中文摘要：

提出一种可以分析任意梯度功能梯度材料的分层模型，并采用该模型研究功能梯度板条平面裂纹问题．采用Fourier变换和传递矩阵法将该混合边值问题化为奇异积分方程组，通过数值求解获得应力强度因子．考察了分层模型的有效性，还讨论了材料梯度变化形式、结构几何尺寸和材料梯度参数对裂纹应力强度因子的影响，发现结构几何尺寸、材料梯度变化形式、以及材料梯度参数均对应力强度因子有显著影响．

英文摘要：

In this paper, a multi-layered model is developed and the plane elasticity problem for a functionally graded strip containing a crack has been considered by using this model. By utilizing the Fourier transformation technique and the transfer matrix method, the mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. The influences of the graded variation of material parameters and geometric parameters on the stress intensi- ty factors are investigated. The numerical results show that the graded variation of material parameter has significant effects on the stress intensity factors.