Two-Scale Asymptotic Homogenization Method for Composite Kirchhoff Plates with in-Plane Periodicity

This paper develops a two-scale asymptotic homogenization method for periodic composite Kirchhoff plates. In this method, three-dimensional (3D) plate problem is simplified as problem, which governed by fourth-order uniformly elliptic partial differential equation (PDE) with periodically oscillating coefficients. Then, solution in an expansion form presented the PDE, and it found that first-order perturbed displacement zero. Additionally, boundary normalization constraint conditions are proposed to determine unique unit cell problems. Moreover, standard finite element formulations calculating displacements derived from principle of virtual work. Physical interpretations influence functions analyzing properties self-balanced quasi-load vectors used solving functions. Numerical comparisons show present physically acceptable highly accurate.