| Issue |
ESAIM: M2AN
Volume 58, Number 1, January-February 2024
|
|
|---|---|---|
| Page(s) | 157 - 189 | |
| DOI | https://doi.org/10.1051/m2an/2023099 | |
| Published online | 16 February 2024 | |
A mixed parameter formulation with applications to linear viscoelastic slender structures
1
Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V Valparaiso, Chile
2
GIMNAP-Departamento de Matemática, Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile
* Corresponding author: jvellojin@ubiobio.cl
Received:
6
December
2022
Accepted:
3
December
2023
We present the analysis of an abstract parameter-dependent mixed variational formulation based on Volterra integrals of second kind. Adapting the classic mixed theory in the Volterra equations setting, we prove the well posedness of the resulting system. Stability and error estimates are derived, where all the estimates are uniform with respect to the perturbation parameter. We provide applications of the developed analysis for a viscoelastic Timoshenko beam and report numerical tests for this problem. We also comment, numerically, the performance of a viscoelastic Reissner–Mindlin plate.
Mathematics Subject Classification: 65M12 / 65M60 / 35Q74 / 45D05 / 65R20 / 65N12 / 74D05
Key words: Viscoelasticity / Volterra integrals / mixed methods / locking-free / error estimates
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.