Stress concentration in a layered plane with an elliptical cutout

The article deals with the problem of stress concentration in an elastic layered plane with an elliptical cutout. The phenomenon is investigated using the concept of stress concentration tensor. Two levels of concentration are studied: because of the layering and because of the cutout. Formulas for the stress concentration tensor components are given separately in the case of an infinite layered plane (first level), as well as in the case of a homogeneous anisotropic plane with an elliptical cutout (second level). Stress concentration tensor in a layered plane with It is represented as a product of concentration tensors at the first and second levels. Approximate formulas for the components of the concentration tensor are given. The case of the coincidence of the orientation of the layers and the main axes of the elliptical hole is considered in detail. In this case, the concentration coefficients at characteristic points are calculated, graphs of the dependence of these coefficients on the ratio of the elastic modulus of the layers are given. In addition, a numerical solution of the problem was carried out using a finite element analysis package. The obtained analytical and numerical results are consistent with good accuracy.