Structural Engineering and Mechanics

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An Extended Force Density Method for the form finding of cable systems with new forms

  • Malerba, P.G. (Department of Structural Engineering, Politecnico di Milano) ;
  • Patelli, M. (Studio Malerba) ;
  • Quagliaroli, M. (Department of Structural Engineering, Politecnico di Milano)
  • Received : 2011.07.22
  • Accepted : 2012.03.13
  • Published : 2012.04.25
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Abstract

The Force Density Method (FDM) is a well known and extremely versatile tool in form finding of cable nets. In its linear formulation such method makes it possible to find all the possible equilibrium configurations of a net of cables having a certain given connectivity and given boundary conditions on the nodes. Each singular configuration corresponds to an assumed force density distribution. Its improvement as Non-Linear Force Density Method (NLFDM) introduces the possibility of imposing assigned relative distances among the nodes, the tensile level in the elements and/or their initial undeformed length. In this paper an Extended Force Density Method (EFDM) is proposed, which makes it possible to set conditions in terms of given fixed nodal reactions or, in other words, to fix the positions of a certain number of nodes and, at the same time, to impose the intensity of the reaction force. Through such extension, the (EFDM) enables us to deal with form findings problems of cable nets subjected to given constraints and, in particular, with mixed structures, made of cables and struts. The efficiency and the robustness of method are assessed through comparisons with other form finding techniques in dealing with characteristic applications to the prestress design of cable systems. As a further extension, the EFDM is applied to structures having some parts not yet geometrically defined, as can happen in designing new creative forms.

Keywords

References

  1. Argyris, J.H., Angelopoulos, T. and Bichat, B. (1974), "A general method for the shape finding of lightweight tension structures", Comput. Meth. Appl. Mech. Eng., 3(1), 135-149. https://doi.org/10.1016/0045-7825(74)90046-2
  2. Barnes, M.R. (1975), "Applications of dynamic relaxation to the design and analysis of cable, membrane and pneumatic structures", International Conference on Space Structures, Guildford.
  3. Fu, F. (2005), "Structural behavior and design methods of tensegrity domes", J. Constr. Steel Res., 61(1), 23-35. https://doi.org/10.1016/j.jcsr.2004.06.004
  4. Geiger, D.H. (1986), "The design and construction of two cable domes for the Korea Olympics. Shells", Membranes and Space Frame, Proceedings of pf IASS Symposium.
  5. Grnding, L., Moncrieff, E., Singer, P. and Strobel, D. (2000), "A history of the principal developments and applications of the force density method in Germany", IASS-IACM 2000 Fourth International Colloquium on Computation of Shell & Spatial Structures, Chania-Crete, Greece.
  6. Haber, R.B. and Abel, J.F. (1982), "Initial equilibrium solution methods for cable reinforced membranes part I-- formulations", Comput. Meth. Appl. Mech. Eng., 30(3), 263-284. https://doi.org/10.1016/0045-7825(82)90080-9
  7. Kiewitt, G. (1960), "The new look of lamella roofs", Architectural Record, February, 226.
  8. Levy, Matthys P. (1994), "Georgia dome and beyond achieving lightweight-longspan structures", Proceedings of the Spatial, Lattice and Tension Structures, 560-562.
  9. Linkwitz, K. (1999), "About formfinding of double-curved structures", Eng. Struct., 21(8), 709-718. https://doi.org/10.1016/S0141-0296(98)00025-X
  10. Pellegrino, S. (1993), "Structural computations with the singular value decomposition of the equilibrium matrix", Int. J. Solids Struct., 30(21), 3025-3035. https://doi.org/10.1016/0020-7683(93)90210-X
  11. Schek, H.J. (1974), "The force density method for form finding and computation of general networks", Comput. Meth. Appl. Mech. Eng., 3, 115-134. https://doi.org/10.1016/0045-7825(74)90045-0
  12. Tibert, G. (1999), "Numerical analyses af cable roof structures", Lic. Thesis, Royal Institute of Technology, Stockholm.
  13. Vassart, N. and Motro, R. (1999), "Multiparametered formfinding method: application to tensegrity systems", International Journal of Space Structures", Int. J. Space Struct., 14(2), 147-154. https://doi.org/10.1260/0266351991494768
  14. Wang, Z., Yuan, X. and Dong, S. (2010), "Simple approach for force finding analysis of circular Geiger domes with consideration of self-weight", J. Constr. Steel Res., 66(2) , 317-322. https://doi.org/10.1016/j.jcsr.2009.09.010
  15. Zong, Z. and Guo, Z. (2009), "Nonlinear numerical analysis of cable dome structure with rigid roof", Eng. Mech., 7, DOI: CNKI:SUN:GCLX.0.2009-07-025.
  16. Yuan, X., Chen, L. and Dong, S. (2007), "Prestress design of cable domes with new forms", Int. J. Solids Struct., 44 , 2773-2782. https://doi.org/10.1016/j.ijsolstr.2006.08.026
  17. Yuan, X. and Dong, S. (2003), "Integral feasible prestress state of cable domes", Comput. Struct., 81(21), 2111-2119. https://doi.org/10.1016/S0045-7949(03)00254-2
  18. Zhang, J.Y. and Ohsaki, M. (2006), "Adaptive force density method for form-finding problem of tensegrity structures", Int. J. Solids Struct., 43, 5658-5673. https://doi.org/10.1016/j.ijsolstr.2005.10.011

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