# Mathematical Elasticity, Volume 2: Theory of Plates (Studies in Mathematics and its Application) download epub

#### by **Phililppe G. Ciarlet**

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**Fb2 Book:**1397 kb.

Mathematical Elasticity, Volume 2: Theory of Plates (Studies in Mathematics and its Applications).

Studies in mathematics and its applications. PHILIPPE G. CIARLET Universitd Pierre et Marie Curie, Paris

Studies in mathematics and its applications. CIARLET Universitd Pierre et Marie Curie, Paris.

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

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.

Mathematical Elasticity, Volume 2: Theory of Plates (Studies in Mathematics and its . Mathematical elasticity.

Mathematical Elasticity, Volume 2: Theory of Plates (Studies in Mathematics and its Applications). Introduction to Mathematical Elasticity.

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. In the nonlinear case

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It provides a thorough description (with emphasis on the nonlinear aspects) of the two competing mathematical models of three-dimensional elasticity, together with a mathematical analysis of these models. The book is as self-contained as possible. Categories: Education. Series: Studies in Mathematics and its Applications.

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Volume II: Theory of Plates. View all volumes in this series: Studies in Mathematics and its Applications.

Volume II: Theory of Plates. Hardcover ISBN: 9780444825704. eBook ISBN: 9780080535913. Imprint: North Holland. Published Date: 22nd July 1997. Page Count: 496. Select country/region

Выделяйте текст, добавляйте закладки и делайте заметки, скачав книгу "Mathematical Elasticity: Volume II. .

Выделяйте текст, добавляйте закладки и делайте заметки, скачав книгу "Mathematical Elasticity: Volume II: Theory of Plates" для чтения в офлайн-режиме. 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.

*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 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.

**Author:**Phililppe G. Ciarlet

**ISBN:**0444825703

**Category:**Science & Math

**Subcategory:**Mathematics

**Language:**English

**Publisher:**North Holland; 1 edition (August 5, 1997)

**Pages:**497 pages