Analysis of stress concentrations in plates with rectangular openings by a combined conformal mapping – Finite element approach

Plates with rectangular openings develop stress concentrations under bending. While these stresses can be determined using finite elements, in many problems this would be difficult because a high density mesh would be needed in the neighborhood of every opening corner. In this paper, it is shown how a complex-variable conformal mapping approach can be numerically coupled with the finite element method to analyze these corner stresses. This approach can be used even with relatively coarse meshes where the finite element results, by themselves, do not resolve the stress concentrations. In essence, the method relies on finite element analysis to obtain information on the stress field in a region surrounding the plate opening; this information is subsequently used to set up the parameters of the conformal mapping approach to obtain the near field stresses at the opening corners.