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Mathematical Elasticity, Volume 27 - Volume II: Theory of Plates (Hardcover) Loot Price: R4,405
Discovery Miles 44 050
Mathematical Elasticity, Volume 27 - Volume II: Theory of Plates (Hardcover): Philippe G. Ciarlet

Mathematical Elasticity, Volume 27 - Volume II: Theory of Plates (Hardcover)

Philippe G. Ciarlet

Series: Studies in Mathematics & Its Applications

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Loot Price R4,405 Discovery Miles 44 050 | Repayment Terms: R413 pm x 12*

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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 "H"1 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 Karman 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.

General

Imprint: North-Holland
Country of origin: United States
Series: Studies in Mathematics & Its Applications
Release date: July 1997
First published: August 1997
Series editors: Philippe G. Ciarlet
Dimensions: 234 x 156 x 33mm (L x W x T)
Format: Hardcover
Pages: 496
ISBN-13: 978-0-444-82570-4
Categories: Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
Books > Science & Mathematics > Mathematics > Applied mathematics > General
Books > Science & Mathematics > Physics > Classical mechanics > General
Books > Professional & Technical > Mechanical engineering & materials > Materials science > Mechanics of solids > General
Books > Academic & Education > Professional & Technical > Mathematics
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LSN: 0-444-82570-3
Barcode: 9780444825704

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