Abstract This paper uses a Fourier transform technique, which uses dislocation density functions, to solve the problem of layered media with finite cracks perpendicular to the interface. This approach reduces the problem to the solution of two coupled integral equations each with a singular kernel which are the solved using Cauchy-Chebyshev polynomials. Two specified loading cases that are symmetric loading and asymmetric loading were considered in this paper respectively. Their corresponding analytical solutions were obtained. With these solutions, the analytical solution of offset loading relative to the crack location can be easily obtained by simple superposition. This has potential applications for solving fracture problems in structures such as broken sidewalks, airport runways, etc. A simple example is used to demonstrate the method proposed in this paper. This paper is the only paper to consider fractures perpendicular to the interface in two layered structures, subjected to asymmetric loading. Furthermore, it is the first paper to illustrate how to account for the effect of off-centred loading for the layered structures with cracks.

中文翻译：

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非对称载荷作用下裂纹层状介质应力强度因子计算

摘要 本文采用傅里叶变换技术，利用位错密度函数来解决层状介质中有限裂纹垂直于界面的问题。这种方法将问题简化为两个耦合积分方程的解，每个方程都有一个奇异核，这些方程使用柯西-切比雪夫多项式求解。本文分别考虑了对称载荷和非对称载荷两种指定载荷情况。得到了它们相应的解析解。有了这些解，通过简单的叠加就可以很容易地得到相对于裂纹位置的偏置载荷的解析解。这对于解决结构中的断裂问题具有潜在的应用，例如破碎的人行道、机场跑道等。用一个简单的例子来演示本文提出的方法。这篇论文是唯一一篇考虑在两层结构中垂直于界面的裂缝，受到不对称载荷的论文。此外，这是第一篇说明如何解释偏心载荷对带有裂纹的层状结构的影响的论文。