Three-dimensional topology optimization of auxetic metamaterial using isogeometric analysis and model order reduction

authored by: Chuong Nguyen, Xiaoying Zhuang, Ludovic Chamoin, Hung Nguyen-Xuan, Xianzhong Zhao, Timon Rabczuk
Abstract: We present an approach for designing material micro-structures by using isogeometric analysis and parameterized level set method. Design variables, which are level set values associated with control points, are updated from the optimizer and represent the geometry of the unit cell. The computational efficiency is further improved in each iteration by employing reduced order modeling when solving linear systems of the equilibrium equations. We construct a reduced basis by reusing computed solutions from previous optimization steps, and a much smaller linear system of equations is solved on the reduced basis. Two- and three-dimensional numerical results show the effectiveness of the topology optimization algorithm coupled with the reduced basis approach in designing metamaterials.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Ho Chi Minh City University of Technology (HUTECH)
Bauhaus-Universität Weimar
Université Paris-Saclay
Tongji University
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 371
No. of pages: 23
ISSN: 0045-7825
Publication date: 01.11.2020
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications, Computational Mechanics
Electronic version(s): https://arxiv.org/abs/1908.11449 (Access: Open)
https://doi.org/10.1016/j.cma.2020.113306 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{9ea02c53d3954ab2a580dd705a189e9f,
title = "Three-dimensional topology optimization of auxetic metamaterial using isogeometric analysis and model order reduction",
abstract = "We present an approach for designing material micro-structures by using isogeometric analysis and parameterized level set method. Design variables, which are level set values associated with control points, are updated from the optimizer and represent the geometry of the unit cell. The computational efficiency is further improved in each iteration by employing reduced order modeling when solving linear systems of the equilibrium equations. We construct a reduced basis by reusing computed solutions from previous optimization steps, and a much smaller linear system of equations is solved on the reduced basis. Two- and three-dimensional numerical results show the effectiveness of the topology optimization algorithm coupled with the reduced basis approach in designing metamaterials.",
keywords = "cs.CE, Isogeometric analysis, B{\'e}zier extraction, Topology optimization, Metamaterials, Reduced order model",
author = "Chuong Nguyen and Xiaoying Zhuang and Ludovic Chamoin and Hung Nguyen-Xuan and Xianzhong Zhao and Timon Rabczuk",
note = "CN acknowledges the support of the ERC project (802205).",
year = "2020",
month = nov,
day = "1",
doi = "10.1016/j.cma.2020.113306",
language = "English",
volume = "371",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}