An overview of the relationships between solutions of the classical and shear deformation plate theories

In this paper an overview of the algebraic relationships between the solutions of the classical plate theory and those of the first-order and third-order shear deformation plate theories is presented. The relationships for deflections, buckling loads, and natural frequencies enable one to obtain the solutions of the first-order shear deformation plate theory from the well-known classical thin-plate theory solutions without solving the governing differential equations of the shear deformation theory.