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A novel approach to the form-finding of membrane structures using dynamic relaxation method

  • Labbafi, S. Fatemeh (Department of Civil Engineering, University of Birjand) ;
  • Sarafrazi, S. Reza (Department of Civil Engineering, University of Birjand) ;
  • Gholami, Hossein (Department of Civil Engineering, University of Birjand) ;
  • Kang, Thomas H.K. (Department of Architecture & Architectural Engineering, Seoul National University)
  • Received : 2017.03.08
  • Accepted : 2017.04.10
  • Published : 2017.07.25

Abstract

Solving a system of linear or non-linear equations is required to analyze any kind of structures. There are many ways to solve a system of equations, and they can be classified as implicit and explicit techniques. The explicit methods eliminate round-off errors and use less memory. The dynamic relaxation method (DR) is one of the powerful and simple explicit processes. The important point is that the DR does not require to store the global stiffness matrix, for which it just uses the residual loads vector. In this paper, a new approach to the DR method is expressed. In this approach, the damping, mass and time steps are similar to those of the traditional method of dynamic relaxation. The difference of this proposed method is focused on the method of calculating the damping. The proposed method is expressed such that the time step is constant, damping is equal to zero except in steps with maximum energy and the concentrated damping can be applied to minimize the energy of system in this step. In this condition, the calculation of damping in all steps is not required. Then the volume of computation is reduced. The DR method for form-finding of membrane structures is employed in this paper. The form-finding of the three plans related to the membrane structures with different loading is considered to investigate the efficiency of the proposed method. The numerical results show that the convergence rate based on the proposed method increases in all cases than other methods.

