Finite element analysis of peak stress and stress gradient at an elliptical through-hole

The peak stress and stress gradient (parameters required for fatigue strength assessment) at an elliptical through-hole in a wide plate under uniaxial tension have been studied by means of three-dimensional finite element analysis with high mesh density. Dimensionless variables have been used throughout the investigation. The accuracy of two-dimensional finite element analysis has been assessed by extrapolating peak stress at an elliptical hole to infinite plate width and mesh density and comparing the extrapolated value with the closed-form Kolosov–Inglis solution (deviation < 0.2%). First- and second-order elements with full and reduced integration have been employed. Methods for determining stress gradients, using a varying number of nodal stresses, have been investigated. The accuracy of three-dimensional finite element analysis has been assessed by comparing the plane-strain peak stress for an elliptical through-hole with the corresponding plane-strain value from two-dimensional analysis (deviation < 0.1%). Peak stresses at the apex of the elliptical through-hole have also been determined for this three-dimensional mesh assuming a free plate surface. In particular, beside the maximum peak stress and its location, peak stresses have been determined at the surface and at the mid-plane of the plate for thicknesses ranging from 0.2 to 10 times the axis of the elliptical hole. The stress gradients at these locations have been determined, too. The minimum stress gradient is observed at the location of maximum stress. For sufficiently thin and thick plates, the mid-plane stresses approach two-dimensional plane-stress and generalised plane-strain solutions, respectively.