Abstract
An exact three-dimensional Lévy-type solution for the bending of an elastic slab is one in which there are edge loads only and the unknown displacement and stresses have very simple polynomial dependence on the thickness coordinate. Lévy obtained such a solution in 1877 for a linearly elastic, isotropic, plate-like body. The most general material that allows bending and stretching to be uncoupled is monoclinic (13 elastic constants). However, it is shown that only transversely isotropic materials (5 elastic constants) admit exact solutions having polynomial dependence in the thickness direction. Such solutions are listed explicitly.
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Simmonds, J. Exact Lévy-Type Solutions for Plate Bending Exist for Transversely Isotropic but Not for General Monoclinic Materials. Journal of Elasticity 75, 49–56 (2004). https://doi.org/10.1023/B:ELAS.0000039923.57601.61
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DOI: https://doi.org/10.1023/B:ELAS.0000039923.57601.61