Topology optimization of microstructures of cellular materials and composites for macrostructures

• Published in: Computational materials science Vol. 67; pp. 397 - 407
• Main Authors: Huang, X., Zhou, S.W., Xie, Y.M., Li, Q.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.02.2013; Elsevier
• Subjects: Bidirectional evolutionary structural optimization (BESO); Exact sciences and technology; Fundamental areas of phenomenology (including applications); Homogenization; Material base cell; Mean compliance; Physics; Solid mechanics; Structural and continuum mechanics; Structural mechanics (beam, string...); Theory and numerical methods; Topology optimization; Topology optimization; Homogenization; Mean compliance; Material base cell; Bidirectional evolutionary structural optimization (BESO); Mechanical compliance; Cellular material; Numerical method; Composite material; Optimization; Heterogeneous material; Anisotropy; Stiffness; Microstructure; Macrostructure
• ISSN: 0927-0256; 1879-0801
• DOI: 10.1016/j.commatsci.2012.09.018

► A new BESO algorithm is proposed for a two-scale optimization problem. ► Optimal designs of materials for macrostructures with the maximum stiffness. ► A clear 0/1 topologies for cellular materials/composites are achieved. ► Various interesting anisotropic microstructures of materials are obtained. This paper introduces a topology optimization algorithm for the optimal design of cellular materials and composites with periodic microstructures so that the resulting macrostructure has the maximum stiffness (or minimum mean compliance). The effective properties of the heterogeneous material are obtained through the homogenization theory, and these properties are integrated into the analysis of the macrostructure. The sensitivity analysis for the material unit cell is established for such a two-scale optimization problem. Then, a bi-directional evolutionary structural optimization (BESO) approach is developed to achieve a clear and optimized topology for the material microstructure. Several numerical examples are presented to validate the proposed optimization algorithm and a variety of anisotropic microstructures of cellular materials and composites are obtained. The various effects on the topological design of the material microstructure are discussed.