Abstract
In the paper, the ranges in application of the classical theory and the first-order shear deformation theory, called the Mindlin theory, for bending problem of a rectangular plate under surface force on an elastic foundation were discussed by comparing the three-dimensional (3-D) theory of elasticity. A circumferentially simply-supported rectangular plate on the Winkler foundation was analyzed when the plate was subjected to a fully distributed uniform load at the top surface. The solutions of the theories are mathematically expressed by using the double Fourier series. We computed the distributions of displacements or stresses along the in-plane or transverse direction of the plate, the strain energies of the plate and the elastic energies of the Winkler foundation. The ranges in application of the classical and Mindlin theories were clarified on the basis of displacements, stresses, strain energies and elastic energies computed with the 3-D theory of elasticity.
