Incompressibility in Rod and Shell Theories

Stuart S. Antman; Friedemann Schuricht

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 33, Issue: 2, page 289-304
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Antman, Stuart S., and Schuricht, Friedemann. "Incompressibility in Rod and Shell Theories." ESAIM: Mathematical Modelling and Numerical Analysis 33.2 (2010): 289-304. <http://eudml.org/doc/197439>.

@article{Antman2010,
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. },
author = {Antman, Stuart S., Schuricht, Friedemann},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Incompressibility; theories of rods; theories of shells.; planar deformation of rods; spatial deformation of rods; shells; thin incompressible bodies; constraints; exact theories},
language = {eng},
month = {3},
number = {2},
pages = {289-304},
publisher = {EDP Sciences},
title = {Incompressibility in Rod and Shell Theories},
url = {http://eudml.org/doc/197439},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Antman, Stuart S.
AU - Schuricht, Friedemann
TI - Incompressibility in Rod and Shell Theories
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 2
SP - 289
EP - 304
AB - 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.
LA - eng
KW - Incompressibility; theories of rods; theories of shells.; planar deformation of rods; spatial deformation of rods; shells; thin incompressible bodies; constraints; exact theories
UR - http://eudml.org/doc/197439
ER -

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