  For natural frequency optimization of engineering structures, cellular
composites have been shown to possess an edge over solid. However, existing
multiscale design methods for cellular composites are either computationally
exhaustive or confined to a single class of microstructures. In this paper, we
propose a data-driven topology optimization (TO) approach to enable the
multiscale design of cellular structures with various choices of microstructure
classes. The key component is a newly proposed latent-variable Gaussian process
(LVGP) model through which different classes of microstructures are mapped into
a low-dimensional continuous latent space. It provides an interpretable
distance metric between classes and captures their effects on the homogenized
stiffness tensors. By introducing latent vectors as design variables, a
differentiable transition of stiffness matrix between classes can be easily
achieved with an analytical gradient. After integrating LVGP with the
density-based TO, an efficient data-driven cellular composite optimization
process is developed to enable concurrent exploration of microstructure
concepts and the associated volume fractions for natural frequency
optimization. Examples reveal that the proposed cellular designs with
multiclass microstructures achieve higher natural frequencies than both
single-scale and single-class designs. This framework can be easily extended to
other multi-scale TO problems, such as thermal compliance and dynamic response
optimization.
