3D Derivations of Static Plate Theories. In : Section on plates. Encyclopedia of Continuum Mechanics
Type de document
CHAPITRE D'OUVRAGE (CO)
Langue
anglais
Auteur
Résumé / Abstract
Plates are three-dimensional structures with a small dimension compared to the other two dimensions. Numerous approaches were suggested in order to replace the three-dimensional problem by a two-dimensional problem while guaranteeing the accuracy of the reconstructed three-dimensional fields. Turning the 3D problem into a 2D plate model is known as dimensional reduction.The approaches for deriving a plate model from 3D elasticity may be separated in two main categories: axiomatic and asymptotic approaches. plates.Both approaches are related but yield different plate models. This choice is motivated by the following considerations. First, ReissnerHencky models are the most widely used plate models in engineering applications. Indeed, their boundary conditions seem more natural than those of the Kirchhoff-Love plate model. They displacement required for finite elements implementations. Second, the Kirchhoff-Love model may be directly retrieved from these ?Direct Derivation of Plate Theories?.Two modifications are made with respect to the historical contributions. First, the membrane model is also included in the present derivation at very little price. Second, the applied load is a body force uniformly distributed through the thickness instead of a force per unit surface applied only on the upper face of the plate. This choice leads to a more compact derivation the membrane and bending problems widely ignored in the historical literature. Finally, all mathematical developments are purely formal and the reader is referred to for rigorous justifications.
Editeur
Springer
