Structural optimization of metamaterials based on periodic surface modeling

Abstract

Metamaterials are engineered microstructures or composites which exhibit novel properties that are not found in nature. Structural optimization methods for shape and topology optimization have been developed in designing metamaterials. The computational cost of the traditional topology optimization methods is high due to the high-dimensional design space. Shape optimization and topology optimization are also performed separately. To improve the search efficiency, a new structural optimization method based on periodic surface modeling is proposed to simultaneously optimize the shape and topology of metamaterials. A wide variety of topology can be represented with a small number of parameters in the periodic surface models. Therefore, the search space is significantly reduced. A mixed-integer Bayesian optimization method is also developed with a new Gaussian process kernel, which incorporates both discrete and continuous design parameters in the periodic surface models. Both the mixed-integer Bayesian optimization method and conventional population-based genetic algorithms are used to solve the structural optimization problem. The design of mechanical metamaterials with high strength–weight ratio and negative Poisson’s ratio is demonstrated.