Stress singularities at angular corners in first-order shear deformation plate theory

The first-known Williams-type singularities caused by homogeneous boundary conditions in the first-order shear deformation plate theory (FSDPT) are thoroughly examined. An eigenfunction expansion method is used to solve the three equilibrium equations in terms of displacement components. Asymptotic solutions for both moment singularity and shear-force singularity are developed. The characteristic equations for moment singularity and shear-force singularity and the corresponding corner functions due to ten different combinations of boundary conditions are explicated in this study. The validity of the present solution is confirmed by comparing with the singularities in the exact solution for free vibrations of Mindlin sector plates with simply supported radial edges, and with the singularities in the three-dimensional elasticity solution for a completely free wedge. The singularity orders of moments and shear forces caused by various boundary conditions are also thoroughly discussed. The singularity orders of moments and shear forces are compared according to FSDPT and classic plate theory.