Large Deflections of Plates on Elastic Foundations

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Abstract
The evaluation of moderately large deflections of uniformly loaded plates on elastic foundations of the Winkler type is presented using Berger's approximation, which neglects the strain energy due to the second invariant of the middle surface strains. Because of this approximation, the problem may be formulated in terms of two decoupled nonlinear equations. Series solutions are obtained for circular and rectangular plates under various support conditions, and are numerically evaluated and presented in the form of graphs for plates of various aspect ratios with simply supported edges. Results obtained are compared with some known solutions, and it is concluded that Berger's approximate method yields results of sufficient accuracy for practical purposes.

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