Relationships between Kirchhoff and Mindlin bending solutions for Levy plates

Abstract

The exact relationships for the deflection, rotations, and stress resultants of Levy plates between the Mindlin and Kirchhoff solutions have been developed. These relationships allow analysts to readily determine the Mindlin Levy plate solutions from the corresponding well-known Kirchhoff Levy plate solutions. The relationships also help to elucidate the effect of transverse shear deformation on the deflection of Levy plates and serve to provide benchmark solutions for checking numerical solutions.