横观各向同性压电材料中裂纹问题的边界元法

采用Somigiliana公式给出了三维横观各向同性压电材料中的非渗漏裂纹问题的一般解和超奇异积分方程，其中未知函数为裂纹面上的位移间断和电势间断．在此基础上，使用有限部积分和边界元结合的方法，建立了超奇异积分方程的数值求解方法，并给出了一些典型数值算例的应力强度因子和电位移强度因子的数值结果，结果令人满意．

BOUNDARY ELEMENT METHOD OF MODE-I CRACK IN TRANSVERSELY ISOTROPIC PIEZOELECTRIC MATERIALS

Using Somigiliana's formula, the general solutions and hypersingular integral equations for a three-dimensional impermeable crack problem in an infinite transversely isotropic piezoelectric solid under mechanical and electrical loads are given. The unknown functions are the discontinuities of the elastic displacements and electrical potential of the crack surface. Then, a numerical technique to solve the hypersingular integral equations is proposed based on the boundary element method combined with the finite-part integral method. Finally, a rectangular crack under mechanical tension and electrical fields is analyzed, and the numerical results of the stress and electric displacement intensity factors are presented. It is shown that the numerical solutions are satisfactory, which shows that the present approach is powerful to solve three-dimensional crack problems of piezoelectric materials.