Advanced Steel Construction

Vol. 7, No. 4, pp. 313-329 (2011)


ADVANCED SHAPE FINDING ALGORITHM OF FORCE DENSITY METHOD BASED ON FEM

 

K.S. Lee 1,* and S.E. Han 2

1 Research Assistant Professor, Department of Architectural Engineering, School of Architecture

Inha University, 253 Yonghyundong, Nam-gu, Incheon, 402-751, South Korea

2 Professor, Department of Architectural Engineering, School of Architecture

Inha University, 253 Yonghyundong, Nam-gu, Incheon, 402-751, South Korea

*(Corresponding author: E-mail:  This email address is being protected from spambots. You need JavaScript enabled to view it. )

Received: 28 October 2010; Revised: 8 March 2011; Accepted: 15 March 2011

 

DOI:10.18057/IJASC.2011.7.4.1

 

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ABSTRACT

This paper proposes a modified formulation of the force density method by adopting finite element method procedures and replacing each edge of a 3-node or 4-node membrane element with a linear line element. The membrane element model, not the cable-net model, is used for simultaneous shape finding and load analysis. The derived force density matrix has a banded, symmetric nature to ensure its effectiveness in an iterative procedure. By using the nonlinear shape finding option, a number of nonlinear shape finding problems can be solved for each force density mode controlling the shape of the surface. Therefore, it is needs not to use the nonlinear numerical method such as NR or DR method. Therefore, the present research may improve the effectiveness and applicability of the FDM in linear and nonlinear shape finding problems. The following numerical examples will verify the various excellent numerical abilities of the proposed FDM.

 

KEYWORDS

Tension structures, Shape finding, Force density method, Equally stressed surface, Geodesic surface


REFERENCES

[1]       Linkwitz, K., “About Formfinding of Double-curved Structures”, Engineering Structures, 1999, Vol. 21, pp. 709-718.

[2]       Sheck, H.J., “The Force Density Method for Form Finding and Computation of General Networks”, Comput. Methods Appl. Mech. Engrg., 1974, Vol. 3, pp. 704-713.

[3]       Grundig, L. and Bahndorf, J., “The Design of Wide-span Roof Structures using Micro-computers”, Computers & Structures, 1988, Vol. 30, No. 3, pp. 495-501.

[4]       Grundig, L., Ekert, L. and Moncrieff, E., “Geodesic and Semi-geodesic Line Algorithms for Cutting Pattern Generation of Architectural Texile Structures”, Proc. Asia-Pacific Conf. on Shell and Spatial Structures, Beijing, China, 1996, pp. 435-443.

[5]       Ishii, K., “State of the Art Report on Form Finding Problem of Membrane Structures”, Research Report on Membrane Structures '89, The Membrane Structures Association of Japan, 1989, Vol. 3, pp. 83-108.

[6]       Ishii, K., “State of the Art Report on the Stress Deformation Analysis of Membrane Structures”, Research Report on Membrane Structures '90, The Membrane Structures Association of Japan, 1990, Vol. 4, pp. 69-105.

[7]       Levy, R. and Spillers, W.R., Analysis of Geometrically Nonlinear Structures, Second Edition, Kluwer Academic Publishers, 2003.

[8]       Bletzinger, K.U. and Ramm, E., “A General Finite Element Approach to the Form Finding of Tensile Structures”, Int. Journal of Space Structures, 1999, Vol. 14, No. 2, pp. 131-145.

[9]       Bletzinger, K.U., Wuechner, R., Daoud, F. and Camprubi, N., “Computational Methods for Form Finding and Optimization of Shells and Membranes”, Comput. Methods Appl. Mech. Engrg., 2005, Vol. 194, pp. 143-166.

[10]     Barnes, M.R., “Form-finding and Analysis of Prestressed Nets and Membranes”, Computers & Structures, 1988, Vol. 30, No. 3, pp. 685-695.

[11]     Wakefield, D.S., “Engineering Analysis of Tension Structures: Theory and Practice”, Engineering Structures, 1999, Vol. 21, pp. 680-690.

[12]     Gosling, P.D. and Lewis, W.J., “Optimal Structural Membranes-II. Form-finding of prestressed Membranes using a Curved Quadrileteral Finite Element for Surface Definition”, Computers & Structures, 1996, Vol. 61, No. 5, pp. 885-895.

[13]     Han, S.E. and Lee, K.S., “A Study of the Stabilizing Process of Unstable Structures by Dynamic Relaxation Method”, Computers & Structures, 2003, Vol. 81, pp. 1677-1688.

[14] Lewis, W.J., Tension Structures: Form and Behaviour, Thomas Telford, 2003.

[15] Topping, B.H.V. and Iványi, P., Computer Aided Design of Cable-membrane Structures”, Saxe-Coburg Publications, 2007

[16] Linhard, J., D'Anza, G., Bletzinger, K.-U., “Rhino-Membrane - Modern State of the Art Application for Tensile Structure Form Finding”, TensiNews, 2008, Vol. 15.

[17] D'Anza, G., ”Rhino-Membrane in Real Modelling Problems”, Structural Membranes 2009. 2009.

[18] Maurin, B. and Motro, R., “The Surface Stress Density Method as a Form-finding Tool for Tensile Membrane”, Engineering Structures, 1999, Vol. 20, pp. 712–719.

[19] Pauletti, R.M.O. and Pimenta, P.M., “The Natural Force Density Method for the Shape Finding of Taut Structures”, Comput. Methods Appl. Mech. Engrg., 2008, Vol. 197, pp. 4419-4428.

[20] Argyris, J.H., Dunne, P.C., Angelopoulos. T. and Bichat, B., “Large Natural Strains and Some Special Difficulties due to Non-linearity and Incompressibility in Finite Elements“, Comput. Methods Appl. Mech. Engrg., 1974, Vol. 4, No. 2, pp. 219–278.

[21] Pauletti, R.M.O., Guirardi, D.M. and Deifeld, T.E.C., “Argyris’s Natural Membrane Finite Element Revisited”, International Conference on Textile Composites and Inflatable Structures, Structural Membranes, 2005.