Title:
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Nonlinear manifold learning for meshfree finite deformation thin shell analysis
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Author:
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Millán, Raúl Daniel; Arroyo Balaguer, Marino; Rosolen, Adrián
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Other authors:
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Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental; Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
Abstract:
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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. |
Abstract:
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Peer Reviewed |
Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics -Numerical methods and algorithms -shells -meshfree methods -partition of unity -point-set surfaces -maximum-entropy approximants -nonlinear dimensionality reduction -Resistència de materials -Classificació AMS::74 Mechanics of deformable solids::74S Numerical methods |
Rights:
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http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
Document type:
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Article - Submitted version Article |
Published by:
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John Wiley & Sons
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