Quasi-harmonic Bezier approximation of minimal surfaces for finding forms of structural membranes

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dc.contributor.authorXu, Gang
dc.contributor.authorRabczuk, Timon
dc.contributor.authorGuler, Erhan
dc.contributor.authorWu, Qing
dc.contributor.authorHui, Kin-chuen
dc.contributor.authorWang, Guozhao
dc.date.accessioned2025-10-18T10:11:04Z
dc.date.created2015
dc.date.issued2015
dc.departmentFakülteler, Fen Fakültesi, Matematik Bölümü
dc.description.abstractNumerical approximation of minimal surface is an important problem in form-finding of structural membranes. In this paper, we present a novel approach to construct minimal surface from a given boundary by quasi-harmonic Bezier approximation. A new energy functional called quasi-harmonic energy functional is proposed as the objective function to obtain the quasi-harmonic Bezier surface from given boundaries. The quasi-harmonic mask is also proposed to generate approximate minimal surfaces by solving a sparse linear system. We propose a framework to construct multi-patch quasi-harmonic Bezier approximation from N-sided boundary curves. The efficiency of the proposed methods is illustrated by several modeling examples. (C) 2015 Elsevier Ltd. All rights
dc.description.sponsorshipNational Nature Science Foundation of China [61472111, 61272300]; Zhejiang Provincial Natural Science Foundation of China [LR16F020003]; Open Project Program of the State Key Lab of CAD CG [A1406]; European Union Initial Training Network (ITN) INSIST from the Framework Programme 7 Integrating Numerical Simulation and Geometric Design Technology [289361]; Chinese University of Hong Kong [2050492]
dc.description.sponsorshipDr. Gang Xu is partially supported by the National Nature Science Foundation of China (Nos. 61472111 and 61272300), the Zhejiang Provincial Natural Science Foundation of China under Grant No. LR16F020003, and the Open Project Program of the State Key Lab of CAD & CG(A1406). Prof. Timon Rabczuk is supported by the European Union Initial Training Network (ITN) INSIST from the Framework Programme 7 (No. 289361) Integrating Numerical Simulation and Geometric Design Technology. Prof. KC Hui is supported by the Direct Grant from the Chinese University of Hong Kong (Project No. 2050492).
dc.identifier.doi10.1016/j.compstruc.2015.09.002
dc.identifier.endpage63
dc.identifier.issn0045-7949
dc.identifier.issn1879-2243
dc.identifier.orcidXu, Gang/0000-0003-3557-9529
dc.identifier.orcidGuler, Erhan/0000-0003-3264-6239;
dc.identifier.scopus2-s2.0-84943387645
dc.identifier.scopusqualityQ1
dc.identifier.startpage55
dc.identifier.urihttps://doi.org/10.1016/j.compstruc.2015.09.002
dc.identifier.urihttps://hdl.handle.net/11772/22186
dc.identifier.volume161
dc.identifier.wosWOS:000364726200005
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherPergamon-Elsevier Science Ltd
dc.relation.ispartofComputers & Structures
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzWoS_20251016
dc.subjectForm Finding
dc.subjectMinimal Surfaces
dc.subjectBezier Approximation
dc.subjectPlateau-Bezier Problem
dc.subjectQuasi-Harmonic Method
dc.subjectMulti-Patch Structure
dc.titleQuasi-harmonic Bezier approximation of minimal surfaces for finding forms of structural membranes
dc.typeArticle
dspace.entity.typePublication

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