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dc.contributor.authorMillán, Raúl Daniel
dc.contributor.authorArroyo Balaguer, Marino
dc.contributor.authorRosolen, Adrián
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental
dc.date.accessioned2015-11-26T13:18:12Z
dc.date.available2015-11-26T13:18:12Z
dc.date.issued2013-02
dc.identifier.citationMillán, D., Arroyo, M., Rosolen, A.M. Nonlinear manifold learning for meshfree finite deformation thin shell analysis. "International journal for numerical methods in engineering", Febrer 2013, vol. 93, núm. 7, p. 685-713.
dc.identifier.issn0029-5981
dc.identifier.urihttp://hdl.handle.net/2117/79963
dc.description.abstractCalculations on general point-set surfaces are attractive because of their flexibility and simplicity in the preprocessing but present important challenges. The absence of a mesh makes it nontrivial to decide if two neighboring points in the three-dimensional embedding are nearby or rather far apart on the manifold. Furthermore, the topology of surfaces is generally not that of an open two-dimensional set, ruling out global parametrizations. We propose a general and simple numerical method analogous to the mathematical theory of manifolds, in which the point-set surface is described by a set of overlapping charts forming a complete atlas. We proceed in four steps: (1) partitioning of the node set into subregions of trivial topology; (2) automatic detection of the geometric structure of the surface patches by nonlinear dimensionality reduction methods; (3) parametrization of the surface using smooth meshfree (here maximum-entropy ) approximants; and (4) gluing together the patch representations by means of a partition of unity. Each patch may be viewed as a meshfree macro-element. We exemplify the generality, flexibility, and accuracy of the proposed approach by numerically approximating the geometrically nonlinear Kirchhoff–Love theory of thin-shells. We analyze standard benchmark tests as well as point-set surfaces of complex geometry and topology.
dc.format.extent29 p.
dc.language.isoeng
dc.publisherJohn Wiley & Sons
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
dc.subject.lcshNumerical methods and algorithms
dc.subject.othershells
dc.subject.othermeshfree methods
dc.subject.otherpartition of unity
dc.subject.otherpoint-set surfaces
dc.subject.othermaximum-entropy approximants
dc.subject.othernonlinear dimensionality reduction
dc.titleNonlinear manifold learning for meshfree finite deformation thin shell analysis
dc.typeArticle
dc.subject.lemacResistència de materials
dc.contributor.groupUniversitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria
dc.identifier.doi10.1002/nme.4403
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::74 Mechanics of deformable solids::74S Numerical methods
dc.relation.publisherversionhttp://cataleg.upc.edu/record=b1000439~S1*cat
dc.rights.accessOpen Access
drac.iddocument11055313
dc.description.versionPostprint (author's final draft)
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/FP7/240487/EU/Predictive models and simulations in nano- and biomolecular mechanics: a multiscale approach/PREDMODSIM
upcommons.citation.authorMillán, D., Arroyo, M., Rosolen, A.M.
upcommons.citation.publishedtrue
upcommons.citation.publicationNameInternational journal for numerical methods in engineering
upcommons.citation.volume93
upcommons.citation.number7
upcommons.citation.startingPage685
upcommons.citation.endingPage713


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