Computational grid generation for the design of free-form shells with complex boundary conditions

Tierui Li, Jun Ye, Paul Shepherd, Hui Wu, Boqing Gao

Research output: Contribution to journalArticle

1 Citation (Scopus)
36 Downloads (Pure)

Abstract

Free-form grid structures have been widely used in various public buildings, and many are bounded by complex curves including internal voids. Modern computational design software enables the rapid creation and exploration of such complex surface geometries for architectural design, but the resulting shapes lack an obvious way for engineers to create a discrete structural grid to support the surface that manifests the architect's intent. This paper presents an efficient design approach for the synthesis of free-form grid structures based on guideline and surface-flattening methods, which consider complex features and internal boundaries. The method employs a fast and straightforward approach, which achieves fluent lines with bars of balanced length. The parametric domain of a complete nonuniform rational basis spline (NURBS) surface is first divided into a number of patches, and a discrete free-form surface is formed by mapping dividing points onto the surface. The free-form surface is then flattened based on the principle of equal area. Accordingly, the flattened rectangular lattices are then fit to the two-dimensional (2D) surface, with grids formed by applying a guideline method. Subsequently, the intersections of the guidelines and the complex boundary are obtained, and the guidelines are divided equally between boundaries to produce grids connected at the dividing points. Finally, the 2D grids are mapped back onto the three-dimensional (3D) surface and a spring-mass relaxation method is employed to further improve the smoothness of the resulting grids. The paper concludes by presenting realistic examples to demonstrate the practical effectiveness of the proposed method.

Original languageEnglish
JournalJournal of Computing in Civil Engineering
Volume33
Issue number3
Early online date29 Jan 2019
DOIs
Publication statusPublished - 1 May 2019

Keywords

  • Complex boundary
  • Free-form gridshell
  • Grid generation
  • Grid relaxation
  • Guideline method
  • Surface flattening

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Computer Science Applications

Cite this

Computational grid generation for the design of free-form shells with complex boundary conditions. / Li, Tierui; Ye, Jun; Shepherd, Paul; Wu, Hui; Gao, Boqing.

In: Journal of Computing in Civil Engineering, Vol. 33, No. 3, 01.05.2019.

Research output: Contribution to journalArticle

@article{1c8b3b7f59f244399027d90f201bc9d3,
title = "Computational grid generation for the design of free-form shells with complex boundary conditions",
abstract = "Free-form grid structures have been widely used in various public buildings, and many are bounded by complex curves including internal voids. Modern computational design software enables the rapid creation and exploration of such complex surface geometries for architectural design, but the resulting shapes lack an obvious way for engineers to create a discrete structural grid to support the surface that manifests the architect's intent. This paper presents an efficient design approach for the synthesis of free-form grid structures based on guideline and surface-flattening methods, which consider complex features and internal boundaries. The method employs a fast and straightforward approach, which achieves fluent lines with bars of balanced length. The parametric domain of a complete nonuniform rational basis spline (NURBS) surface is first divided into a number of patches, and a discrete free-form surface is formed by mapping dividing points onto the surface. The free-form surface is then flattened based on the principle of equal area. Accordingly, the flattened rectangular lattices are then fit to the two-dimensional (2D) surface, with grids formed by applying a guideline method. Subsequently, the intersections of the guidelines and the complex boundary are obtained, and the guidelines are divided equally between boundaries to produce grids connected at the dividing points. Finally, the 2D grids are mapped back onto the three-dimensional (3D) surface and a spring-mass relaxation method is employed to further improve the smoothness of the resulting grids. The paper concludes by presenting realistic examples to demonstrate the practical effectiveness of the proposed method.",
keywords = "Complex boundary, Free-form gridshell, Grid generation, Grid relaxation, Guideline method, Surface flattening",
author = "Tierui Li and Jun Ye and Paul Shepherd and Hui Wu and Boqing Gao",
year = "2019",
month = "5",
day = "1",
doi = "10.1061/(ASCE)CP.1943-5487.0000828",
language = "English",
volume = "33",
journal = "Journal of Computing in Civil Engineering",
issn = "0887-3801",
publisher = "American Society of Civil Engineers (ASCE)",
number = "3",

}

TY - JOUR

T1 - Computational grid generation for the design of free-form shells with complex boundary conditions

AU - Li, Tierui

AU - Ye, Jun

AU - Shepherd, Paul

AU - Wu, Hui

AU - Gao, Boqing

PY - 2019/5/1

Y1 - 2019/5/1

N2 - Free-form grid structures have been widely used in various public buildings, and many are bounded by complex curves including internal voids. Modern computational design software enables the rapid creation and exploration of such complex surface geometries for architectural design, but the resulting shapes lack an obvious way for engineers to create a discrete structural grid to support the surface that manifests the architect's intent. This paper presents an efficient design approach for the synthesis of free-form grid structures based on guideline and surface-flattening methods, which consider complex features and internal boundaries. The method employs a fast and straightforward approach, which achieves fluent lines with bars of balanced length. The parametric domain of a complete nonuniform rational basis spline (NURBS) surface is first divided into a number of patches, and a discrete free-form surface is formed by mapping dividing points onto the surface. The free-form surface is then flattened based on the principle of equal area. Accordingly, the flattened rectangular lattices are then fit to the two-dimensional (2D) surface, with grids formed by applying a guideline method. Subsequently, the intersections of the guidelines and the complex boundary are obtained, and the guidelines are divided equally between boundaries to produce grids connected at the dividing points. Finally, the 2D grids are mapped back onto the three-dimensional (3D) surface and a spring-mass relaxation method is employed to further improve the smoothness of the resulting grids. The paper concludes by presenting realistic examples to demonstrate the practical effectiveness of the proposed method.

AB - Free-form grid structures have been widely used in various public buildings, and many are bounded by complex curves including internal voids. Modern computational design software enables the rapid creation and exploration of such complex surface geometries for architectural design, but the resulting shapes lack an obvious way for engineers to create a discrete structural grid to support the surface that manifests the architect's intent. This paper presents an efficient design approach for the synthesis of free-form grid structures based on guideline and surface-flattening methods, which consider complex features and internal boundaries. The method employs a fast and straightforward approach, which achieves fluent lines with bars of balanced length. The parametric domain of a complete nonuniform rational basis spline (NURBS) surface is first divided into a number of patches, and a discrete free-form surface is formed by mapping dividing points onto the surface. The free-form surface is then flattened based on the principle of equal area. Accordingly, the flattened rectangular lattices are then fit to the two-dimensional (2D) surface, with grids formed by applying a guideline method. Subsequently, the intersections of the guidelines and the complex boundary are obtained, and the guidelines are divided equally between boundaries to produce grids connected at the dividing points. Finally, the 2D grids are mapped back onto the three-dimensional (3D) surface and a spring-mass relaxation method is employed to further improve the smoothness of the resulting grids. The paper concludes by presenting realistic examples to demonstrate the practical effectiveness of the proposed method.

KW - Complex boundary

KW - Free-form gridshell

KW - Grid generation

KW - Grid relaxation

KW - Guideline method

KW - Surface flattening

UR - http://www.scopus.com/inward/record.url?scp=85060812609&partnerID=8YFLogxK

U2 - 10.1061/(ASCE)CP.1943-5487.0000828

DO - 10.1061/(ASCE)CP.1943-5487.0000828

M3 - Article

VL - 33

JO - Journal of Computing in Civil Engineering

JF - Journal of Computing in Civil Engineering

SN - 0887-3801

IS - 3

ER -