Suspension Footbridge Form-Finding with Laplacian Smoothing Algorithm
- PDF / 1,425,091 Bytes
- 7 Pages / 595.276 x 790.866 pts Page_size
- 97 Downloads / 167 Views
International Journal of Steel Structures https://doi.org/10.1007/s13296-020-00396-4
Suspension Footbridge Form‑Finding with Laplacian Smoothing Algorithm Zhuo‑ju Huang1,2 · Jie‑min Ding2 · Sheng‑yi Xiang2 Received: 21 January 2020 / Accepted: 26 August 2020 © Korean Society of Steel Construction 2020
Abstract In this paper, Laplacian smoothing, which is an algorithm originally used to smooth polygon meshes in computer graphics (CG), is applied to solve a structural form-finding problem with the proof that the result of such algorithm is equivalent to force density method. Such CG algorithm is used on the design of a new-built suspension footbridge in Shaoxing, China and the algorithm works well. Since Laplacian smoothing is a pure geometric algorithm without any mechanical concept, the algorithm shows the inner relationship between force and shape, more structural applicable CG algorithms are expected to be found in the future. Keywords Form-finding · Laplacian smoothing · Force density method · Footbridge
1 Introduction 1.1 Suspension Structure The first appearance of Suspension footbridge can be traced back for connecting two sides of a valley in the form of ropes and timber plates. Early in 200 B.C., people in south western China began to use iron chain to build a suspension bridge. The prior bridge knowledge was pread to Europe from about 1650 A.C. (Harris and Li 1996). With the development of modern structural engineering knowledge, suspension structure became known by its high efficiency for large span structure. This is because structures in large scale are hardly to be achieved by using a low efficient bending beams (Schlaich et al. 2004). But in a suspension system, which remains all the major bearing parts tensional without any materials in low stress, this can ensure structural members are fully utilized, results in high bearing efficiency. Normally, a symmetrical shape is the most ideal form for a suspension bridge with its complicated force distribution and geometric nonlinearity. This situation was changed after
* Zhuo‑ju Huang [email protected] 1
Tongji University, Shanghai 200092, China
Tongji Architectural Design (Group) Co., Ltd., Shanghai 200092, China
2
World War II, with the deeper understandings in the principles of tensegrity system by engineers, more light-weight footbridges were designed in various shapes. Especially after the 1960s when computer and numerical methods became available, an increasing number of suspension footbridges with spatial shape emerged.
1.2 The Footbridge The target footbridge in this report locates in Shaoxing, a fast-developing city and famous with its textile industry in south-eastern China. The footbridge is the annexe of Shaoxing International Conference and Exhibition Center, which looks like a dancing girl’s dress. This suspension bridge contributes to an essential element of the landmark with its huge mast. Figure 1 shows the overlook of the whole footbridge with its surrounding buildings. The footbridge connects the three banks of the
Data Loading...
