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Buckling analysis of imperfect I-section beam-columns with stochastic shell finite elements

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Abstract

Buckling loads of thin-walled I-section beam-columns exhibit a wide stochastic scattering due to the uncertainty of imperfections. The present paper proposes a finite element based methodology for the stochastic buckling simulation of I-sections, which uses random fields to accurately describe the fluctuating size and spatial correlation of imperfections. The stochastic buckling behaviour is evaluated by crude Monte-Carlo simulation, based on a large number of I-section samples, which are generated by spectral representation and subsequently analyzed by non-linear shell finite elements. The application to an example I-section beam-column demonstrates that the simulated buckling response is in good agreement with experiments and follows key concepts of imperfection triggered buckling. The derivation of the buckling load variability and the stochastic interaction curve for combined compression and major axis bending as well as stochastic sensitivity studies for thickness and geometric imperfections illustrate potential benefits of the proposed methodology in buckling related research and applications.

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References

  1. Argyris J, Tenek L, Olofsson L (1997) TRIC: a simple but sophisticated 3-node triangular element based on 6 rigid body and 12 straining modes for fast computational simulations of arbitrary isotropic and laminated composite shells. Comput Methods Appl Mech Eng 145: 11–85

    Article  MATH  Google Scholar 

  2. Argyris J, Tenek L, Papadrakakis M, Apostolopoulou C (1998) Postbuckling performance of the TRIC natural mode triangular element for isotropic and laminated composite shells. Comput Methods Appl Mech Eng 145: 11–85

    Article  Google Scholar 

  3. Argyris J, Papadrakakis M, Apostolopoulou C, Koutsourelakis S (2000) The TRIC shell element: theoretical and numerical investigation. Comput Methods Appl Mech Eng 166: 211–231

    Article  Google Scholar 

  4. Argyris J, Papadrakakis M, Stefanou G (2002) Stochastic finite element analysis of shells. Comput Methods Appl Mech Eng 191: 4781–4804

    Article  MATH  Google Scholar 

  5. Argyris J, Papadrakakis M, Karapitta L (2002) Elastoplastic analysis of shells with the triangular element TRIC. Comput Methods Appl Mech Eng 191(33): 3613–3637

    Article  MATH  Google Scholar 

  6. Basudhar A, Missoum S (2009) A sampling-based approach for probabilistic design with random fields. Comput Methods Appl Mech Eng. 189(47–48): 3647–3655

    Article  Google Scholar 

  7. Blyfield MP, Nethercot DA (1997) Material and geometric properties of structural steel for use in design. Struct Eng 75(21): 1–5

    Google Scholar 

  8. Budiansky B (1974) Theory of buckling and post-buckling behavior of elastic structures. In: Advances in applied mechanics, vol 14. Academic Press, New York, pp 1–65

  9. Bushnell D (1985) Computerized buckling analysis of shells. Springer, New York

    Google Scholar 

  10. Bazant ZP, Cedolin L (1991) Stability of structures: elastic, inelastic, fracture, and damage theories. Kluwer, Dordrecht

    MATH  Google Scholar 

  11. Chen N-Z, Guedes Soares C (2008) Spectral stochastic finite element analysis for laminated composite plates. Comput Methods Appl Mech Eng 197: 4830–4839

    Article  Google Scholar 

  12. Craig KJ, Roux WJ (2008) On the investigation of shell buckling due to random geometrical imperfections implemented using Karhunen-Loève expansions. Int J Numer Methods Eng 73: 1715–1726

    Article  MATH  Google Scholar 

  13. Crisfield MA (1997) Non-linear finite element analysis of solids and structures, vol 1+2. Wiley, New York

    Google Scholar 

  14. Deodatis G, Spanos PD (eds) (2006) Computational stochastic mechanics. In: Proceedings of the 5th International conference on computational stochastic mechanics (CSM-5), IOS Press, Amsterdam

