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Nonlinear analysis of thin shallow arches subject to snap-through using truss models

  • Xenidis, H. (Department of Civil Engineering, Aristotle University of Thessaloniki) ;
  • Morfidis, K. (Institute of Engineering Seismology and Earthquake Engineering) ;
  • Papadopoulos, P.G. (Department of Civil Engineering, Aristotle University of Thessaloniki)
  • Received : 2012.09.21
  • Accepted : 2013.01.11
  • Published : 2013.02.25

Abstract

In this study a truss model is used for the geometrically nonlinear static and dynamic analysis of a thin shallow arch subject to snap-through. Thanks to the very simple geometry of a truss, the equilibrium conditions can be easily written and the global stiffness matrix can be easily updated with respect to the deformed structure, within each step of the analysis. A very coarse discretization is applied; so, in a very simple way, the high frequency modes are suppressed from the beginning and there is no need to develop a complicated reduced-order technique. Two short computer programs have been developed for the geometrically nonlinear static analysis by displacement control of a plane truss model of a structure as well as for its dynamic analysis by the step-by-step time integration algorithm of trapezoidal rule, combined with a predictor-corrector technique. These two short, fully documented computer programs are applied on the geometrically nonlinear static and dynamic analysis of a specific thin shallow arch subject to snap-through.

Keywords

References

  1. Argyris, J.H. (1978), International Conferences FENoMech (Finite Elements in Nonlinear Mechanics), Institute for Statics and Dynamics, Stuttgart, I. 1978, II. 1981, III. 1984, Proceedings in the Journal of Computer Methods in Applied Mechanics and Engineering.
  2. Armero, F. and Romero, I. (2001a), "On the formulation of high frequency dissipative time-stepping algorithms for nonlinear dynamics. Part I: Low-order methods for two model problems in nonlinear elastodynamics", Computer Methods in Applied Mechanics and Engineering, 190(20-21), 2603-2649. https://doi.org/10.1016/S0045-7825(00)00256-5
  3. Armero, F. and Romero, I. (2001b), "On the formulation of high frequency dissipative time-stepping algorithms for nonlinear dynamics.Part II: Second order methods", Computer Methods in Applied Mechanics and Engineering, 190(50-51), 6783-6824. https://doi.org/10.1016/S0045-7825(01)00233-X
  4. Bathe, K.J. (2007), "Conserving energy and momentum in nonlinear dynamics: a simple implicit timeintegration scheme", Computer and Structures, 85, 437-445. https://doi.org/10.1016/j.compstruc.2006.09.004
  5. Bradford, M.A., Uy, B. and Pi, Y. L. (2002), "In plane elastic stability of arches under a central concentrated load", Journal of Engineering Mechanics ASCE, 128(7), 710-719. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:7(710)
  6. Chandra, Y. (2009), "Snap-through of curved beam", Master Thesis, University of Illinois at Urbana- Champaign.
  7. Chen, J.S., Ro, W.C. and Lin, J.S. (2009), "Exact static and dynamic critical load of a sinusoidal arch under a point force at the midpoint", International Journal of Non-Linear Mechanics, 44, 66-70. https://doi.org/10.1016/j.ijnonlinmec.2008.08.006
  8. Felippa, C.A. (2009), Introduction to Finite Element Methods (Class notes), http://www.colorado.edu/engineering/CAS/courses.d/IFEM.d/Home.html
  9. Hollkamp, J. J. and Gordon, R.W. (2008), "Reduced-order models for nonlinear response prediction: Implicit condensation and expansion", Journal of Sound and Vibration, 318, 1139-1153. https://doi.org/10.1016/j.jsv.2008.04.035
  10. Papadopoulos, P.G., Arethas, I., Lazaridis, P., Mitsopoulou, E. and Tegos, J. (2008a), "A simple method using truss model for in-plane nonlinear static analysis of a cable-stayed bridge with a plate deck section", Engineering Structures, 30(1), 42-53. https://doi.org/10.1016/j.engstruct.2007.03.001
  11. Papadopoulos, P.G., Papadopoulou, A.K. and Papaioannou, K.K. (2008b), "Simple nonlinear static analysis of steel portal frame with pitched roof exposed to fire", Structural Engineering and Mechanics, 29(1), 37- 53. https://doi.org/10.12989/sem.2008.29.1.037
  12. Papadopoulos, P.G., Lazaridis, P., Xenidis, H., Lambrou, P. and Diamantopoulos, A. (2012), "Modelling snap-through of thin shallow arches using coarse truss models", Paper 78 from CCP: 96, ISBN 978-1- 905088-55-3, Proceedings of 13th International Conference on Civil, Structural and Environmental Engineering Computing (CC2011), Platanias, Chania, Crete, Greece, September.
  13. Papadopoulos, P.G., Diamantopoulos, A., Xenidis, H. and Lazaridis, P. (2012), "Simple program to investigate hysteresis damping effect of cross-ties on cables vibration of cable-stayed bridges", Hindawi Publishing Corporation, Advances in Civil Engineering, Article ID463134, doi:10.1155/2012/463134.
  14. Pi, Y.L., Bradford, M.A. and Uy, B. (2002), "In-plane stability of arches", International Journal of Solids and Structures, 39, 105-125. https://doi.org/10.1016/S0020-7683(01)00209-8
  15. Pi, Y.L. and Bradfordm M.A. (2008a), "Dynamic buckling of shallow pin-ended arches under sudden central concentrated load", Journal of Sound and Vibration, 317, 898-917. https://doi.org/10.1016/j.jsv.2008.03.037
  16. Pi, Y.L., Bradford, M.A. and Tin-Loi, F. (2008b), "Non-linear in-plane buckling of rotationally restrained shallow arches under a central concentrated load", International Journal of Non-Linear Mechanics, 43, 1- 17. https://doi.org/10.1016/j.ijnonlinmec.2007.03.013
  17. Przekop, A. and Rizzi, S.A. (2006), "Nonlinear reduced-order response analysis of structures with shallow curvatures", AIAA Journal, 44(8), 1767-1778. https://doi.org/10.2514/1.18868
  18. Przekop, A. and Rizzi, S.A. (2007), "Dynamic snap-through of thin-walled structures by a reduced-order method", AIAA Journal, 45(10), 2510-2519. https://doi.org/10.2514/1.26351
  19. Spottswood, S.M., Hollkamp, J.J. and Eason, T.G. (2010), "Reduced-order models for a shallow curved beam under combined loading", AIAA Journal, 48(1), 47-55. https://doi.org/10.2514/1.38707
  20. Taylor, R.L. (2008), "FEAP, A Finite Element Analysis Program", Department of Civil and Environmental Engineering, University of California at Berkeley, version 8.2.

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