An automatic grid generation approach over free-form surface for architectural design

Su, Liang; Zhu, Shun-lai; Xiao, Nan; Gao, Boqing

doi:10.1007/s11771-014-2198-7

Cited by 17 publications

(8 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These methods are mainly designed for specific building projects or certain kind of surfaces and thus their application scopes are very narrow. In Su et al (2014), an improved advancing front technique was presented with the main stress trajectories used to orientate the gird directions. However, this method lacks robustness and the resultant meshes are not very uniform.…”

Section: Related Workmentioning

confidence: 99%

Triangular mesh generation on free-form surfaces based on bubble dynamics simulation

Wang

Gao

2019

View full text Add to dashboard Cite

Purpose Modern CAD systems facilitate the creation of any surface geometry imaginable, and complex surfaces for free-form grid shells are often represented by a set of Non-Uniform Rational B-Splines surface patches. But it remains an intractable issue how to generate high-quality grids on complex surfaces efficiently. To solve this issue, an automatic triangular mesh generation method is presented, based on bubble dynamics simulation and a modified Delaunay method. Design/methodology/approach A moderate amount of points are first distributed on a given surface. Next, by regarding the points as elastic bubbles with the same size and introducing the forces acting on bubbles, the motion control equations of bubbles are established. The equilibrium state of the bubble system is found by Verlet algorithm. Then, the Voronoi diagram on the surface is obtained by calculating the intersection between the surface and the three-dimensional (3D) Voronoi diagram of the centers of bubbles. Finally, a triangular mesh, Delaunay triangulation on the surface, is determined based on the dual change of the Voronoi diagram. Findings This method generates meshes on the surface directly, unlike mapping-based methods, avoiding the mapping distortion. Examples are given to demonstrate the successful execution of this method. The result also illustrates that this method is applicable to various surfaces in high automation level and resultant meshes are highly uniform and well-shaped. Originality/value Thus, this method provides the convenience for the geometry design of complex free-form grid structure.

show abstract

Section: Related Workmentioning

confidence: 99%

Triangular mesh generation on free-form surfaces based on bubble dynamics simulation

Wang

Gao

2019

View full text Add to dashboard Cite

show abstract

“…Shepherd and Richens (2012) proposed the use of the Subdivision Surface method to generate grids, where an initial triangular or quadrilateral mesh is first imposed onto a free-form surface and then subdivided over a number of iterations, snapping back to the original surface at each step. Su et al (2014) developed a grid generation procedure using the principle-stress trajectories of a surface under specific dominant load. A modified 'advancing front' mesh technique was used for the grid generation, however this involved FE analysis, which required significant computational time and the fluidity and equal rod length of grid cells was not guaranteed.…”

Section: Curve Fluiditymentioning

confidence: 99%

Computational Grid Generation for the Design of Free-Form Shells with Complex Boundary Conditions

Jun

Shepherd

et al. 2019

J. Comput. Civ. Eng.

View full text Add to dashboard Cite

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 manifest the architect's intent. This paper presents an efficient design approach for the synthesis of free-form grid structures based on "guide line" 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 NURBS (Non-Uniform Rational B-Spline) surface is firstly divided into a number of patches, and a discrete free-form surface formed by mapping dividing points onto the surface. The free-form surface was then flattened based on the principle of equal area. Accordingly, the flattened rectangular lattices are then fit to the 2D surface, with grids formed by applying a guide-line method. Subsequently, the intersections of the guide-lines and the complex boundary are obtained, and the guide-lines divided equally between boundaries to produce grids connected at the dividing points. Finally, the 2D grids are mapped back onto the 3D surface and a spring-mass relaxation method is employed to further improve the smoothness of the resulting grids. The paper concludes bypresenting realistic examples to demonstrate the practical effectiveness of the proposed method.

show abstract

“…There are some works on structure optimization that inspired by principal stress lines. Su et al [SZXG14] presented an algorithm to generate grid that are concordant with the force flow. Kwok et al [KLC16] provided a novel growth method based on principal stress lines to define the geometry and topology of structure.…”

Section: Related Workmentioning

confidence: 99%

Rib‐reinforced Shell Structure

Zheng

You

et al. 2017

Computer Graphics Forum

View full text Add to dashboard Cite

Figure 1: We present a computational framework to generate ribs to enhance the structural strength and stiffness of a shell (a). Our ribreinforced shell structure (c) costs the same amount of material as a pure shell without any ribs (a), while achieving much better mechanical performance. And (b) and (d) are coloring visualizations of the magnitude of von Mises stress of (a) and (c), respectively, under the same load and boundary conditions. Warmer color represents higher stress and red encodes stress exceeding the yield strength 42 MPa. The maximum stress in (b) is 109.84 MPa, which far exceeds 42 MPa, while the maximum stress in (d) is below 40 MPa with the contribution from ribs. The maximum stress of the shell is about 3 times of the stress of the rib-reinforced shell structure, indicating the latter achieves much higher strength than the former. We also fabricated the two structures by 3D printing and made a stiffness comparison as shown in Figure 19 which indicates much higher stiffness of the rib-reinforced shell structure. AbstractShell structures are extensively used in engineering due to their efficient load-carrying capacity relative to material volume. However, large-span shells require additional supporting structures to strengthen fragile regions. The problem of designing optimal stiffeners is therefore becoming a major challenge for shell applications. To address it, we propose a computational framework to design and optimize rib layout on arbitrary shell to improve the overall structural stiffness and mechanical performance. The essential of our method is to place ribs along the principal stress lines which reflect paths of material continuity and indicates trajectories of internal forces. Given a surface and user-specified external loads, we perform a Finite Element Analysis. Using the resulting principal stress field, we generate a quad-mesh whose edges align with this cross field. Then we extract an initial rib network from the quad-mesh. After simplifying rib network by removing ribs with little contribution, we perform a rib flow optimization which allows ribs to swing on surface to further adjust rib distribution. Finally, we optimize rib cross-section to maximally reduce material usage while achieving certain structural stiffness requirements. We demonstrate that our rib-reinforced shell structures achieve good static performances. And experimental results by 3D printed objects show the effectiveness of our method.

show abstract

An automatic grid generation approach over free-form surface for architectural design

Cited by 17 publications

References 12 publications

Triangular mesh generation on free-form surfaces based on bubble dynamics simulation

Triangular mesh generation on free-form surfaces based on bubble dynamics simulation

Computational Grid Generation for the Design of Free-Form Shells with Complex Boundary Conditions

Rib‐reinforced Shell Structure

Contact Info

Product

Resources

About