A new method of stiffness prediction for composite plate structures with in-plane periodicity

This paper proposes an equivalence principle of macroscopic internal virtual work and microscopic internal virtual work, and uses it to predict the effective stiffnesses of composite plate structures with in-plane periodicity. The macroscopic internal virtual work is produced by internal forces acting on generalized virtual strains, and the microscopic internal virtual work is produced by microscopic stresses acting on microscopic virtual strains. The microscopic virtual strains consist of macroscopic strains and perturbed strains solved from the self-equilibrium equation of a unit cell. According to the equivalence principle, the effective stiffness matrix of periodic heterogeneous plates is presented in a product form of microscopic stresses and microscopic strains. To determine the unique solution of the self-equilibrium equation, five normalization conditions are given and elaborated physically. Moreover, standard finite element formulations for calculating the perturbed displacements are derived with the principle of virtual work. The present method of predicting the effective stiffnesses of composite plates can be easily implemented in the commercial software COMSOL Multiphysics. Finally, numerical comparisons with the results in literature validate the effectiveness and accuracy of the proposed method.