Three-dimensional effects for through-thickness cylindrical inclusions in an elastic plate

A quasi-three-dimensional theoretical closed-form solution for a cylindrical inclusion embedded in an isotropic elastic plate of finite thickness is obtained using the Kane-Mindlin theory. The present solution gives an insight into the transition from plane stress to plane strain. It is shown that strong three-dimensional effects exist near the inclusion even in very thin plates. Moreover, it is shown that two-dimensional plane stress and plane strain solutions are not always the two limits for a three-dimensional problem. The effects of plate thickness and inclusion radius, material constants of the inclusion and the matrix, as well as interference fitting on the stress concentration factor are discussed. The three-dimensional affected zone around the inclusion can be determined from the present solution. The variation of the lateral contraction and shear stresses is discussed. The comparison between the finite element results and the present results shows good agreement.