Theory of Plates

  1. Home
  2. Bookstore
  3. Theory of Plates

Theory of Plates

By AUTHOR, UNKNOWN

Rent or Buy eTextbook

Expires on Apr 12th, 2022
$230

Publisher List Price: $234.99
Savings: $4.99

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.

Subject: Mathematics & Statistics -> Mathematics -> Mathematics General

Theory of Plates
Publisher: Elsevier S & T 07/1997
Imprint: North Holland
Language: English
Length: 496 pages

ISBN 10: 0444825703
ISBN 13: 9780444825704
Print ISBN: 9780444825704

Live Chats