  15. Elishakoff I (2000) Uncertain buckling: its past, present and future. Int J Solids Struct 37: 6869–6889

    Article  MATH  MathSciNet  Google Scholar 

  16. Galambos T (1998) Guide to stability design criteria for metal structures. Wiley, New York

    Google Scholar 

  17. Godoy LA (1999) Theory of elastic stability: analysis and sensitivity, Taylor and Francis, London

  18. Greiner R, Kettler M, Lechner A, Freytag B, Linder J, Jaspart J-P, Boissonnade N, Bortolotti E, Weynand K, Ziller C, Oerder R (2008) Plastic member capacity of semi-compact steel sections - a more Economic Design, Final Report, European Research Fund for Coal and Steel

  19. Hasham AS, Rasmussen KJR (1997) Member capacity of thin-walled I-sections in combined compression and major axis bending, Research Report No R746, School of Civil Engineering, University of Sydney

  20. Hasham AS, Rasmussen KJR (2001) Nonlinear analysis of locally buckled I-section steel beam-columns. In: Zaras J, Kowal- Michalska K, Rhodes J (eds) Thin-walled structures–advances and developments, Proc. 3rd Int. Conf. on thin-walled structures, Elsevier, Krakow, pp 427–436

  21. Hasham AS, Rasmussen KJR (2002) Interaction curves for locally buckled I-section beam-columns. J Constr Steel Res 58: 213– 241

    Article  Google Scholar 

  22. Kala Z (2005) Sensitivity analysis of the stability problems of thin-walled structures. J Constr Steel Res 61(3): 415–422

    Article  Google Scholar 

  23. Kolanek K, Jendo S (2008) Random field models of geometrically imperfect structures with “clamped” boundary conditions. Probab Eng Mech 23(2): 219–226

    Google Scholar 

  24. Newland DE (1993) An introduction to random vibrations, spectral and wavelet analysis. Wiley, New York

    Google Scholar 

  25. Papadopoulos V, Papadrakakis M (2004) Finite element analysis of cylindrical panels with random initial imperfections. J Eng Mech 130: 867–876

    Article  Google Scholar 

  26. Papadopoulos V, Papadrakakis M (2005) The effect of material and thickness variability on the buckling load of shells with random initial imperfections. Comput Methods Appl Mech Eng 194: 1405–1426

    Article  MATH  Google Scholar 

  27. Papadopoulos V, Iglesis P (2007) The effect of non-uniformity of axial loading on the buckling behaviour of shells with random imperfections. Int J Solids Struct 44: 6299–6317

    Article  MATH  Google Scholar 

  28. Papadopoulos V, Charmpis DC, Papadrakakis M (2008) A computationally efficient method for the buckling analysis of shells with stochastic imperfections. Comput Mech 43: 687–700

    Article  Google Scholar 

  29. Papadopoulos V, Stefanou G, Papadrakakis M (2009) Buckling analysis of imperfect shells with stochastic non- Gaussian material and thickness properties. Int J Solids Struct 46: 2800–2808

    Article  MATH  Google Scholar 

  30. Papoulis A, Pillai SU (2002) Probability, random variables and stochastic processes. McGraw-Hill, New York

    Google Scholar 

  31. Priestley MB (1981) Spectral analysis and time series. Academic Press, London

    MATH  Google Scholar 

  32. Priestley MB (1988) Nonlinear and non-stationary time series analysis. Academic Press, London

    Google Scholar 

  33. Ramm E, Wall W (2004) Shell structures. A sensitive interrelation between physics and numerics. Int J Numer Methods Eng 60: 381–427

    Article  MATH  MathSciNet  Google Scholar 

  34. Rasmussen KJR, Hancock GJ (2000) Buckling analysis of thin-walled structures: numerical developments and applications. Prog Struct Eng Mater 2(3): 359–368

    Article  Google Scholar 

  35. Schafer BW, Grigoriu M, Peköz T (1998) A probabilistic examination of the ultimate strength of cold-formed steel elements. Thin Walled Struct 31: 271–288

