Mathematical Elasticity
：Volume II: Theory of Plates
( Volume 27 )
Publication subTitle ：Volume II: Theory of Plates
Publication series ：Volume 27
Author： Ciarlet Philippe G.
Publisher： Elsevier Science
Publication year： 1997
E-ISBN: 9780080535913
P-ISBN(Paperback): 9780444825704
P-ISBN(Hardback): 9780444825704
Subject： O343 弹性力学
Language： ENG
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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 studie
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