Hybrid Extended Displacement Discontinuity-Fundamental Solution Method For Two-Dimensional Piezoelectric/Magnetoelectroelastic Medium

In this thesis, Hybrid Extended Displacement Discontinuity-Fundamental Solution Method for Two-Dimensional Piezoelectric/Magnetoelectroelastic Medium is proposed.By using this method, fracture of finite piezoelectric medium and magnetoelectroelastic material is studied.The influence of different boundary condition and different kinds of loading on the result is investigated.The main achievements are as follow:(1)The proposed hybrid EDD-FSM is applied to solve the problems of cracks under electrically permeable condition, as well as under semi-permeable conditions by using an iterative approach.Two important crack problems in fracture mechanics, the center crack and edge crack in piezoelectric strips, are analyzed by the proposed method.The stress intensity factor and the electric displacement intensity factor are calculated.The effects of finite domain size and the electric boundary conditions on these intensity factors are studied.(2)The hybrid extended displacement discontinuity-fundamental solution method is used to analysis of cracks in 2D finite magnetoelectroelastic media. The extended stress intensity factors are calculated under different electric and magnetic boundary conditions.The examples have showed the good performance of extended displacement discontinuity-fundamental solution method in analyzing cracks in finite magnetoelectroelastic media.The results have demonstrated that the solutions depend greatly on the electric and magnetic boundary conditions on crack faces, as well as the geometry of the finite media.(3)The extended Crouch fundamental solutions of parabolic elements for 2D piezoelectric media are derived based on the extended displacement discontinuity fundamental solution.Extended displacement discontinuity method (EDDM) using parabolic elements at crack tips under impermeable boundary condition is implemented.Numerical results show that the precision and efficiency of the EDDM can be greatly improved by using the parabolic elements. (4)The Crouch fundamental solution for a parabolic element at the crack tip of magnetoelectroelastic media is derived to model the square root variations of near tip fields.The parabolic element is used in the extended displacement discontinuity-fundamental solution method.The results have demonstrated that parabolic elements at crack tips can improve the accuracy of the extended displacement discontinuity-fundamental solution method.