    Article  Google Scholar 

  36. Schenk CA, Schuëller GI (2003) Buckling analysis of cylindrical shells with random geometric imperfections. Int J Non Linear Mech 38: 1119–1132

    Article  MATH  Google Scholar 

  37. Schenk CA, Schuëller GI (2005) Uncertainty assessment of large finite element systems, Lecture Notes in applied and computational mechanics, vol. 24. Springer, Berlin

    Google Scholar 

  38. Schenk CA, Schuëller GI (2007) Buckling analysis of cylindrical shells with cutouts including random boundary and geometric imperfections. Comput Methods Appl Mech Eng 196: 3424–3434

    Article  MATH  Google Scholar 

  39. Schillinger D, Papadopoulos V (2010) Accurate estimation of evolutionary power spectra for strongly narrow-band random fields. Comput Methods Appl Mech Eng 199(17–20): 947–960

    Article  Google Scholar 

  40. Shinozuka M, Deodatis G (1991) Simulation of stochastic processes by spectral representation. Appl Mech Rev (ASME) 44: 191–203

    Article  MathSciNet  Google Scholar 

  41. Shinozuka M, Deodatis G (1996) Simulation of multi-dimensional Gaussian stochastic fields by spectral representation. Appl Mech Rev (ASME) 49: 29–53

    Article  Google Scholar 

  42. Stefanou G, Papadrakakis M (2004) Stochastic finite element analysis of shells with combined random material and geometric properties. Comput Methods Appl Mech Eng 193: 139–160

    Article  MATH  Google Scholar 

  43. Stefanou G, Papadrakakis M (2007) Assessment of spectral representation and Karhunen-Loève expansion methods for the simulation of Gaussian stochastic fields. Comput Methods Appl Mech Eng 196: 2465–2477

    Article  MATH  Google Scholar 

  44. Stefanou G (2009) The stochastic finite element method: past, present and future. Comput Methods Appl Mech Eng 198: 1031–1051

    Article  Google Scholar 

  45. Sudret B, Der Kiureghian A (2000) Stochastic finite element methods and reliability: a state-of-the-art report, Rep. No. UCB/SEMM-2000/08, University of California at Berkeley, USA

  46. Tootkaboni M, Graham-Brady L, Schafer BW (2009) Geometrically non-linear behavior of structural systems with random material property: an asymptotic spectral stochastic approach. Comput Methods Appl Mech Eng 198: 3173–3185

    Article  MathSciNet  Google Scholar 

  47. Trahair NS, Bradford MA, Nethercot DA, Gardner L (2008) The behaviour and design of steel structures to EC3, Taylor and Francis, London

  48. Vanmarcke E (1983) Random fields analysis and synthesis. The MIT Press, MA, Cambridge

    Google Scholar 

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Authors and Affiliations

  1. Lehrstuhl für Computation in Engineering, Technische Universität München, Arcisstr. 21, 80333, Munich, Germany

    Dominik Schillinger

  2. Institute of Structural Analysis and Seismic Research, National Technical University of Athens, 9 Iroon Polytechneiou, 15780, Athens, Greece

    Vissarion Papadopoulos & Manolis Papadrakakis

  3. Institut für Baustatik und Baudynamik, Universität Stuttgart, Pfaffenwaldring 7, 70550, Stuttgart, Germany

    Manfred Bischoff

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  1. Dominik Schillinger
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  2. Vissarion Papadopoulos
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  3. Manfred Bischoff
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  4. Manolis Papadrakakis
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Correspondence to Dominik Schillinger.

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Schillinger, D., Papadopoulos, V., Bischoff, M. et al. Buckling analysis of imperfect I-section beam-columns with stochastic shell finite elements. Comput Mech 46, 495–510 (2010). https://doi.org/10.1007/s00466-010-0488-y

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  • DOI: https://doi.org/10.1007/s00466-010-0488-y

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