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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 73
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Paper 23

Development of an Advanced System for Analysis and Design of Tensile Structures

T.H. Zhang and S.L. McCabe

Department of Civil and Environmental Engineering, University of Kansas, Lawrence, United States of America

Full Bibliographic Reference for this paper
T.H. Zhang, S.L. McCabe, "Development of an Advanced System for Analysis and Design of Tensile Structures", in B.H.V. Topping, (Editor), "Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 23, 2001. doi:10.4203/ccp.73.23
Keywords: tensile structures, form finding, non-linear, direct stiffness, finite element, DLTG, Newton-Raphson.

Summary
This paper reports on a project that has developed a windows-based analysis system for tension structures. The analysis procedure includes Direct Stiffness and FEM and is interpreted as an application in AutoCAD 2000. The result is an analysis system that is freely integrated with AutoCAD and permits building the analysis model graphically and then viewing the results. Fabrication or shop drawings then are developed.

23.1 Form Finding Methods

A non-linear program was developed to find the natural shape of the tension fabric roof. Direct Stiffness and Finite-Element analysis procedures were developed for use on different types of structures. The large displacement theory was implemented and the solution using iterative numerical method. The methods are using to find the initial form of the structures as well as computation the displacements under loading. Results are compared with theory and predicted results. The Direct Stiffness method is applied for relatively simple and truss or cable structures such as single layer, double layer or cable tensegrity domes. In this case, the final shape can always be predicted. Assuming the final shape, modeling the coordinates of every node and applying prestress at the beginning, the node coordinates can be adjusted by computing their displacements to get the final shape. For this method, a simultaneous nonlinear equilibrium equations were built as . In this equation, represents stiffness matrix for the single cable element as well as the whole structure including only linear displacement items, and is a residual force that represents non-linear displacement. In a structure, which has relatively complicated curvature such as cable nets or membrane structures, it is hard to obtain an exact shape in advance. A more general method using geometric nonlinear analysis was used in this case. The shape of the tensioned fabric was obtained by displacing the selected points in the two- dimensional cable net model with a three-dimension one. A meshing routine was put in place to produce the Finite Element mesh according to the prestressing applied to the cable and boundary conditions to find the displacements of the supporting points. The lengths of the cable net and the edge cables attached to the fabric were adjusted by changing the prestressing forces to achieve the desired stable design shape. For this method, the terms go away, but matrix includes both linear and non-linear matrices. After the matrix was obtained for the entire structure, displacements were obtained by solving the nonlinear simultaneous equations. For both the Direct Stiffness and FEM solution, the Newton-Raphson method, which provides quick convergence, was used for the iterative solution. The displacement and internal stress under external loads were then analyzed using this method after obtaining the initial shape.

23.2 Software Development Environment

This software was designed to assist engineers in analyzing and designing tension structures by finding the form and calculating the large displacements of the tension structure. The software has both the robust nonlinear calculation and capability of GUI. AutoCAD2000 is used as application engine. All the computational procedures of the software are placed the external application programming environments to AutoCAD. Microsoft Visual C++6.0(VC++) is utilized to conduct all the calculation processes. The final shape of the structure can be drawn automatically from the results. Also, this software can draft the various elements that make up the roofing system and show the bill of material costs. This software will simplify the complex design process of tension structures and save time for designers. The utilization of this software will make the design of tension structures a more straitforward processes and allowing development of new results for the structures.

References
1
Maritz Wandenberg, Cable nets, 1998.
2
Otto, F., 1969, Tensile Structures, M.I.T. Press, Cambridge.
3
Schek, H. J., "The Force Density Method for Form-Finding and Computation of General Networks", Computer Methods in Applied Mechanics and Engineering, 3, North Holland Publishing Company, pp 115 - 134, 1974. doi:10.1016/0045-7825(74)90045-0
4
R.E. Shaeffer, Tensioned Fabric structures, The American Society of Civil Engineers, 1996.
5
A. Caner and R. Hsu, "Tensioned Fabric Shape-Finding", Journal of Structural Engineering, Vol.125, No 9,September, 1999. doi:10.1061/(ASCE)0733-9445(1999)125:9(1065)
6
A. Hanaor, "Double �Layer Tensegrity Grids: Static Load Response: Experimental Study", Journal of Structural Engineering. Vol 117, No.6. June, 1991. doi:10.1061/(ASCE)0733-9445(1991)117:6(1675)
7
David M. Campbell, "The Unique Role of Computing in the Design and Construction of Tensile Membrane Structures", 1995.

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