Clustering-based multiscale topology optimization of thermo-elastic lattice structures
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ORIGINAL PAPER
Clustering‑based multiscale topology optimization of thermo‑elastic lattice structures Jun Yan1 · Qianqian Sui1 · Zhirui Fan1 · Zunyi Duan2 · Tao Yu1 Received: 26 December 2019 / Accepted: 24 July 2020 / Published online: 27 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A multiscale clustering-based topology optimization for thermo-elastic lattice structures is studied based on the extended multiscale finite element method (EMsFEM). The strain energy of thermo-elastic lattice structures is chosen as the objective function. The microstructural configuration and the macrostructural distribution of the thermo-elastic lattice material are designed through topology optimization concurrently. The K-means clustering-based method is proposed to group the microstructures of the lattice materials. The effects of the number of clusters (groups), magnitude of the thermal loads, size factor of the microstructure, and material volume fraction on the optimization results are discussed. The results show that the clustering-based multiscale design optimization is superior to the classical multiscale design optimization of lattice structures. Keywords Thermo-elastic structures · Clustering-based optimization · Multiscale topology optimization · Extended multiscale finite element method · K-means clustering-based method
1 Introduction The design of thermo-elastic structures is a basic and important activity in aerospace industries. Here, thermo-elastic structures are loaded with both mechanical and thermal stresses simultaneously. Numerous studies have been devoted to topology optimization of the design of thermal structures to realise light-weight components and improve their structural performance [1–4] in terms of thermal stress, thermal deformation, and frequency of the thermo-elastic structure. Rodrigues and Fernandes [5] proposed the development of a computational model for the topology optimization problem, using a material distribution approach, wherein a 2-dimensional linear-elastic solid is subjected to thermal loads. By applying a three-phase topology optimization method, Sigmund and Torquato [6] achieved microstructural design of * Jun Yan [email protected] 1
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, International Research Center for Computational Mechanics, Dalian University of Technology, Dalian 116024, China
Institute of Structural Health Monitoring and Control, School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710072, China
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materials with extreme thermal properties. Xia and Wang [7] implemented topology optimization of thermo-elastic structures with a level set method. The objective here is to minimise the mean compliance of the thermal structure with a material volume constraint. Pedersen and Pedersen [8] studied the strength optimised design of a thermo-elastic structure with the maximum von Mises stress as an objective function. Deng e
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