Topological constraints in 2D structural topology optimization
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RESEARCH PAPER
Topological constraints in 2D structural topology optimization Haitao Han 1,2 & Yuchen Guo 1,2 & Shikui Chen 3 & Zhenyu Liu 1 Received: 17 September 2019 / Revised: 22 August 2020 / Accepted: 26 October 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract One of the straightforward definitions of structural topology optimization is to design the optimal distribution of the holes and the detailed shape of each hole implicitly in a fixed discretized design domain. However, typical numerical instability phenomena of topology optimization, such as the checkerboard pattern and mesh dependence, all take the form of an unexpected number of holes in the optimal result in standard density-type design methods, such as SIMP and ESO. Typically, the number of holes is indirectly controlled by tuning the value of the radius of the filter operator during the optimization procedure, in which the choice of the value of the filter radius is one of the most opaque and confusing issues for a beginner unfamiliar with the structural topology optimization algorithm. Based on the soft-kill bi-directional evolutionary structural optimization (BESO) method, an optimization model is proposed in this paper in which the allowed maximal number of holes in the designed structure is explicitly specified as an additional design constraint. The digital Gauss-Bonnet formula is used to count the number of holes in the whole structure in each optimization iteration. A hole-filling method (HFM) is also proposed in this paper to control the existence of holes in the optimal structure. Several 2D numerical examples illustrate that the proposed method cannot only limit the maximum number of holes in the optimal structure throughout the whole optimization procedure but also mitigate the phenomena of the checkerboard pattern and mesh dependence. The proposed method is expected to provide designers with a new way to tangibly manage the optimization procedure and achieve better control of the topological characteristics of the optimal results. Keywords Topological constraints . Topological optimization . Digital Gauss-Bonnet formulation . Burning method
1 Introduction Topological optimization is one of the design methods used to determine material distribution in a specified domain. Currently, it has been extended to the areas of structural mechanics (Lazarov et al. 2016; Sigmund 2009; Rozvany 2001; Chen et al. 2010), electromagnetism (Deng and Korvink 2018; Okamoto et al. 2016; Labbe and Dehez 2011), Responsible Editor: Ji-Hong Zhu Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/s00158-02002771-5. * Zhenyu Liu [email protected] 1
Changchun Institute of Optics, Fine Mechanics and Physics (CIOMP), Chinese Academy of Sciences, Changchun 130033, China
2
University of Chinese Academy of Sciences, Beijing 100049, China
3
Department of Mechanical Engineering, State University of New York, Stony Brook, USA
thermology (Sigmund 2001b, c), and fluid mechanics
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