Exact Mixed-Kirchhoff Solutions for the Bending Analysis of Reissner Plates

The plate theory has been and is still a subject which has been very extensively studied for a century. In the theory of plates usually two different limit cases are considered: the Kirchhoff and the shear deformable plate. Of the many shear deformable plate theories proposed over the years, the Reissner plate theory is fundamentally simpler to adopt for modeling the shear deformation behavior of thick plates. This paper presents exact axisymmetric bending solutions of thick plates based on the Reissner plate theory. The solutions are displayed in terms of the corresponding Kirchhoff (or classical thin) plate solutions. These Kirchhoff-Reissner bending relationships are derived using the mathematical similarity of the governing equations of the two plate theories and the basis of load equivalence. The relationships allow one to readily deduce the more accurate Reissner plate solutions that account for the effect of transverse shear deformation, without having to solve the more complicated Reissner plate equations.

Keywords:

Kirchhoff plate theory , Reissner plate theory , Axisymmetric bending relationships