The Three-Dimensional Stress Field in an Arbitrary Thickness Plate Holding a Circular Hole

This paper presents theoretical solutions for the three-dimensional (3D) stress field in an infinite isotropic elastic plate containing a through-the-thickness circular hole subjected to uni-axial tension at far field by using Kane and Mindlin assumption based on the displacement function method. The expressions of the stress concentration factor and the out-of-plane stress constraint factor are obtained in a concise, explicit form. A comprehensive analysis displays the effects of the plate thickness and Poisson’s ratio on the character of the in-plane stress field, stress concentration and out-of-plane constraint. The present solutions show that, in spite of their well coincidence with the related plane stress solutions for very thin plate cases, the deviated degree of the in-plane stress based on the 3D solutions is significant, as compared with the related plane stress solutions at some locations due to the influence of the plate thickness. It shows that Poisson’s ratio has an appreciate effect on the tangential stress near the surface of the hole. Outside this region, all the in-plane stresses are nearly independent of Poisson’s ratio. It is also found that the plate thickness and Poisson’s ratio has an appreciate effect on the stress concentration and out-of-plane constraint. The present theoretical solutions are verified by comparing them with some related result.