Mode III edge-crack in magneto-electro-elastic media by symplectic expansion

An analytical method using symplectic expansion is introduced to find the solutions of edge-cracked circular magneto-electro-elastic media to handle general boundary conditions. A symplectic system is established so that these unknowns are expanded in terms of the symplectic eigenfunctions. The coefficients of the eigenfunctions series are determined from the lateral boundary conditions along the crack faces and the outer boundary conditions along the geometric domain. The evaluation of the intensity of stress, electric displacement and magnetic induction near the crack is processed and it will be useful for assessing the structural integrity. Numerical examples including the complex mixed boundary conditions are given.