Abstract
An exact three dimensional solution for the problem of a transversely loaded, simply supported rectangular plate of arbitrary thickness is presented within the linear theory of elastostatics. The solution, obtained in a semi-inverse fashion, satisfies all the boundary conditions of the problem in a pointwise manner and is in the form of a double Fourier sine series. The classical Navier solution for the problem is shown to be the limit of the present solution as the plate thickness aspect ratio approaches zero. It is noted that the solution presented provides a benchmark against which approximate theories of transversely loaded plates may be measured. The new elasticity solution also provides a heuristic basis for a novel theory of thick plates of arbitrary planform and edge support recently given by the author.
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Levinson, M. The simply supported rectangular plate: An exact, three dimensional, linear elasticity solution. J Elasticity 15, 283–291 (1985). https://doi.org/10.1007/BF00041426
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DOI: https://doi.org/10.1007/BF00041426