On three-dimensional asymptotic solution, and applicability of Saint–Venant’s principle to pie-shaped wedge and end face (of a semi-infinite plate) boundary value problems

Abstract Three-dimensional asymptotic singular stress fields near the fronts of infinite wedges are presented. This investigation is devoted to establishment of rigorous conditions as to whether the presence of wedge or end face stress singularity, which depends on the prescribed boundary condition, can validate or invalidate the heuristic assumption implicit in Saint–Venant’s principle. This is accomplished by applying a general approach to the solution of canonically singular problems, based on the concept of proper boundary-value problem, the theorem of homogeneous solutions, and classification of boundary value problems (BVP) of three-dimensional elasticity theory into class S (Saint–Venant) or class N (non-Saint–Venant).