Bending of Clamped Plates

Abstract

Abstract The exact solution of thin rectangular plates clamped on all or part of the boundary requires the solution of two infinite sets of simultaneous equations in two sets of unknowns. A method of obtaining an approximate solution based upon minimization of energy and requiring the solution of the first i equations of a single infinite set of simultaneous equations is described and illustrated in this paper. The approximation functions are derived from functions representing the normal modes of a freely vibrating membrane for the same region. Solutions are obtained for a rectangular clamped plate supporting a uniform or a central point load and for a square plate clamped on two adjacent edges and pinned on the other two edges with either a uniform or a central point load. Analytical results are compared with experimentally determined deflections and stresses.