Semianalytical Solution of Rectangular Plates

Abstract

A general procedure is developed for the static analysis of a single transversely loaded rectangular plate. Boundary displacements are expressed as linear functions plus sine series, and boundary normal moments by sine series. Unknown coefficients are determined to make stationary a modified total potential energy principle, which is shown to be equivalent to a weighted integral method. The procedure enables any rectangular plate with uniform boundary conditions on each side, with or without corner displacements, to be analyzed. Equations obtained using the method are identical to those obtained for solving a number of well-known plate problems that have been treated in a range of ways, and in a sense the method unifies those procedures. The method also enables additional cases to be treated in a semianalytical manner. As an example, a cantilever plate is treated in some detail.