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An exact theory of the bending of transversely inextensible elastic plates

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Abstract

In this article, the exact solution of elasticity equations for transversally inextensible plates obtained using a symbolic integration method is given. In the limiting case, the theory is shown to lead to the Mindlin plate model. The theory is also applied to several cases, including the torsion of a rectangular plate, a rectangular plate under a double sinusoidal load, a strip under linearly variable pressure, a disk under uniform pressure, and an infinite plate with a circular hole subject to cylindrical bending. For the last case, it is shown by asymptotic expansion that the maximum circumferential stress concentration factor tends to a value of 3 for a very small hole.

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  1. Faculty of Maritime Studies and Transport, University of Ljubljana, Portorož, Slovenia

    Milan Batista

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  1. Milan Batista
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Correspondence to Milan Batista.

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Batista, M. An exact theory of the bending of transversely inextensible elastic plates. Acta Mech 226, 2899–2924 (2015). https://doi.org/10.1007/s00707-015-1356-9

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  • DOI: https://doi.org/10.1007/s00707-015-1356-9

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