Large Deflections of Inextensible Cantilevers: Modeling, Theory, and Simulation

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dc.contributor.authorDeliyianni, Maria
dc.contributor.authorGudibanda, Varun
dc.contributor.authorHowell, Jason
dc.contributor.authorWebster, Justin
dc.date.accessioned2019-12-19T14:46:59Z
dc.date.available2019-12-19T14:46:59Z
dc.date.issued2020-09-24
dc.description.abstractA recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam’s inextensibility—local arc length preservation—rather than traditional extensible effects attributed to fully restricted boundary conditions. Enforcing inextensibility leads to: nonlinear stiffness terms, which appear as quasilinear and semilinear effects, as well as nonlinear inertia effects, appearing as nonlocal terms that make the beam implicit in the acceleration. In this paper we discuss the derivation of the equations of motion via Hamilton’s principle with a Lagrange multiplier to enforce the effective inextensibility constraint. We then provide the functional framework for weak and strong solutions before presenting novel results on the existence and uniqueness of strong solutions. A distinguishing feature is that the two types of nonlinear terms prevent independent challenges: the quasilinear nature of the stiffness forces higher topologies for solutions, while the nonlocal inertia requires the consideration of Kelvin-Voigt type damping to close estimates. Finally, a modal approach is used to produce mathematically-oriented numerical simulations that provide insight to the features and limitations of the inextensible model.en_US
dc.description.sponsorshipThe authors acknowledge the generous support of the National Science Foundation: M. Deliyianni and J.T. Webster’s research contributions here were partially supported by NSF-DMS-1907620; J.Howell’s research contributions here were partially supported by NSF-DMS-1908033. V. Gudibanda acknowledges support through Carnegie Mellon’s SURF program.en_US
dc.description.urihttps://www.mmnp-journal.org/articles/mmnp/abs/2020/01/mmnp190148/mmnp190148.htmlen_US
dc.format.extent34 pagesen_US
dc.genrejournal articlesen_US
dc.identifierdoi:10.13016/m2jhnq-ea5k
dc.identifier.citationDeliyianni, Maria et al. "Large deflections of inextensible cantilevers: modeling, theory, and simulation." Math. Model. Nat. Phenom. 15 (24 September 2020). DOI: https://doi.org/10.1051/mmnp/2020033en_US
dc.identifier.urihttp://hdl.handle.net/11603/16916
dc.identifier.urihttps://doi.org/10.1051/mmnp/2020033
dc.language.isoen_USen_US
dc.publisherEDP Sciences
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics Department Collection
dc.relation.ispartofUMBC Student Collection
dc.relation.ispartofUMBC Faculty Collection
dc.rightsThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
dc.rightsAttribution 4.0 International (CC BY 4.0)
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectnonlinear beamen_US
dc.subjectcantileveren_US
dc.subjectinextensibilityen_US
dc.subjectlarge deflectionsen_US
dc.subjectquasilinearityen_US
dc.titleLarge Deflections of Inextensible Cantilevers: Modeling, Theory, and Simulationen_US
dc.typeTexten_US
dcterms.creatorhttps://orcid.org/0000-0002-2443-3789

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