A new Navier-type three-dimensionally exact solution for small deflections in bending of linear elastic isotropic homogeneous rectangular plates of constant thickness is presented. In this solution the transversal normal stresses identically vanish, and the loading is a volume force with a distribution across the plate thickness being a characteristic of the solution. The presented solution can be used for the evaluation of approximate plate theories and numerical solutions which comprise the assumption of transversal normal stresses vanishing in the whole plate.
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Heinrich Werner (1999) studied this question.
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