Topological design of microstructures using periodic material-field series-expansion and gradient-free optimization algorithm

• Published in: Materials & design Vol. 199; p. 109437
• Main Authors: Liu, Pai, Yan, Yi, Zhang, Xiaopeng, Luo, Yangjun, Kang, Zhan
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2021; Elsevier
• Subjects: Gradient-free method; Kriging surrogate model; Material microstructure design; Material-field series-expansion method; Topology optimization; Topology optimization; Kriging surrogate model; Material microstructure design; Gradient-free method; Material-field series-expansion method
• ISSN: 0264-1275; 1873-4197
• DOI: 10.1016/j.matdes.2020.109437

Light-weight cellular materials with periodic repetitive microstructures are widely used in various fields due to their superior mechanical/multi-physical performances. As the microstructural design problem is known to have multiple local minima, most gradient-based topology optimization methods significantly depend on the initial guess of the microstructural geometry, thus requiring the designer’s experiences. This paper presents an effective gradient-free framework for periodic microstructure design, which exhibits powerful global searching capabilities and requires no sensitivity information. The proposed framework combines the material-field series-expansion (MFSE) topology representation of periodic microstructures and the sequential Kriging-based optimization algorithm. The MFSE method decouples the topological representation from the finite element discretization, and describes a relatively complex microstructural topology with high-quality boundary description using a greatly reduced number of design variables. Based on the Kriging surrogate model, a solution scheme is suggested to solve material microstructural topology optimization successively in a sequence of sub-optimization problems with self-adaptive design spaces. With the present gradient-free optimization method, high-performance cellular materials that approach the H-S upper bound with porosities from 0.2 to 0.6, or that achieve negative Poisson’s ratios of -0.94 in the principal directions for materials with square symmetry, are obtained without prior knowledge of the optimum microstructural topology. Illustration: A gradient-free topological design methods for periodic cellular material microstructures is proposed. This optimization method requires no experienced-based guesses of the initial microstructural topologies and requires no sensitivity information. Microstructure geometries with high-quality boundaries and high performances are obtained with the present method. [Display omitted] •A gradient-free microstructural topology optimization method for cellular materials is proposed.•This method does not require experience-based guesses of the initial design and the sensitivity information.•The performances of the optimized cellular materials approach the H-S upper bound.•This method provides high-quality microstructural boundary descriptions.