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

• Published in: Computer methods in applied mechanics and engineering Vol. 371; p. 113306
• Main Authors: Nguyen, Chuong, Zhuang, Xiaoying, Chamoin, Ludovic, Zhao, Xianzhong, Nguyen-Xuan, H., Rabczuk, Timon
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.11.2020; Elsevier BV; Elsevier
• Subjects: Algorithms; Bézier extraction; Engineering Sciences; Equilibrium equations; Isogeometric analysis; Iterative methods; Linear systems; Mathematical models; Metamaterials; Model reduction; Optimization; Reduced order model; Reduced order models; Three dimensional models; Topology optimization; Unit cell; Isogeometric analysis; Topology optimization; Bézier extraction; Metamaterials; Reduced order model
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2020.113306

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. •Topology optimization algorithm is coupled with reduced order modeling to improve computational efficiency.•Isogeometric analysis based on Bézier extraction provides solutions with smoother manifold for constructing the reduced basis.•Sensitivity analysis including the residual error is derived in the framework of level set method.