Abstract
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.
Highlights
This paper focuses on soft-kill evolutionary techniques, and in particular, in the bi-directional evolutionary (BESO) approach proposed by Huang and Xie [101]
The designs obtained from Solid Isotropic Material with Penalization (SIMP)(I), SIMP(III), Variational Topology Optimization (VARTOP), and Level-set illustrate a much simpler design based on bars, while SOFTBESO produces an optimal design with a thin web, with almost constant thickness
The corresponding results have been assessed in terms of the optimal topology, the robustness in convergence, the objective function, and the computational cost
Summary
In the past three decades, topology optimization has become an active research field to seek new optimal counterintuitive designs in a wide range of problems governed by different physics, i.e., solid mechanics [1,2,3,4,5,6], fluid dynamics [7,8,9], thermal dynamics [10,11,12], acoustics [13,14,15,16,17,18] and electromagnetism [19,20,21], among others. The main disadvantage of the former group is their extremely high computational cost as the number of unknowns increases. This computational cost may become prohibitive for current computational systems since thousands of different layouts must be tested to find the optimal configuration. The algorithms included in the second set are the most widespread algorithms, e.g., (a) topology optimization within homogenization theory [51], (b) density-based optimization (SIMP) techniques [45, 52, 53], (c) evolutionary methodologies (ESO)2 [54, 55], (d) Level-set approaches [2, 3, 56], (e) Topological Derivative method [57], (f) Phase
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