A high-order asymptotic expansion analysis method for generalized periodic lattice structures

This paper proposes a novel high-order asymptotic expansion analysis method for generalized periodic lattice structures, aimed at accurately predicting their physical and mechanical behaviors and equivalent performances. The proposed method converts the homogenization problem of generalized periodic lattice structures into the classical two-scale homogenization problem for a cubic unit cell, thereby elucidating the intrinsic mapping mechanisms of the generalized two-scale homogenization approach. This conversion clarifies the fundamental properties of the equivalent performance of generalized periodic two-scale homogenization, substantially reducing the computational and programming complexities involved. By employing typical numerical examples, this paper compares the outcomes from the proposed mapping method with those derived from classical periodic two-scale homogenization and fine-scale finite element methods. The results affirm the universality and effectiveness of the proposed method, which exhibits high computational precision for addressing both static and dynamic issues, such as natural frequency calculations, thus providing strong theoretical support and practical pathways for designing high-performance, lightweight structures in generalized periodic lattice configurations.