含椭圆孔的压电材料反平面应变问题的精确解

EXACT SOLUTION OF ANTIPLANE STRAIN PROBLEM FOR THE PIEZOELECTRIC MATERIALS WITH AN ELLIPTIC HOLE

考虑椭圆孔内空气介质对电场的作用，用复变函数的Ｆａｂｅｒ级数展开方法，分析了含椭圆孔的压电材料反平面应变问题的耦合场，给出了问题的精确解。将精确解与齐次边界条件结果（近似解）进行了比较，两者的弹性均完全一致，产生弹性场奇异性的物理因素相同。

The electric field boundary conditions for the holes and voids at the material surfaces were considered as the homogeneous or constant boundary conditions by the previous researches.In this paper,in consideration of air medium inside the hole defects acting on the electric field, a coupled field of antiplane strain problem for the piezoelectric material with an elliptic hole is analyzed with an expression for potential function of complex veriable in Faber series. An exact solution of the problem is given.These results are compared with some results of previous researches by using homogeneous boundary conditions.