中文摘要：

利用奇异积分方程方法研究两个半无限大的功能梯度压电压磁材料粘结，在渗透和非渗透边界条件下的Ⅲ型裂纹问题．首先通过积分变换构造出原问题的形式解，然后利用边界条件通过积分变换与留数定理得到‘组奇异积分方程，最后利用Gauss—Chebyshev方法进行数值求解，讨论材料参数、材料非均匀参数以及裂纹几何形状等对裂纹尖端应力强度因子的影响．从结果中可以看出，压电压磁复合材料中反平面问题的应力奇异性形式与一般弹性材料中的反平面问题应力奇异形式相同，但材料梯度参数对功能梯度压电压磁复合材料中的应力强度因子和电位移强度因子有很大的影响．

英文摘要：

In this paper, the mode Ⅲ crack in two bonded half infinite functionally graded magneto-electroelastic materials is investigated. It is assumed that the elastic stiffness, piezoelectric constant, and dielectric permittivity of the magneto-electro-elastic material vary continuously along the thickness of the strip. The crack is assumed to be either magneto-electrically impermeable or permeable. Integral transforms and dislocation density functions are employed to reduce the problem to Cauchy singular integral equations which can be solved numerically by Gauss-Chebyshev method. Numerical results are obtained to illustrate the variations of the stress intensity factors （SIFs） with the parameters such as material nonhomogeneity factor, crack sizes, loading conditions, which are shown graphically.