Analysis Of Thin Structures And Fracture Problems For 2D Piezoelectric Media Via Boundary Element Method

Smart materials are key components of the electronic control of the car, and the research of its mechanical and electrical performances are two important problems for smart materials. In this thesis, based on the Mathematica software, the boundary element method(BEM) is utilized to analyze the two-dimensional(2D) piezoelectric thin structure and dielectric/piezoelectric fracture problems. The main results of this thesis are as follows:(1) 2D piezoelectric thin structures are analyzed via the traditional BEM. Analytical expressions for the integrals of the kennel functions are obtained. Numerical results for three types of piezoelectric thin structures models are given based on the built-in linear solver in Mathematica, with results being accurate and better than the existing methods.(2) A sub-region BEM formulation is developed for solving the 2D fracture problem in a dielectric medium where the crack region is considered as an independent thin zone. The stress and electric displacement intensity factors are calculated for different dielectric constants and loads applied. By comparing the present exact solutions with those based on the simplified crack surface conditions(impermeable, permeable, semi-permeable), the suitability of the simplified crack surface models is identified.(3) The piezoelectric fracture problem is analyzed by the sub-region BEM. Considering the nonlinearity of electromechanical coupling along the crack surface, an iterative approach is proposed. Based on the new formulation, the intensity factors on the crack tip are calculated for different dielectric constants, piezoelectric constants and load magnitudes. Solutions based on the three simplified electric boundary conditions on the crack surface are also given and are further compared with the one based on the exact electric boundary condition.