Novel implementation of extrusion constraint in topology optimization by Helmholtz-type anisotropic filter
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RESEARCH PAPER
Novel implementation of extrusion constraint in topology optimization by Helmholtz-type anisotropic filter Bo Wang 1 & Yan Zhou 1 & Kuo Tian 1 & Guangming Wang 1 Received: 23 September 2019 / Revised: 26 March 2020 / Accepted: 2 April 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, a novel implementation of extrusion constraint in topology optimization is proposed based on Helmholtz-type anisotropic filter approach. The main idea is to set a far larger filter feature size along the extrusion direction than other directions, and thus, the density field is kept constant along the extrusion direction. The Helmholtz-type anisotropic filter can be easily implemented by adding a few more parameters to the isotropic one. Three illustrative examples, including 3D cantilever, spherical frame, and S-shape curved shell, are carried out to verify the effectiveness and robustness of the proposed method. Example results corroborate that the proposed method is suitable for both regular and irregular meshes regardless of geometrical complexity. Compared with the traditional variable mapping method, the proposed method needs less manual setup in the preprocessing of the analysis model for implementing extrusion constraint in topology optimization, which can be easily integrated into the solid isotropic materials with penalization (SIMP) topology optimization or commercial topology optimization software. Keywords Topology optimization . Helmholtz-type anisotropic filter . Extrusion constraints . Complex curved surface structure
1 Introduction Topology optimization has been widely used in the fields of civil engineering, architecture, aerospace engineering, etc. (Zhu et al. 2016; Beghini et al. 2014). The main idea of topology optimization is to automatically distribute materials in the design domain by means of an iterative manner, in order to optimize the objective function under specific constraints until the optimal layout of the structure is obtained. In recent years, topology optimization has gained rapid development, and several representative methods have been established such as the homogenization method (Bendsøe and Kikuchi 1988), the solid isotropic material with penalization (SIMP) approach (Bendsøe 1989; Zhou and Rozvany 1991), the evolutionary structural optimization (ESO) method (Xie and Steven 1993), Responsible Editor: Qing Li * Kuo Tian [email protected] 1
Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China
the level-set based method (Wang et al. 2003; Luo et al. 2008), and the moving morphable component (MMC) method (Zhang et al. 2016). However, when designing actual structures using topology optimization methods, the manufacturability should be reasonably considered. Otherwise, it may result in an optimal design that could not be manufactured. In order to integrate the topology optimization with the manufacturability, manufacturing constraints
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