含不可渗透边裂纹压电材料反平面问题的解

Solutions of an antiplane edge-crack in a rectangular piezoelectric material

研究了含边缘裂纹的矩形截面压电材料在平面内电场和反平面荷载作用下的问题。得到了满足拉普拉斯方程、裂纹面边界条件的位移函数解和电势函数解及电弹场的基本解。最后,用边界配置法计算了能量释放率。本文提出的这种半解析半数值的方法计算简便,而且具有广泛的应用性。

The problem involving an edge-crack in a rectangular material under inplane electrical loading and antiplane mechanical shear loading is analyzed, a general solution of electro-mechanical field is obtained, which satisfies both Laplace equation and the boundary conditions of the crack sufraces, the unknown constant can be solved by the boundary condition around the rectangular piezoelectric body. At last, the boundary collocation method is used to calculate the energy release rate. It is shown that the method of semi-analytical and semi-numeral is simple, and widely applicable.