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For natural frequency optimization of engineering structures, cellularcomposites have been shown to possess an edge over solid. However, existingmultiscale design methods for cellular composites are either computationallyexhaustive or confined to a single class of microstructures. In this paper, wepropose a data-driven topology optimization (TO) approach to enable themultiscale design of cellular structures with various choices of microstructureclasses. The key component is a newly proposed latent-variable Gaussian process(LVGP) model through which different classes of microstructures are mapped intoa low-dimensional continuous latent space. It provides an interpretabledistance metric between classes and captures their effects on the homogenizedstiffness tensors. By introducing latent vectors as design variables, adifferentiable transition of stiffness matrix between classes can be easilyachieved with an analytical gradient. After integrating LVGP with thedensity-based TO, an efficient data-driven cellular composite optimizationprocess is developed to enable concurrent exploration of microstructureconcepts and the associated volume fractions for natural frequencyoptimization. Examples reveal that the proposed cellular designs withmulticlass microstructures achieve higher natural frequencies than bothsingle-scale and single-class designs. This framework can be easily extended toother multi-scale TO problems, such as thermal compliance and dynamic responseoptimization.

Data-Driven Multiscale Design of Cellular Composites with Multiclass Microstructures for Natural Frequency Maximization