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

Research output: Contribution to journalArticle

6 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 languageEnglish
Pages (from-to)55-63
Number of pages9
JournalComputers and Structures
Volume161
DOIs
Publication statusPublished - 2015 Dec 1
Externally publishedYes

Fingerprint

Form-finding
Minimal surface
Membrane
Harmonic
Membranes
Approximation
Energy Functional
Sparse Linear Systems
Linear systems
Masks
Numerical Approximation
Mask
Patch
Objective function
Curve
Modeling

Keywords

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

ASJC Scopus subject areas

  • Computer Science Applications
  • Civil and Structural Engineering
  • Mechanical Engineering
  • Modelling and Simulation
  • Materials Science(all)

Cite this

Quasi-harmonic Bézier approximation of minimal surfaces for finding forms of structural membranes. / Xu, Gang; Rabczuk, Timon; Güler, Erhan; Wu, Qing; Hui, Kin Chuen; Wang, Guozhao.

In: Computers and Structures, Vol. 161, 01.12.2015, p. 55-63.

Research output: Contribution to journalArticle

Xu, Gang ; Rabczuk, Timon ; Güler, Erhan ; Wu, Qing ; Hui, Kin Chuen ; Wang, Guozhao. / Quasi-harmonic Bézier approximation of minimal surfaces for finding forms of structural membranes. In: Computers and Structures. 2015 ; Vol. 161. pp. 55-63.
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