Existence Theorems in the Geometrically Non-linear 6-Parameter Theory of Elastic Plates

In this paper we show the existence of global minimizers for the geometrically non-linear equations of elastic plates, in the framework of the general 6-parameter shell theory. A characteristic feature of this model for shells is the appearance of two independent kinematic fields: the translation ve...

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Bibliographic Details
Published in:Journal of elasticity 2013-07, Vol.112 (2), p.185-198
Main Authors: Bîrsan, Mircea, Neff, Patrizio
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Physics
Physics and Astronomy
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Summary:In this paper we show the existence of global minimizers for the geometrically non-linear equations of elastic plates, in the framework of the general 6-parameter shell theory. A characteristic feature of this model for shells is the appearance of two independent kinematic fields: the translation vector field and the rotation tensor field (representing in total 6 independent scalar kinematic variables). For isotropic plates, we prove the existence theorem by applying the direct methods of the calculus of variations. Then, we generalize our existence result to the case of anisotropic plates.
ISSN:0374-3535
1573-2681
DOI:10.1007/s10659-012-9405-2