Two-scale topology optimization of structural fundamental eigenfrequency using a data-driven microstructure model based on M-VCUT level set

For the optimization of fundamental eigenfrequency in vibrating structures, it has been proven that multi-scale structures have advantages over single scale structures. This study introduces a two-scale topology optimization method using a data-driven microstructure model based on a multiple variable cutting (M-VCUT) level set approach. This method aims to maximize the fundamental eigenfrequency of two-scale structures. The method consists of two parts: offline database construction and online topology optimization. In the process of offline database construction, many microstructures are obtained by varying the value of geometric parameters according to the M-VCUT level set approach; then, a mapping relationship between the geometric parameters and the homogenized mechanical properties of microstructures is established by compactly supported radial basis function interpolation, which gives the data-driven microstructure model. In the process of online optimization, the homogenized mechanical properties corresponding to arbitrary design variables are obtained by using the data-driven microstructure model, whose computational costs are much less than those of the homogenization. Topology optimization is carried out with this data-driven model to enhance computational efficiency. In order to adapt the method of moving asymptotes (MMA), the eigenfrequency maximization problem is converted to its reciprocal minimization problem for sensitivity calculation. The method’s effectiveness is proved through several numerical examples.