A higher-order linear theory for isotropic plates—I. Theoretical considerations

Abstract

Using estimates of the strain field a new refined version of the linear theory of isotropic plates is constructed. The theory is expressed in terms of the same independent parameters of displacements as in the first-order shear deformation theory. The accuracy of the strain energy in this theory is of the order (h/L)4 (h-thickness, L-wavelength of deformation patterns) whereas the classical theory of plates has accuracy of the order h/L)2. The results of the present analysis provide evidence that some of the earlier proposed higher-order theories of isotropic plates are based on an incorrect hypothesis for the displacement field.