Multiscale topology optimization for coated structures with multifarious-microstructural infill
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RESEARCH PAPER
Multiscale topology optimization for coated structures with multifarious-microstructural infill Sheng Chu 1 & Liang Gao 1 & Mi Xiao 1
&
Yan Zhang 1
Received: 14 March 2019 / Revised: 5 October 2019 / Accepted: 9 October 2019 # Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract In engineering, cellular structures are often manufactured with coating for protection or to improve certain functionalities. This paper concentrates on the design of coated structures consisting of an exterior solid shell and an inner base part filled by multifarious microstructures, and a novel multiscale topology optimization method is proposed. Firstly, a representation method and a material interpolation model are developed to describe a coated structure with multifarious-microstructural infill and define its properties, respectively. At macroscale, coating-base distribution is determined by the parametric level set method (PLSM) with re-initialization. To optimize structural performance at a computationally affordable cost, controllable kinds of microstructures are considered, and their spatial distribution over the whole base region is optimized by the ordered SIMP method with a threshold scheme. At microscale, the configurations of microstructures are generated by PLSM with the numerical homogenization method, in which the volume fraction limit values correspond to the design variables of the ordered SIMP method in macroscale. The compliance minimization problem subject to a material mass constraint is investigated, and sensitivity analysis is derived. Numerical examples are provided to demonstrate the effectiveness of the proposed method. Keywords Multiscale topology optimization . Coated structures . Multifarious-microstructural infill . Level set . Ordered SIMP method
1 Introduction Up to now, architected microstructures have attracted a lot of attention owing to their ability to manipulate material behavior (Olson III and Martins 2005; Meza et al. 2014; Wang et al. 2017; Chu et al. 2019a). As a growing subfield of structural optimization, topology optimization has presented a powerful systematic design strategy for cellular structures (Allaire 2002; Bendsøe and Sigmund 2004; Wang et al. 2017). By incorporating the homogenization method (Lurie et al. 1982; Murat and Tartar 1985; Francfort and Murat 1986) in topology optimization, Sigmund (1994) develops an inverse homogenization method for design of microstructures with the prescribed
Responsible Editor: Ole Sigmund * Mi Xiao [email protected] 1
State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
properties (Guedes and Kikuchi 1990; Sigmund 1994; Xia and Breitkopf 2015; Gao et al. 2019). Based on this design approach, a lot of cellular structures, having arrays of periodic microstructures with ordinary material constituents, have been achieved with desired properties, such as negative Poisson’s ratio (Andreassen et al. 2014; Wang et al. 2014), extremal th
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