压电材料中椭圆片状裂纹问题精确解的一种方法

在线性压电陶瓷本构关系和裂纹边界绝缘的框架下，用超奇异积分方程的方法对椭圆类片状裂纹问题进行了重新研究．超奇异积分方程中的未知位移间断和电势间断近似地表示为基本密度函数与多项式之积，其中基本密度函数反映了椭圆片状裂纹前沿电弹性场的奇异性，而多项式在均布载荷作用下可用一个常数来表达．引入椭球坐标系后，得到了均布载荷作用下未知位移间断和电势间断的解析解．使用这些解析解和电弹性场强度的定义，得到了裂纹前沿Ⅰ型、Ⅱ型和Ⅲ型应力强度因子以及电位移强度因子的精确表达式．法向均布载荷作用下的结果与现有精确解完全一致，切向均布载荷作用下的结果则尚未见有其它报道．

A NOVAL METHOD ON EXACT SOLUTIONS OF ELLIPTICAL CRACKS IN PIEZOELECTRICS

According to the constitutive relationship in linear piezoceramics,elliptical crack problems in impermeable case are analyzed with hypersingular integral equation method.Unknown displacement and electric potential jumps in the integral equations are approximated with a product of fundamental density function and polynomials,in which the fundamental density function reflects singular behavior of electroelastic fields near the crack front and the polynomials can be reduced to a real constant under uniform loading.The ellipsoidal coordinates are introduced to solve the unknown displacement and electric potential jumps in the integral equations under uniform loading.With the help of these solutions and definitions of electroelastic field intensity factors,exact expressions for mode I,mode II and mode III stress intensity factors as well as mode IV electric displacement intensity factor are obtained.The present results under uniform normal loading are the same as the available exact solutions,but those under uniform shear loading have not been found in the literature.