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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.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.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.publisherJohn Wiley & Sons
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
dc.subject.lcshNumerical methods and algorithms
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.subject.lemacResistència de materials
dc.contributor.groupUniversitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::74 Mechanics of deformable solids::74S Numerical methods
dc.rights.accessOpen Access
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.publicationNameInternational journal for numerical methods in engineering

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