中文摘要：

3-D 的答案在 piezoelectric/piezomagnetic 的矩形的可渗透的快克合成材料被使用概括 Almansi 的定理和 Schmidt 方法调查。这个问题通过 Fourier 变换被提出进三个双不可分的方程，未知变量在是排水量跳过裂缝表面。解决双不可分的方程，排水量跳过裂缝表面直接作为一系列 Jacobi 多项式被扩展。最后，关系在之间电走，裂缝边附近的磁性的流动地和压力地被获得并且在 piezoelectric/piezomagnetic 的压力，电的排水量和磁性的流动紧张因素上的矩形的裂缝的形状的效果合成材料被分析。

英文摘要：

The solution of a 3-D rectangular permeable crack in a piezoelectric/piezomagnetic composite material was investigated by using the generalized Almansi＇s theorem and the Schmidt method.The problem was formulated through Fourier transform into three pairs of dual integral equations,in which the unknown variables are the displacement jumps across the crack surfaces.To solve the dual integral equations,the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials.Finally,the relations between the electric filed,the magnetic flux field and the stress field near the crack edges were obtained and the effects of the shape of the rectangular crack on the stress,the electric displacement and magnetic flux intensity factors in a piezoelectric/piezomagnetic composite material were analyzed.