Optimal Design of Elastic Plates: Hybrid Numerical Method Based on Homogenization and Shape Derivative

This paper focuses on optimal design problems in the context of the Kirchhoff‐Love model for pure bending of a thin, solid, symmetric plate under a transverse load. The objective is to simultaneously determine the optimal outer shape of the domain and the distribution of two isotropic materials within the domain in order to minimize compliance. The proposed optimization strategy integrates homogenization techniques with shape optimization. The level‐set function is utilized to propagate the movement of the outer boundary through a calculated shape derivative, while the interior is optimized using a known optimality criteria method for the single‐state compliance minimization problem. A numerical scheme implementing this coupled approach is presented and validated through several examples. Finally, the proposed method is compared with the pure homogenization and the pure shape optimization method and is shown to yield improved performance.