Antiplane problem of periodic crack in a strip of functionally graded materials
弹性功能梯度材料板条中周期裂纹的反平面问题

In this paper, a single crack problem and a periodic crack antiplane problem of functionally graded materials (FGMs) are studied. An elementary solution is obtained, which represents the influence caused by a point dislocation placed at a point t on the real axis. The Fourier transform method is used to derive the elementary solution. After using the obtained elementary solution, the singular integral equation is formulated for the periodic crack problem. In the solution of the singular integral equation, the influence at the center crack caused by the many remote cracks is considered approximately. Finally, numerical results are presented, and the influence caused by the materials property a is addressed.