Mathematical Elasticity - 1st Edition - ISBN: 9780444825704, 9780080535913

Mathematical Elasticity, Volume 27

1st Edition

Volume II: Theory of Plates

Serial Editors: Philippe G. Ciarlet
eBook ISBN: 9780080535913
Hardcover ISBN: 9780444825704
Imprint: North Holland
Published Date: 22nd July 1997
Page Count: 496
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Table of Contents

Part A. Linear Plate Theory. 1. Linearly elastic plates. 2. Junctions in linearly elastic multi-structures. 3. Linearly elastic shallow shells in Cartesian coordinates. Part B. Nonlinear Plate Theory. 4. Nonlinearly elastic plates. 5. The von Kármán equations.


Description

The objective of Volume II is to show how asymptotic methods, with the thickness as the small parameter, indeed provide a powerful means of justifying two-dimensional plate theories. More specifically, without any recourse to any a priori assumptions of a geometrical or mechanical nature, it is shown that in the linear case, the three-dimensional displacements, once properly scaled, converge in H1 towards a limit that satisfies the well-known two-dimensional equations of the linear Kirchhoff-Love theory; the convergence of stress is also established.

In the nonlinear case, again after ad hoc scalings have been performed, it is shown that the leading term of a formal asymptotic expansion of the three-dimensional solution satisfies well-known two-dimensional equations, such as those of the nonlinear Kirchhoff-Love theory, or the von Kármán equations. Special attention is also given to the first convergence result obtained in this case, which leads to two-dimensional large deformation, frame-indifferent, nonlinear membrane theories. It is also demonstrated that asymptotic methods can likewise be used for justifying other lower-dimensional equations of elastic shallow shells, and the coupled pluri-dimensional equations of elastic multi-structures, i.e., structures with junctions. In each case, the existence, uniqueness or multiplicity, and regularity of solutions to the limit equations obtained in this fashion are also studied.


Details

No. of pages:
496
Language:
English
Copyright:
© North Holland 1997
Published:
Imprint:
North Holland
eBook ISBN:
9780080535913
Hardcover ISBN:
9780444825704

Reviews

@qu:...It is an important work describing the justification of two-dimentional engineering theories of plates and shallow shells and should be purchased by university libraries. @source:Applied Mechanics Reviews, Vol.51, No.6


About the Serial Editors

Philippe G. Ciarlet Serial Editor

Affiliations and Expertise

Universite Pierre et Marie Curie, Paris