A coupled formulation of finite and boundary element methods for flexoelectric solids

摘要

A numerical method for analyzing the mechanical deformation and electric polarization of flexoelectric solids is proposed that considers the electric interactions among flexoelectric solids, electric charges, and their surrounding medium. The proposed method uses finite and boundary elements simultaneously. Finite elements are used to model flexoelectric solids, and boundary elements are applied along the boundary of the solids and an arbitrary surface encompassing the solids and electric charges. To account for the couple stress and flexoelectric terms, a C-1 continuous finite element formulation is introduced. Next, a coupled formation between the finite elements and boundary elements is developed. The coupled method provides a converged solution for any system composed of flexoelectric solids and electric charges without prescribing electric boundary conditions on the boundary of solids. Several numerical examples prove that the method is convergent and effective for systems containing multiple solids and electric charges.