Stress singularities resulting from various boundary conditions in angular corners of plates of arbitrary thickness in extension

The stress singularities in angular corners of plates of arbitrary thickness with various boundary conditions subjected to in-plane loading are studied within the first-order plate theory. By adapting an eigenfunction expansion approach a set of characteristic equations for determining the structure and orders of singularities of the stress resultants in the vicinity of the vertex is developed. The characteristic equations derived in this paper incorporate that obtained within the classical plane theory of elasticity (M.L. Williams’ solution) and also describe the possible singular behaviour of the out-of-plane shear stress resultants induced by various boundary conditions.