rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Mathematical elasticity
    part number: Volume II
    part name: Theory of plates
  title info:
    title: Theory of plates
  name:
    name part: Ciarlet, Philippe G.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: ScienceDirect (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: ne
    date issued: 1997
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource : illustrations
  abstract: 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 K̀rm̀n 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.
  table of contents: v. 1. Three-dimensional elasticity -- v. 2. Theory of plates -- v. 3. Theory of shells.
  note: Philippe G. Ciarlet.
  note: Includes bibliographical references and indexes.
  subject:
    topic: Elasticity
  subject:
    topic: Elastic plates and shells
  subject:
    topic: Elasticity
  subject:
    topic: Élasticité
  subject:
    topic: Plaques et coques élastiques
  subject:
    topic: SCIENCE
    topic: Mechanics
    topic: General
  subject:
    topic: SCIENCE
    topic: Mechanics
    topic: Solids
  subject:
    topic: Elastic plates and shells
  subject:
    topic: Elasticity
  subject:
    topic: Elasticiteit
  classification: QA931 .C59 1997
  classification: 531/.381
  related item:
    title info:
      title: Mathematical elasticity
    name:
      name part: Ciarlet, Philippe G.
    origin info:
      publisher: Amsterdam ; New York : North-Holland ; New York, N.Y., U.S.A. : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1988-2000
    identifier: (DLC) 87023741
    identifier: (OCoLC)16684938
  related item:
    title info:
      title: Studies in mathematics and its applications ; v. 27
  identifier: 9780444825704
  identifier: 0444825703
  identifier: 9780080535913
  identifier: 0080535917
  identifier: 129374:129625 Elsevier Science & Technology
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: OPELS
    record creation date: 070806
    record change date: 20260326152022.4
    record identifier: in00005733176
    language of cataloging:
      language term: eng