Asymptotic considerations shedding light on incompressible shell models - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Elasticity Year : 2004

Asymptotic considerations shedding light on incompressible shell models


The incompressible singularity found in 3D elasticity when Poisson's ratio approaches 1/2 is not present in classical shell models, nor in the limit models obtained from 3D elasticity when performing an asymptotic analysis with respect to the thickness parameter. However, some specific shell models - such as the 3D-shell model - do retain the incompressible singularity. These observations raise the issue of how adequately shell models can represent incompressible conditions, which this paper aims at investigating. We first perform a combined asymptotic analysis of 3D elasticity with respect to both the thickness parameter and Poisson's ratio and we obtain a commuting property, which is very valuable as a justification of the concept of an "incompressible shell", and substantiates the use of classical shell models with incompressible materials.We then show that the 3D-shell model does not enjoy a similar commuting property; nevertheless we propose a simple modification of this model for which commuting is obtained, hence consistency with incompressibility is recovered. We also illustrate our discussions with some numerical results.

Dates and versions

hal-00839225 , version 1 (27-06-2013)



Dominique Chapelle, Cristinel Mardare, Arnaud Münch. Asymptotic considerations shedding light on incompressible shell models. Journal of Elasticity, 2004, 76, pp.199-246. ⟨10.1007/s10659-005-0929-6⟩. ⟨hal-00839225⟩
146 View
0 Download



Gmail Facebook X LinkedIn More