Hybrid material topology optimization of solid-lattice structures for natural frequency maximization

Abstract

This paper presents a topology optimization design approach for hybrid materials used to generate solid-lattice structures. Specifically, the approach aims to maximize the natural frequencies of hybrid structures by optimizing the topological distribution of solid and lattice materials, as well as the lattice relative density. For this purpose, a hybrid material interpolation model is developed. In this approach, the modal assurance criterion (MAC) is applied to optimize the target-order natural frequency accurately. Additionally, a hybrid structure post-processing framework based on the signed distance field (SDF) is proposed. This framework adaptively refines the lattice resolution at model boundaries, ensuring geometric integrity. Moreover, a circular geometry transition strategy is employed to improve structural connectivity, which significantly reduces model errors in non-transition regions. 2D and 3D numerical examples demonstrate the proposed method’s effectiveness in maximizing the natural frequency of hybrid structures. In particular, the dynamic performance of hybrid structures surpasses that of pure solid structures under multiple mass loading cases.