A finite magnetoelectroelastic plate with a cavity under mechanical-electric-magnetic loading

The 2D problem of a finite plate with a circular/elliptic cavity under anti-plane shear and in-plane electric-magnetic field loadings is studied in this paper. Laurent series is adopted to express the analytical function inside the circular cavity and the finite plate, and Faber series with conjunction of conformal mapping is applied to express the analytical function inside the elliptic cavity. Numerical algorithm is developed based on boundary collocation method (BCM) to deal the traction boundary condition (i.e. Neumann BC) at the edges of the plate and exactly permeable, natural boundary condition (i.e. Dirichlet BC) at the cavity surface. Graphical results are presented to discuss the effect of the loading condition and the plate size on the behaviors of local stresses. The solution shows that the electric field inside the cavity is uniform in the case of a finite plate, which is the same to the case of an infinite plate.