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

Gang Xu; Timon Rabczuk; Erhan Güler; Qing Wu; Kin Chuen Hui; Guozhao Wang

doi:10.1016/j.compstruc.2015.09.002

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

Gang Xu^*, Timon Rabczuk, Erhan Güler, Qing Wu, Kin Chuen Hui, Guozhao Wang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

32 Citations (Scopus)

Abstract

Numerical 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 Bézier approximation. A new energy functional called quasi-harmonic energy functional is proposed as the objective function to obtain the quasi-harmonic Bézier 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 Bézier approximation from N-sided boundary curves. The efficiency of the proposed methods is illustrated by several modeling examples.

Original language	English
Pages (from-to)	55-63
Number of pages	9
Journal	Computers and Structures
Volume	161
DOIs	https://doi.org/10.1016/j.compstruc.2015.09.002
Publication status	Published - 2015 Dec 1

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Ltd. All rights reserved.

Keywords

Bézier approximation
Form finding
Minimal surfaces
Multi-patch structure
Plateau-Bézier problem
Quasi-harmonic method

ASJC Scopus subject areas

Civil and Structural Engineering
Modelling and Simulation
General Materials Science
Mechanical Engineering
Computer Science Applications

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10.1016/j.compstruc.2015.09.002

Cite this

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title = "Quasi-harmonic B{\'e}zier approximation of minimal surfaces for finding forms of structural membranes",

abstract = "Numerical 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 B{\'e}zier approximation. A new energy functional called quasi-harmonic energy functional is proposed as the objective function to obtain the quasi-harmonic B{\'e}zier 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 B{\'e}zier approximation from N-sided boundary curves. The efficiency of the proposed methods is illustrated by several modeling examples.",

keywords = "B{\'e}zier approximation, Form finding, Minimal surfaces, Multi-patch structure, Plateau-B{\'e}zier problem, Quasi-harmonic method",

author = "Gang Xu and Timon Rabczuk and Erhan G{\"u}ler and Qing Wu and Hui, \{Kin Chuen\} and Guozhao Wang",

year = "2015",

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doi = "10.1016/j.compstruc.2015.09.002",

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journal = "Computers and Structures",

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T1 - Quasi-harmonic Bézier approximation of minimal surfaces for finding forms of structural membranes

AU - Xu, Gang

AU - Rabczuk, Timon

AU - Güler, Erhan

AU - Wu, Qing

AU - Hui, Kin Chuen

AU - Wang, Guozhao

PY - 2015/12/1

Y1 - 2015/12/1

N2 - Numerical 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 Bézier approximation. A new energy functional called quasi-harmonic energy functional is proposed as the objective function to obtain the quasi-harmonic Bézier 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 Bézier approximation from N-sided boundary curves. The efficiency of the proposed methods is illustrated by several modeling examples.

AB - Numerical 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 Bézier approximation. A new energy functional called quasi-harmonic energy functional is proposed as the objective function to obtain the quasi-harmonic Bézier 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 Bézier approximation from N-sided boundary curves. The efficiency of the proposed methods is illustrated by several modeling examples.

KW - Bézier approximation

KW - Form finding

KW - Minimal surfaces

KW - Multi-patch structure

KW - Plateau-Bézier problem

KW - Quasi-harmonic method

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DO - 10.1016/j.compstruc.2015.09.002

M3 - Article

AN - SCOPUS:84943387645

SN - 0045-7949

VL - 161

SP - 55

EP - 63

JO - Computers and Structures

JF - Computers and Structures

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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