Corner stress singularities in a high-order plate theory

In the context of Loʹs high-order plate theory, the present work applies the eigenfunction expansion approach to investigating the Williams-type stress singularities at the vertex of a wedge. The characteristic equations for determining the orders of singularities in stress resultants are separately developed for plates under extension and bending. The characteristic equations of plates under extension differ from those in generalized plane stress cases when the clamped boundary condition is imposed along one of the radial edges around the vertex. For plates under bending, the presented characteristic equations are identical to those of first-order shear deformation plate theory (FSDPT) if the clamping is not involved in boundary conditions along the radial edges of the vertex. The orders of singularities in stress resultants, which vary with the vertex angle, are plotted for various types of boundary conditions. The results are also comprehensively compared with those obtained according to other plate theories such as classical plate theory, FSDPT and Reddyʹs refined plate theory.