Relationships between Mindlin and Kirchhoff bending solutions for tapered circular and annular plates

Abstract

This paper concerns the problem of elastic, axisymmetric bending of tapered circular plates and tapered annular plates with a free edge. Exact relationships between Mindlin and Kirchhoff solutions for stress-resultants and deflections in such tapered axisymmetric plates are presented. The relationships apply for plates with the supported edge being either simply supported, or clamped or elastically restrained against rotation. Based on these relationships, the stress-resultants and the deflection due to transverse shear deformation in such plates can be readily determined from their corresponding Kirchhoff plate solutions without the necessity of a more complicated shear deformable plate analysis. The calculation of the Mindlin plate deflection is illustrated by a tapered annular plate example. These relationships should be useful for checking the convergence, validity and accuracy of numerical solutions.