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Nonlinear manifold learning for meshfree finite deformation thin shell analysis
dc.contributor.author | Millán, Raúl Daniel |
dc.contributor.author | Arroyo Balaguer, Marino |
dc.contributor.author | Rosolen, Adrián |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental |
dc.date.accessioned | 2015-11-26T13:18:12Z |
dc.date.available | 2015-11-26T13:18:12Z |
dc.date.issued | 2013-02 |
dc.identifier.citation | Millán, 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.issn | 0029-5981 |
dc.identifier.uri | http://hdl.handle.net/2117/79963 |
dc.description.abstract | Calculations 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.extent | 29 p. |
dc.language.iso | eng |
dc.publisher | John Wiley & Sons |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics |
dc.subject.lcsh | Numerical methods and algorithms |
dc.subject.other | shells |
dc.subject.other | meshfree methods |
dc.subject.other | partition of unity |
dc.subject.other | point-set surfaces |
dc.subject.other | maximum-entropy approximants |
dc.subject.other | nonlinear dimensionality reduction |
dc.title | Nonlinear manifold learning for meshfree finite deformation thin shell analysis |
dc.type | Article |
dc.subject.lemac | Resistència de materials |
dc.contributor.group | Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
dc.identifier.doi | 10.1002/nme.4403 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::74 Mechanics of deformable solids::74S Numerical methods |
dc.relation.publisherversion | https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.4403 |
dc.rights.access | Open Access |
local.identifier.drac | 11055313 |
dc.description.version | Postprint (author's final draft) |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/FP7/240487/EU/Predictive models and simulations in nano- and biomolecular mechanics: a multiscale approach/PREDMODSIM |
local.citation.author | Millán, D.; Arroyo, M.; Rosolen, A.M. |
local.citation.publicationName | International journal for numerical methods in engineering |
local.citation.volume | 93 |
local.citation.number | 7 |
local.citation.startingPage | 685 |
local.citation.endingPage | 713 |
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