Relationships between classical and shear deformation theories of axisymmetric circular plates

Abstract

The exact relationships between the deflections, slopes/rotations, shear forces, and bending moments of a third-order theory and those of the classical theory and the first-order shear deformation theory for axisymmetric bending of isotropic circular plates are developed. The relationships enable one to obtain the solutions of the third-order theory from any known classical or first-order theory solutions of axisymmetric circular plates for any set of boundary conditions and transverse loads. The relationships may also be used to develop finite element models of axisymmetric bending of circular plates according to the first-order and third-order theories.