Mathematical justification of a viscoelastic elliptic membrane problem

Gonzalo Castiñeira; Ángel Rodríguez-Arós

doi:10.1016/j.crme.2017.09.007

Mathematical justification of a viscoelastic elliptic membrane problem

Gonzalo Castiñeira ¹ ; Ángel Rodríguez-Arós ²

¹ Facultade de Matemáticas, C/ Lope Gómez de Marzoa, s/n, 15782, Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, Spain
² E.T.S. Náutica e Máquinas, Paseo de Ronda, 51, 15011, Departamento de Matemáticas, Universidade da Coruña, Spain

Comptes Rendus. Mécanique, Volume 345 (2017) no. 12, pp. 824-831

Abstract

We consider a family of linearly viscoelastic elliptic shells, and we use asymptotic analysis to justify that what we have identified as the two-dimensional viscoelastic elliptic membrane problem is an accurate approximation when the thickness of the shell tends to zero. Most noticeable is that the limit problem includes a long-term memory that takes into account the previous history of deformations. We provide convergence results which justify our asymptotic approach.

Received: 2016-12-09
Accepted: 2017-09-25
Published online: 2017-10-06

DOI: 10.1016/j.crme.2017.09.007

Keywords: Shells, Viscoelasticity, Elliptic membrane, Asymptotic analysis, Convergence

Author's affiliations:

Gonzalo Castiñeira ¹; Ángel Rodríguez-Arós ²

¹ Facultade de Matemáticas, C/ Lope Gómez de Marzoa, s/n, 15782, Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, Spain
² E.T.S. Náutica e Máquinas, Paseo de Ronda, 51, 15011, Departamento de Matemáticas, Universidade da Coruña, Spain

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     title = {Mathematical justification of a viscoelastic elliptic membrane problem},
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     pages = {824--831},
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Gonzalo Castiñeira; Ángel Rodríguez-Arós. Mathematical justification of a viscoelastic elliptic membrane problem. Comptes Rendus. Mécanique, Volume 345 (2017) no. 12, pp. 824-831. doi: 10.1016/j.crme.2017.09.007

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Cited by

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