Data-driven multiscale design of cellular composites with multiclass microstructures for natural frequency maximization

For natural frequency optimization of engineering structures, cellular composites have been shown to possess an edge over solid. However, existing multiscale design methods are either computationally exhaustive or confined to a restrictive class of microstructures. In this paper, we propose a data-driven topology optimization (TO) approach to enable the multiscale cellular designs with multiple choices of microstructure classes. The key component is a newly proposed latent-variable Gaussian process enhanced with the sum of separable kernels (LVGP-SoS). It maps different classes of microstructures into a low-dimensional continuous latent space that could capture the correlation of different classes. By introducing latent vectors as design variables, a continuous and differentiable transition of the stiffness matrices between different classes can be achieved, together with an analytical gradient. After integrating the LVGP models with the classical TO, an efficient data-driven cellular composite optimization process is developed to enable concurrent exploration of microstructure classes and their volume fractions for natural frequency optimization. Examples reveal that the proposed designs with multiclass microstructures achieve better performance in maximizing natural frequencies than both single-scale and single-class designs. The same design framework can be easily extended to other multiscale TO problems, such as thermal compliance minimization and dynamic response optimization.