Asymptotic modelling of viscoelastic von Kármán membrane shells-Reference-Cited by-同舟云学术

Asymptotic modelling of viscoelastic von Kármán membrane shells

Published:2023-08-01 Issue:0 Volume:0 Page:
ISSN:0174-4747
Container-title:Analysis
language:en
Short-container-title:

Author:

Legougui Marwa¹,Ghezal Abderrezak¹^ORCID

Affiliation:

1. Laboratoire de mathématiques appliquées , Université Kasdi Merbah , B.P. 511 , Ouargla 30000 , Algeria

Abstract

Abstract The objective of this work is to study the asymptotic justification of the two-dimensional model of viscoelastic von Kármán membrane shells. More precisely, we consider a three-dimensional model for a nonlinearly viscoelastic membrane shell with a specific class of boundary conditions of von Kármán type. Using techniques from formal asymptotic analysis with the thickness of the shell as a small parameter, we show that the scaled three-dimensional solution still leads to the two-dimensional model of viscoelastic von Kármán membrane shells.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Numerical Analysis,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/anly-2022-1106/pdf

Reference20 articles.

1. G. Andreoiu-Banica, Justification of the Marguerre–von Kármán equations in curvilinear coordinates, Asymptot. Anal. 19 (1999), no. 1, 35–55.

2. G. Castiñeira and A. Rodríguez-Arós, Linear viscoelastic shells: An asymptotic approach, Asymptot. Anal. 107 (2018), no. 3–4, 169–201.

3. D. A. Chacha, A. Ghezal and A. Bensayah, Existence result for a dynamical equations of generalized Marguerre–von Kármán shallow shells, J. Elasticity 111 (2013), no. 2, 265–283.

4. P. G. Ciarlet, A justification of the von Kármán equations, Arch. Ration. Mech. Anal. 73 (1980), no. 4, 349–389.

5. P. G. Ciarlet, Mathematical Elasticity. Vol. II. Theory of Plates, Stud. Math. Appl. 27, North-Holland, Amsterdam, 1997.