Investigation of thickness effects on the bending singularities of a notched plate

In this paper, the bending singularities of a notched plate are investigated through the finite element method. The computed singular parameters, including the singularity orders and associated corner functions, are compared with those of classical plate theory and first-order shear deformation plate theory (FSDPT); the comparisons demonstrate the inaccuracy of the boundary conditions in classical plate theory. The thickness effects are then investigated through the finite element method. The results show that although the singularity parameters computed by finite element agree with those of the FSDPT in the interior of the plate, the FSDPT is not applicable at the notch tip on the top or bottom surface because of substantial free surface effects. For a very thin plate, the inconsistence in the comparison slightly increases because of the free surface effects.