Theory of Solutions for An Inextensible Cantilever

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dc.contributor.authorDeliyianni, Maria
dc.contributor.authorWebster, Justin
dc.date.accessioned2020-06-11T16:41:55Z
dc.date.available2020-06-11T16:41:55Z
dc.date.issued20201-07-12
dc.description.abstractRecent equations of motion for the large deflections of a cantilevered elastic beam are analyzed. In the traditional theory of beam (and plate) large deflections, nonlinear restoring forces are due to the effect of stretching on bending; for an inextensible cantilever, the enforcement of arc-length preservation leads to quasilinear stiffness effects and inertial effects that are both nonlinear and nonlocal. For this model, smooth solutions are constructed via a spectral Galerkin approach. Additional compactness is needed to pass to the limit, and this is obtained through a complex procession of higher energy estimates. Uniqueness is obtained through a non-trivial decomposition of the nonlinearity. The confounding effects of nonlinear inertia are overcome via the addition of structural (Kelvin-Voigt) damping to the equations of motion. Local well-posedness of smooth solutions is shown first in the absence of nonlinear inertial effects, and then shown with these inertial effects present, taking into account structural damping. With damping in force, global-in-time, strong well-posedness result is obtained by achieving exponential decay for small data.en_US
dc.description.sponsorshipThe authors are generously supported by NSF-DMS-1907620en_US
dc.description.urihttps://link.springer.com/article/10.1007/s00245-021-09798-0en_US
dc.format.extent41 pagesen_US
dc.genrejournal articlesen_US
dc.genrepreprints
dc.identifierdoi:10.13016/m2xkxv-qqln
dc.identifier.citationDeliyianni, M., Webster, J.T. Theory of Solutions for an Inextensible Cantilever. Appl Math Optim 84 (Suppl 2), 1345–1399 (2021). https://doi.org/10.1007/s00245-021-09798-0en_US
dc.identifier.urihttp://hdl.handle.net/11603/18870
dc.identifier.urihttps://doi.org/10.1007/s00245-021-09798-0
dc.language.isoen_USen_US
dc.publisherSpringer Nature
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics Department Collection
dc.relation.ispartofUMBC Faculty Collection
dc.relation.ispartofUMBC Student 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.titleTheory of Solutions for An Inextensible Cantileveren_US
dc.typeTexten_US
dcterms.creatorhttps://orcid.org/0000-0002-2443-3789

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