Definition
Justifying plate models consists in deriving limit bidimensional models (membrane or bending models) starting from the complete three-dimensional models considering the thickness as a small parameter supposed to vanish. The mathematical approach avoids any mechanical or geometrical simplification.
Introduction
The interest of lower dimensional models for elastic structures relies on simpler mathematical formulation and on gain of space and time in numerical computations. In order to get bidimensional models, some mechanical or geometrical assumptions are made; for example, by imposing vanishing in-plane stresses, or preventing any rotation of the normal to the cross section, one can obtain bending models for plates. In this chapter the formal asymptotic expansion method is investigated to justify rigorously (i.e., without any mechanical assumptions) the equilibrium equations of the Kirchhoff-Love elastic plate...
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Miara, B. (2018). Mathematical Justifications of Plate Models. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_138-1
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DOI: https://doi.org/10.1007/978-3-662-53605-6_138-1
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