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Mathematical Elasticity: Volume II: Theory of Plates als Buch
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Mathematical Elasticity: Volume II: Theory of Plates

Sprache: Englisch.
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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 … weiterlesen
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Mathematical Elasticity: Volume II: Theory of Plates als Buch

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Titel: Mathematical Elasticity: Volume II: Theory of Plates

ISBN: 0444825703
EAN: 9780444825704
Sprache: Englisch.
Herausgegeben von Philippe G. Ciarlet
ELSEVIER LTD

August 1997 - gebunden - 496 Seiten

Beschreibung

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 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.

Inhaltsverzeichnis

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 Karman equations.

Pressestimmen

...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. Applied Mechanics Reviews, Vol.51, No.6
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