mesh resolutions in a parallel environment and efficient iterative solvers. Furthermore, the optimization algorithm needs to be implemented with the same discretization that is used to represent the design field. To show the efficacy and versatility of our framework, we minimize the mass of a three-dimensional L-bracket subject to a maximum stress constraint and maximize the efficiency of a three-dimensional compliant mechanism subject to a maximum stress constraint.

能够产生针对任意成本和约束函数进行优化的高分辨率设计的结构优化软件对于解决实际工程问题至关重要。由于需要进行大规模的仿真和软件工程，因此很难满足这些要求。在本文中，我们提出了一种适用于应力约束问题的具有自适应网格细化（AMR）的大规模拓扑优化框架。AMR允许我们通过优化域的区域以提高设计分辨率和仿真精度来节省计算资源，而使空白区域变得粗糙。我们讨论了用AMR解决此类大规模问题所必需的挑战，即需要一种在并行环境中跨不同网格分辨率工作的正则化方法和高效的迭代求解器。此外，优化算法需要使用与代表设计领域相同的离散化来实现。为了显示我们框架的有效性和多功能性，我们将承受最大应力约束的三维L型支架的质量降至最低，并将承受最大应力约束的三维顺应机构的效率最大化。