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

• Three-dimensional asymptotic singular stress field in the vicinity of a point located at the front of an infinite wedge.
• Dependence of stress singularity on wedge aperture angle for free–free, clamped–clamped, and free–clamped cases.
• The class of end face problem with free–free and clamped–clamped counterparts belong to the class S.
• The class of end face problem with free-clamped boundary condition belongs to class N.

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).