Keywords

References

  1. Alamatian, J. (2012), "A new formulation for fictitious mass of the dynamic relaxation method with kinetic damping", Comput. Struct., 90, 42-54.
  2. Al-Shawi, F.A.N. and Mardirosian, A.H. (1987), "An improved dynamic relaxation method for the analysis of plate bending problems", Comput. Struct., 27(2), 237-240. https://doi.org/10.1016/0045-7949(87)90091-5
  3. Bagrianski, S. and Halpern, A.B. (2014), "Form-finding of compressive structures using prescriptive dynamic relaxation", Comput. Struct., 132, 65-74. https://doi.org/10.1016/j.compstruc.2013.10.018
  4. Barnes, M.R. (1988), "Form-finding and analysis of prestressed nets and membranes", Comput. Struct., 30(3), 685-695. https://doi.org/10.1016/0045-7949(88)90304-5
  5. Brew, J.S. and Brotton, D.M. (1971), "Non-linear structural analysis by dynamic relaxation", Int. J. Numer. Meth. Eng., 3(4), 463-483. https://doi.org/10.1002/nme.1620030403
  6. Bunce, J.W. (1972), "A note on the estimation of critical damping in dynamic relaxation", Int. J. Numer. Meth. Eng., 4(2), 301-303. https://doi.org/10.1002/nme.1620040214
  7. Cassell, A.C. and Hobbs, R.E. (1976), "Numerical stability of dynamic relaxation analysis of non-linear structures", Int. J. Numer. Meth. Eng., 10(6), 1407-1410.
  8. Cundall, P.A. (1976), Explicit Finite-Difference Method in Geomechanics, Presented at the Numerical Methods in Geomechanics, Blacksburg, 132-150.
  9. Frankel, S.P. (1950), "Convergence rates of iterative treatments of partial differential equations. Math", Tab. Aid. Comput., 4(30), 65-75. https://doi.org/10.2307/2002770
  10. Frieze, P.A., Hobbs, R.E. and Dowling, P.J. (1978), "Application of dynamic relaxation to the large deflection elasto-plastic analysis of plates", Comput. Struct., 8(2), 301-310. https://doi.org/10.1016/0045-7949(78)90037-8
  11. Gil Perez, M., Kang, T.H.K., Sin, I. and Kim, S.D. (2016), "Nonlinear design and analysis of membrane fabric structures: Modeling procedure and case studies", ASCE J. Struct. Eng., 142.
  12. Gil Perez, M., Kim, S.D. and Kang, T.H.K. (2017), "Development of design aid for barrel vault shaped membrane fabric structures", J. Struct. Integr. Mainten., 2(1), 12-21. https://doi.org/10.1080/24705314.2017.1280592
  13. Kadkhodayan, M., Alamatian, J. and Turvey, G.J. (2008), "A new fictitious time for the dynamic relaxation (DXDR) method", Int. J. Numer. Meth. Eng., 74(6), 996-1018
  14. Labbafi, S.F., Sarafrazi, S.R. and Kang, T.H.K. (2017), "Comparison of viscous and kinetic dynamic relaxation methods in form-finding of membrane structures", Adv. Comput. Des., 2(1), 71-87. https://doi.org/10.12989/ACD.2017.2.1.071
  15. Levy, R. and Spillers, W.R. (2003), Analysis of Geometrically Nonlinear Structures, 2nd Edition, Springer, Dordrecht, New York, U.S.A.
  16. Lewis, W.J. (2003), Tension Structures: Form and Behaviour. Thomas Telford.
  17. Nabaei, S.S., Baverel, O. and Weinand, Y. (2013), "Mechanical form-finding of the timber fabric structures with dynamic relaxation method", Int. J. Space Struct., 28(3-4), 197-214. https://doi.org/10.1260/0266-3511.28.3-4.197
  18. Otter, J.R.H. (1966), "Dynamic relaxation compared with other iterative finite difference methods", Nucl. Eng. Des., 3(1), 183-185. https://doi.org/10.1016/0029-5493(66)90157-9
  19. Papadrakakis, M. (1981), "A method for the automatic evaluation of the dynamic relaxation parameters", Comput. Meth. Appl. Mech. Eng., 25(1), 35-48. https://doi.org/10.1016/0045-7825(81)90066-9
  20. Qiang, S. (1988), "An adaptive dynamic relaxation method for nonlinear problems", Comput. Struct., 30(4), 855-859. https://doi.org/10.1016/0045-7949(88)90117-4
  21. Rezaiee-Pajand, M. and Alamatian, J. (2010), "The dynamic relaxation method using new formulation for fictitious mass and damping", Struct. Eng. Mech., 34.
  22. Rezaiee-Pajand, M. and Taghavian Hakkak, M. (2006), "Nonlinear analysis of truss structures using dynamic relaxation(research note)", Int. J. Eng.-Trans. B Appl., 19, 11.
  23. Rezaiee-Pajand, M., Kadkhodayan, M., Alamatian, J. and Zhang, L.C. (2011), "A new method of fictitious viscous damping determination for the dynamic relaxation method", Comput. Struct., 89(9), 783-794. https://doi.org/10.1016/j.compstruc.2011.02.002
  24. Rezaiee-Pajand, M. and Rezaee, H. (2014), "Fictitious time step for the kinetic dynamic relaxation method", Mech. Adv. Mater. Struct., 21(8), 631-644. https://doi.org/10.1080/15376494.2012.699603
  25. Rezaiee-Pajand, M. and Sarafrazi, S.R. (2010), "Nonlinear structural analysis using dynamic relaxation method with improved convergence rate", Int. J. Comput. Meth., 7(4), 627-654. https://doi.org/10.1142/S0219876210002386
  26. Rezaiee-Pajand, M. and Sarafrazi, S.R. (2011), "Nonlinear dynamic structural analysis using dynamic relaxation with zero damping", Comput. Struct., 89(13), 1274-1285. https://doi.org/10.1016/j.compstruc.2011.04.005
  27. Rushton, K.R. (1969), "Dynamic-relaxation solution for the large deflection of plates with specified boundary stresses", J. Strain Anal. Eng. Des., 4(2), 75-80. https://doi.org/10.1243/03093247V042075
  28. Spillers, W.R., Schlogel, M. and Pilla, D. (1992), "A simple membrane finite element", Comput. Struct., 45(1), 181-183. https://doi.org/10.1016/0045-7949(92)90355-4
  29. Topping, B.H.V. and Ivanyi, P. (2008), Computer Aided Design of Cable Membrane Structures, Saxe-Coburg Publications, Kippen, Stirlingshire, Scotland.
  30. Underwood, P. (1983), Dynamic Relaxation (in Structural Transient Analysis) Computational Methods for Transient Analysis, Amsterdam, North-Holland, 245-265.
  31. Veenendaal, D. and Block, P. (2012), "An overview and comparison of structural form finding methods for general networks", Int. J. Sol. Struct., 49(26), 3741-3753. https://doi.org/10.1016/j.ijsolstr.2012.08.008
  32. Veenendaal, D., West, M. and Block, P. (2011), "History and overview of fabric formwork: Using fabrics for concrete casting", Struct. Concrete, 12(3), 164-177. https://doi.org/10.1002/suco.201100014
  33. Wood, R.D. (2002), "A simple technique for controlling element distortion in dynamic relaxation form-finding of tension membranes", Comput. Struct., 80(27), 2115-2120. https://doi.org/10.1016/S0045-7949(02)00274-2
  34. Wood, W.L. (1971), "Note on dynamic relaxation", Int. J. Numer. Meth. Eng., 3(1), 145-147. https://doi.org/10.1002/nme.1620030115
  35. Xu, R., Li, D.X., Liu, W., Jiang, J.P., Liao, Y.H. and Wang, J. (2015), "Modified nonlinear force density method for form-finding of membrane SAR atenna", Struct. Eng. Mech., 54(6), 1045-1059.
  36. Zhang, L.C., 3.Kadkhodayan, M. and Mai, Y.W. (1994), "Development of the maDR method", Comput. Struct., 52(1), 1-8. https://doi.org/10.1016/0045-7949(94)90249-6
  37. Zhang, L.G. and Yu, T.X. (1989), "Modified adaptive dynamic relaxation method and its application to elastic-plastic bending and wrinkling of circular plates", Comput. Struct., 33(2), 609-614. https://doi.org/10.1016/0045-7949(89)90035-7