Stress concentration in a solid with symmetric U-shaped grooves

The two-dimensional and three-dimensional stress concentrations of thin and thick plates with symmetric U-shaped grooves under tension and bending wer e analysed using a combination of two kinds of three-dimensional special hy brid stress finite element: one contains a traction-free cylindrical surfac e and the other contains a traction-free planar surface. The computed resul ts show that three-dimensional stress concentration factors of thick plates with symmetric U-shaped grooves are always larger than those corresponding to thin plate and Neuber's analytical values underestimate the stress conc entration factors. The results also confirm Kikukawa's observation that the maximum stress concentration may occur in plate with grooves of finite dep th rather than in plate with infinitely deep grooves.