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Incompressibility in Rod and Shell Theories

Published online by Cambridge University Press:  15 August 2002

Stuart S. Antman  and
Friedemann Schuricht
Stuart S. Antman
Affiliation:
Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742-4015, USA. ssa@math.umd.edu.
Friedemann Schuricht
Affiliation:
Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstraße 22-26, 04103 Leipzig, Germany. schur@mis.mpg.de.
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Abstract

We treat the problem of constructing exact theories of rods and shells for thin incompressible bodies. We employ a systematic method that consists in imposing constraints to reduce the number of degrees of freedom of each cross section to a finite number. We show that it is very difficult to produce theories that exactly preserve the incompressibility and we show that it is impossible to do so for naive theories. In particular, many exact theories have nonlocal effects.

Keywords

Incompressibilitytheories of rodstheories of shells.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 2 , March 1999 , pp. 289 - 304
Copyright
© EDP Sciences, SMAI, 1999

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