带周期裂纹的不同材料拼接的弹性长条基本问题

On Problems of Strip Bonded by Two Different Elastic Materials with Arbitrary Periodic Cracks

本文讨论了具有任意形状和个数的周期裂纹的不同材料拼接的弹性长条基本问题(裂纹彼此不相交且不与边界和拼接线相交)。把此问题变成了求解拼接线、裂纹。反边界上的奇异积分方程,由此可得出解的存在和唯一性。其次,利用分拆函数的方法,对带周期共线直裂纹的情形给出了封闭形式的解。

In this paper, the first and the second fundamental static problems of two elastic strips bonded by different materials with arbitrary cracks are discussed (the cracks intersect with neither the boundary lines nor the interface nor themselves). We assume the stresses to be periodic and bounded. We reduce such problems to a singular integral equation of normal type along the cracks, the boundary lines and the interface, for which, the existence and uniquenses of the solution is proved. Using the method of sepcration, we obtain the solution in closed form in case of horizontal colinearperiodic cracks.