Exact in-plane stress field solution for isotropic plates with circular holes reinforced with cylindrically orthotropic rings

Abstract

In this paper an analytical solution for the stress distribution in an infinite plate with a concentrically reinforced hole under a general loading condition is derived. The developed solution explicitly accounts for the elastic properties of the plate and of the reinforcing annulus, for the hole radius to reinforcing ring thickness ratio, as well as the loading conditions, including loads applied onto the hole boundary and on the plate, far away from the hole. A careful validation of the proposed framework is carried out by comparing the newly developed solution with the results from a number of finite element analyses, documenting a very satisfactory agreement.The solution derived represents a useful tool toward the understanding of the stress fields in polymeric components with reinforced holes and made with fused deposition modelling technologies.