Abstract
For the deformation of an isotropic thick plate, a refined theory to derive two-dimensional approximate equations with any desired accuracy is proposed. Especially, for a plate under any distributed load at the surfaces, equations for extensional deformation as well as flexural deflection in the general n-th order approximation are derived from fundamental equations. Approximate equations presented are solved for a plate subjected to a sinusoidally distributed load at the upper surface, and the results are compared with the exact solution and with those derived from several approximate theories hitherto obtained through numerical calculation. It is shown that approximate equations presented in this paper have the following properties: (1) With increasing the order of approximation, the solution of approximate equation improves in accuracy and approaches the exact solution. (2) Approximate solution of stress satisfies the boundary conditions at the surfaces of the plate. (3) The accuracy of the approximate solution decreases monotonically with increasing the thickness of the plate. (4) The effect of Poisson's ratio on the accuracy of the solution is small and can be neglected for practical purposes.
