---
_id: '39400'
abstract:
- lang: eng
  text: <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>
article_number: '108128652211080'
author:
- first_name: Jacky
  full_name: Cresson, Jacky
  last_name: Cresson
- first_name: Khaled
  full_name: Hariz Belgacem, Khaled
  id: '98857'
  last_name: Hariz Belgacem
citation:
  ama: Cresson J, Hariz Belgacem K. About the structure of the discrete and continuous
    Eringen’s nonlocal elastica. <i>Mathematics and Mechanics of Solids</i>. Published
    online 2022. doi:<a href="https://doi.org/10.1177/10812865221108094">10.1177/10812865221108094</a>
  apa: Cresson, J., &#38; Hariz Belgacem, K. (2022). About the structure of the discrete
    and continuous Eringen’s nonlocal elastica. <i>Mathematics and Mechanics of Solids</i>,
    Article 108128652211080. <a href="https://doi.org/10.1177/10812865221108094">https://doi.org/10.1177/10812865221108094</a>
  bibtex: '@article{Cresson_Hariz Belgacem_2022, title={About the structure of the
    discrete and continuous Eringen’s nonlocal elastica}, DOI={<a href="https://doi.org/10.1177/10812865221108094">10.1177/10812865221108094</a>},
    number={108128652211080}, journal={Mathematics and Mechanics of Solids}, publisher={SAGE
    Publications}, author={Cresson, Jacky and Hariz Belgacem, Khaled}, year={2022}
    }'
  chicago: Cresson, Jacky, and Khaled Hariz Belgacem. “About the Structure of the
    Discrete and Continuous Eringen’s Nonlocal Elastica.” <i>Mathematics and Mechanics
    of Solids</i>, 2022. <a href="https://doi.org/10.1177/10812865221108094">https://doi.org/10.1177/10812865221108094</a>.
  ieee: 'J. Cresson and K. Hariz Belgacem, “About the structure of the discrete and
    continuous Eringen’s nonlocal elastica,” <i>Mathematics and Mechanics of Solids</i>,
    Art. no. 108128652211080, 2022, doi: <a href="https://doi.org/10.1177/10812865221108094">10.1177/10812865221108094</a>.'
  mla: Cresson, Jacky, and Khaled Hariz Belgacem. “About the Structure of the Discrete
    and Continuous Eringen’s Nonlocal Elastica.” <i>Mathematics and Mechanics of Solids</i>,
    108128652211080, SAGE Publications, 2022, doi:<a href="https://doi.org/10.1177/10812865221108094">10.1177/10812865221108094</a>.
  short: J. Cresson, K. Hariz Belgacem, Mathematics and Mechanics of Solids (2022).
date_created: 2023-01-24T10:18:34Z
date_updated: 2023-08-01T11:52:17Z
doi: 10.1177/10812865221108094
keyword:
- Mechanics of Materials
- General Materials Science
- General Mathematics
language:
- iso: eng
publication: Mathematics and Mechanics of Solids
publication_identifier:
  issn:
  - 1081-2865
  - 1741-3028
publication_status: published
publisher: SAGE Publications
status: public
title: About the structure of the discrete and continuous Eringen’s nonlocal elastica
type: journal_article
user_id: '98857'
year: '2022'
...