About the structure of the discrete and continuous Eringen’s nonlocal elastica

J. Cresson, K. Hariz-Belgacem, Mathematics and Mechanics of Solids (2022).

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Journal Article | Published | English
Author
Cresson, Jacky; Hariz-Belgacem, Khaled
Abstract
<jats:p> The Eringen’s nonlocal elastica equation does not possess a Lagrangian formulation. In this article, we find a variational integrating factor which enables us to provide a Lagrangian and Hamiltonian structure associated to this equation. Explicit expressions of the solutions in terms of elliptic integrals of the first kind are then deduced. We then derive discrete version of the Eringen’s nonlocal elastica preserving the Lagrangian and Hamiltonian structure and compare it with Challamel’s and co-worker definition of a discrete Eringen’s nonlocal elastica. </jats:p>
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Journal Title
Mathematics and Mechanics of Solids
Article Number
108128652211080
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Cresson J, Hariz-Belgacem K. About the structure of the discrete and continuous Eringen’s nonlocal elastica. Mathematics and Mechanics of Solids. Published online 2022. doi:10.1177/10812865221108094
Cresson, J., & Hariz-Belgacem, K. (2022). About the structure of the discrete and continuous Eringen’s nonlocal elastica. Mathematics and Mechanics of Solids, Article 108128652211080. https://doi.org/10.1177/10812865221108094
@article{Cresson_Hariz-Belgacem_2022, title={About the structure of the discrete and continuous Eringen’s nonlocal elastica}, DOI={10.1177/10812865221108094}, number={108128652211080}, journal={Mathematics and Mechanics of Solids}, publisher={SAGE Publications}, author={Cresson, Jacky and Hariz-Belgacem, Khaled}, year={2022} }
Cresson, Jacky, and Khaled Hariz-Belgacem. “About the Structure of the Discrete and Continuous Eringen’s Nonlocal Elastica.” Mathematics and Mechanics of Solids, 2022. https://doi.org/10.1177/10812865221108094.
J. Cresson and K. Hariz-Belgacem, “About the structure of the discrete and continuous Eringen’s nonlocal elastica,” Mathematics and Mechanics of Solids, Art. no. 108128652211080, 2022, doi: 10.1177/10812865221108094.
Cresson, Jacky, and Khaled Hariz-Belgacem. “About the Structure of the Discrete and Continuous Eringen’s Nonlocal Elastica.” Mathematics and Mechanics of Solids, 108128652211080, SAGE Publications, 2022, doi:10.1177/10812865221108094.

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