This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to Saved Citations Download to citation manager Request Permissions Request Reprints Add to My Marked Citations Citing Articles Citing Articles via Google Scholar Citing Articles via Scopus Google Scholar Articles by Genevey, K. Search for Related Content Social Bookmarking                         What's this?

Remarks on Nonlinear Membrane Shell Problems

Laboratoire d'Analyse Numrique, Universit Pierre et Marie Curie, 75252 Paris Cedex 05, France

We analyze the membrane model established by Miara for nonlinearly elastic shells. In particular, we show that the associated energy functional is coercive but not sequentially weakly lower semicontinuous. To prove this last property, it is shown that the energy density is not rank-1 convex and thus not quasi-convex. The authors also consider the membrane models derived by Le Dret and Raoult, using F- convergence methods. An expression of the F-limit energy density is given in terms of the partial derivatives of the displacement, valid for certain classes of deformations. It is also shown that, for plane membranes as for membrane shells, the formal asymptotic method and the F-convergence approach coincide, provided that the singular values of the deformation gradient belong to a specific subset of R².

Mathematics and Mechanics of Solids, Vol. 2, No. 2, 215-237 (1997)
DOI: 10.1177/108128659700200208


CiteULike    Complore    Connotea    Del.icio.us    Digg    Reddit    Technorati    Twitter    What's this?