The work provides an exhaustive comparison of some representative families of topology optimization methods for 3D structural optimization, such as the Solid Isotropic Material with Penalization (SIMP), the Level-set, the Bidirectional Evolutionary Structural Optimization (BESO), and the Variational Topology Optimization (VARTOP) methods. The main differences and similarities of these approaches are then highlighted from an algorithmic standpoint. The comparison is carried out via the study of a set of numerical benchmark cases using industrial-like fine-discretization meshes (around 1 million finite elements), and Matlab as the common computational platform, to ensure fair comparisons. Then, the results obtained for every benchmark case with the different methods are compared in terms of computational cost, topology quality, achieved minimum value of the objective function, and robustness of the computations (convergence in objective function and topology). Finally, some quantitative and qualitative results are presented, from which, an attempt of qualification of the methods, in terms of their relative performance, is done.

中文翻译：

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3D 结构问题的拓扑优化方法：比较研究

这项工作对 3D 结构优化的一些代表性拓扑优化方法系列进行了详尽的比较，例如带有惩罚的固体各向同性材料 (SIMP)、水平集、双向演化结构优化 (BESO) 和变分拓扑优化(VARTOP) 方法。然后从算法的角度突出了这些方法的主要区别和相似之处。比较是通过使用类似工业的精细离散化网格（大约 100 万个有限元）和 Matlab 作为通用计算平台，通过研究一组数值基准案例来进行的，以确保公平比较。然后，在计算成本、拓扑质量、实现了目标函数的最小值，以及计算的鲁棒性（目标函数和拓扑的收敛性）。最后，给出了一些定量和定性结果，从中尝试根据它们的相对性能对方法进行鉴定。