Analysis of a Frictionless Electro Viscoelastic Contact Problem with Signorini Conditions
Received: 10 July 2022 | Revised: 27 July 2022 | Accepted: 31 July 2022 | Online: 2 October 2022
Corresponding author: A. Ourahmoun
This study considered a mathematical model to describe the process of a quasi-static contact between a piezoelectric body and an electrically conductive foundation. The behavior of the material was modeled with a nonlinear electro-viscoelastic constitutive law, the contact was frictionless, and the result was described with the Signorini condition. A variational formulation was derived for the problem, proving the existence and uniqueness of a weak solution of the model. The proof was based on arguments for nonlinear equations with maximal monotone operators.
Keywords:electo-viscopastic material, frictionless contact;, Signorini conditions, maxmal monotone operators, weak solution
Y. Letoufa, H. Benseridi, S. Boulaaras, and M. Dilmi, "On the asymptotic behavior of solutions of anisotropic viscoelastic body," Boundary Value Problems, vol. 2021, no. 1, Nov. 2021, Art. no. 89. DOI: https://doi.org/10.1186/s13661-021-01567-w
R. D. Mindlin, "Elasticity, piezoelectricity and crystal lattice dynamics," Journal of Elasticity, vol. 2, no. 4, pp. 217–282, Dec. 1972. DOI: https://doi.org/10.1007/BF00045712
S. Drabla and Z. Zellagui, "Analysis of a Electro-Elastic Contact Problem with Friction and Adhension," Mathematica, vol. 24, no. 1, pp. 75–99, Mar. 2009.
O. Chau, M. Shillor, and M. Sofonea, "Dynamic frictionless contact with adhesion," Zeitschrift für angewandte Mathematik und Physik ZAMP, vol. 55, no. 1, pp. 32–47, Jan. 2004. DOI: https://doi.org/10.1007/s00033-003-1089-9
O. Chau, J. R. Fernández, W. Han, and M. Sofonea, "Variational and numerical analysis of a dynamic frictionless contact problem with adhesion," Journal of Computational and Applied Mathematics, vol. 156, no. 1, pp. 127–157, Jul. 2003. DOI: https://doi.org/10.1016/S0377-0427(02)00909-3
S. Drabla and Z. Zellagui, "Variational Analysis and the Convergence of the Finite Element Approximation of an Electro-Elastic Contact Problem with Adhesion," Arabian Journal for Science and Engineering, vol. 36, no. 8, pp. 1501–1515, Dec. 2011. DOI: https://doi.org/10.1007/s13369-011-0131-z
S. Migórski, A. Ochal, and M. Sofonea, Nonlinear Inclusions and Hemivariational Inequalities: Models and Analysis of Contact Problems. New York, NY, USA: Springer Science & Business Media, 2012. DOI: https://doi.org/10.1007/978-1-4614-4232-5
A. Guediri, A. Guediri, and S. Touil, "Modeling and Comparison of Fuzzy-PI and Genetic Control Algorithms for Active and Reactive Power Flow between the Stator (DFIG) and the Grid," Engineering, Technology & Applied Science Research, vol. 12, no. 3, pp. 8640–8645, Jun. 2022. DOI: https://doi.org/10.48084/etasr.4905
A. Z. Al-Khazaal and N. Ahmad, "A Study of the Impact of Iron Content on the Thermal Response of the sPP/Fe Composites," Engineering, Technology & Applied Science Research, vol. 12, no. 3, pp. 8555–8558, Jun. 2022. DOI: https://doi.org/10.48084/etasr.4884
T. N. Le, H. M. V. Nguyen, T. A. Nguyen, T. T. Phung, and B. D. Phan, "Optimization of Load Ranking and Load Shedding in a Power System Using the Improved AHP Algorithm," Engineering, Technology & Applied Science Research, vol. 12, no. 3, pp. 8512–8519, Jun. 2022. DOI: https://doi.org/10.48084/etasr.4862
How to Cite
MetricsAbstract Views: 406
PDF Downloads: 208
Copyright (c) 2022 A. Boulaouad, A. Ourahmoun, T. Serrar
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.