We consider a linearly elastic shell with a hyperbolic, or parabolic, middle surface, clamped along a large enough portion of its lateral face and sub- jected to body forces. We then show that the two-dimensional limit model found by the asymptotic analysis from the three-dimensional shell problem is the “gen- eralized membrane” shell model, according to the terminology introduced by P.G. Ciarlet and V. Lods. We also identify the functional space where this model is well posed.
Publié le : 1998-07-04
Classification:
rigidity,
membrane model,
elasticity,
Shells,
[MATH]Mathematics [math],
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP],
[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA],
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph],
[PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Mechanics of the solides [physics.class-ph]
@article{hal-01478650,
author = {Mardare, Cristinel},
title = {The generalized membrane problem for linearly elastic shells with hyperbolic or parabolic middle surface},
journal = {HAL},
volume = {1998},
number = {0},
year = {1998},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01478650}
}
Mardare, Cristinel. The generalized membrane problem for linearly elastic shells with hyperbolic or parabolic middle surface. HAL, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/hal-01478650/