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.

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