3D stress concentration around circular hole under remote biaxial loading

In this study, a theoretical model is proposed to analyze the stress concentration in a plate of finite thickness containing a circular hole under remote biaxial loading. The stresses in a plate with a circular hole under remote biaxial loading is a superposition of the stresses in the unperforated plate and the released stresses induced by opening the hole. For the latter, the stresses at the edge of the hole can be further decomposed into a spherical component and a deviatoric component. The solution due to a spherical component can be readily obtained but the solution due to a deviatoric component is hard to find. According to the literature, the solution of three-dimensional stress distributions in a plate of finite thickness containing a circular hole can be found by four potential functions. The available fundamental solutions of the potential functions satisfying the boundary conditions on the surfaces of the plate contain numerous complicated integrals, which limits their application to the current problem. Nevertheless, these fundamental solutions can be found explicitly by constructing the orthogonal function, which is composed of the Bessel functions. A system of linear equations is established to satisfy the boundary conditions at the edge of the hole. Therefore, the stresses due to a deviatoric component are obtained by solving the linear simultaneous equations. The stress concentration factor calculated by the proposed model is validated with the available numerical and theoretical solutions. It is concluded that the stress ratio, the thickness of the plate, and Poisson's ratio have an important influence on the distribution of the stress concentration factor along the thickness of the plate, especially on the distribution near the surface. Moreover, the proposed model can be extended to analyze the stress concentration at the edge of a circular hole in a plate of finite thickness under remote bending. The model is efficient and reliable, and it can provide a powerful analytical method to analyze three-dimensional stress concentrations around holes under various remote loading in engineering.