Concurrent Shape and Topology Optimization of Metamaterials Based on Periodic Surface Modeling

In the most recent decades, structural optimization (SO) methods including shape and topology optimization have been employed in designing metamaterials. However, shape optimization and topology optimization are usually performed separately. Conventional topology optimization techniques are limited by high computational cost because of the high-dimensional search space. Maintaining the structural continuity and smooth boundaries of metamaterials is also challenging. In this paper, a new SO method based on periodic surface (PS) modeling is proposed to optimize the shape and topology of metamaterials concurrently. The PS model can represent a wide variety of topology with only a small number of design parameters, including periodic moments, basis vectors, and scale parameters. By limiting the number of available basis vectors to choose from, the search efficiency of topology optimization is significantly improved. To solve the mix-integer optimization problem, a mixed-integer Bayesian optimization method is also developed with a new Gaussian process kernel, which is customized for the design parameters in the PS model. The new SO approach is applied to design mechanical metamaterials with high strength-weight ratio and negative Poisson’s ratio. The comparison with other topology optimization methods shows the high efficiency of the proposed approach.