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.
Accepted:
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Gonzalo Castiñeira 1; Ángel Rodríguez-Arós 2
@article{CRMECA_2017__345_12_824_0, author = {Gonzalo Casti\~neira and \'Angel Rodr{\'\i}guez-Ar\'os}, title = {Mathematical justification of a viscoelastic elliptic membrane problem}, journal = {Comptes Rendus. M\'ecanique}, pages = {824--831}, publisher = {Elsevier}, volume = {345}, number = {12}, year = {2017}, doi = {10.1016/j.crme.2017.09.007}, language = {en}, }
TY - JOUR AU - Gonzalo Castiñeira AU - Ángel Rodríguez-Arós TI - Mathematical justification of a viscoelastic elliptic membrane problem JO - Comptes Rendus. Mécanique PY - 2017 SP - 824 EP - 831 VL - 345 IS - 12 PB - Elsevier DO - 10.1016/j.crme.2017.09.007 LA - en ID - CRMECA_2017__345_12_824_0 ER -
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. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.09.007/
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