Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
509638 | Computers & Structures | 2015 | 9 Pages |
•A novel form-finding approach to construct minimal surface from a given boundary by quasi-harmonic Bézier approximation.•Quasi-harmonic mask method to generate approximate minimal surfaces by solving a sparse linear system.•A framework to construct multi-patch quasi-harmonic Bézier approximation from N-sided boundary curves.
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.