Extended Displacement Discontinuity Boundary Integral Equation Method For Magnetoelectroelastic Media

In this thesis, the extended displacement discontinuity boundary integral equation method for transversely isotropic magnetoelectroelatic solid is proposed. The fundamental theories, such as Green's function, the singular behaviors of the near tip fields of a crack tip, intensity factor, etc., are studied. By using the boundary integral equation method, the interference of co-plane and parallel cracks in three-dimensional (3D) magnetoelectroelatic solids and collinear and parallel cracks in two-dimensional (2D) magnetoelectroelatic solids is analyzed. The influence of different boundary conditions on crack faces is studied. The main achievements are as follows:(1) The relationship between Green's functions of point forces and Green's functions of displacement discontinuity is established, and a versatile method is presented to derive the extended displacement discontinuity Green's functions. And, then, the extended Crouch fundamental solutions of 3D magnetoelectroelatic solid are obtained.(2) By use of the Somigliana identity for magnetoelectroelastic media and the extended displacement discontinuity Green's functions, the boundary integral equations are obtained in terms of the extended displacement discontinuities across the crack faces. The extended stress intensity factors in terms of the extended displacement discontinuities are also derived. A solution method is proposed by use of the analogy between the boundary integral equations of the magnetoelectroelastic media and the purely elastic materials. The influence of different electric and magnetic boundary conditions on the solutions is studied. By using this method, multiple cracks are analyzed.(3) The crack opening model in the magnetoelectroelastic media is first proposed to consider the real crack opening and the electric and magnetic fields in the crack cavity. An iteration approach is presented for the solution of the non-linear model.(4) Green's functions for extended displacement discontinuities in 2D magnetoelectroelatic solid are obtained by the means of integrating the corresponding solutions of 3D magnetoelectroelatic solid. The extended Crouch fundamental solutions for 2D magnetoelectroelatic solid are derived.(5) The extended displacement discontinuity boundary integral equation method for 2D transversely isotropic magnetoelectroelatic solid is proposed. The influence of different electric and magnetic boundary conditions on the solutions is studied.