Three-dimensional asymptotic stress field in the vicinity of the line of intersection of a circular cylindrical through/part–through open/rigidly plugged hole and a plate

Abstract

Heretofore unavailable asymptotic solutions to a class of problems pertaining to the stress fields in the neighborhood of the circumferential corner line or line of intersection of a circular cylindrical through or part-through (embedded) open or rigidly plugged hole and a bounding or interior surface of an isotropic plate, subjected to far-field extension-bending (mode I), inplane shear-twisting (mode II) and torsional (mode III) loadings, are presented. A local orthogonal curvilinear coordinate system (ρ,φ,θ), is selected to describe the local deformation behavior of the afore-mentioned plate in the vicinity of the afore-mentioned circumferential corner line. One of the components of the Euclidean metric tensor, namely g₃₃, is approximated (ρ/a⋘1) in the derivation of the kinematic relations and the ensuing governing system of three partial differential equations. Nine different combinations of boundary conditions are considered, five of which relate to a through hole or infinitely rigid inclusion, while the remaining four pertain to a part–through (embedded) hole or infinitely rigid inclusion. Numerical results presented include the effect of Poisson's ratio, wherever applicable, on the computed lowest eigenvalue(s).