article published Jacky Cresson author Khaled Hariz Belgacem author 98857 <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> SAGE Publications2022 eng Mechanics of MaterialsGeneral Materials ScienceGeneral Mathematics 1081-2865 1741-302810.1177/10812865221108094 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>. 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> 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>. J. Cresson, K. Hariz Belgacem, Mathematics and Mechanics of Solids (2022). 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>. @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} } 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> 394002023-01-24T10:18:34Z2023-08-01T11:52:17Z