Structural Engineering and Mechanics

  • 제25권3호
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  • Pages.311-330
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  • 2007
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

The effects of uncertainties in structural analysis

  • Pellissetti, M.F. (Institute of Engineering Mechanics, Leopold-Franzens University) ;
  • SchueIler, G.I. (Institute of Engineering Mechanics, Leopold-Franzens University)
  • 투고 : 2006.06.27
  • 심사 : 2006.08.18
  • 발행 : 2007.02.20
⟨ 이전 논문 다음 논문 ⟩

초록

Model-based predictions of structural behavior are negatively affected by uncertainties of various type and in various stages of the structural analysis. The present paper focusses on dynamic analysis and addresses the effects of uncertainties concerning material and geometric parameters, mainly in the context of modal analysis of large-scale structures. Given the large number of uncertain parameters arising in this case, highly scalable simulation-based methods are adopted, which can deal with possibly thousands of uncertain parameters. In order to solve the reliability problem, i.e., the estimation of very small exceedance probabilities, an advanced simulation method called Line Sampling is used. In combination with an efficient algorithm for the estimation of the most important uncertain parameters, the method provides good estimates of the failure probability and enables one to quantify the error in the estimate. Another aspect here considered is the uncertainty quantification for closely-spaced eigenfrequencies. The solution here adopted represents each eigenfrequency as a weighted superposition of the full set of eigenfrequencies. In a case study performed with the FE model of a satellite it is shown that the effects of uncertain parameters can be very different in magnitude, depending on the considered response quantity. In particular, the uncertainty in the quantities of interest (eigenfrequencies) turns out to be mainly caused by very few of the uncertain parameters, which results in sharp estimates of the failure probabilities at low computational cost.

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참고문헌

  1. Au, S.-K. and Beck, J.L. (2001), 'Estimation of small failure probabilities in high dimensions by subset simulation', Probabilistic Engineering Mechanics, 16(4), 263-277 https://doi.org/10.1016/S0266-8920(01)00019-4
  2. Babuska, I. and Chatzipantelidis, P. (2002), 'On solving elliptic stochastic partial differential equations', Comput. Meth. App!. Mech. Eng., 191, 4093-4122 https://doi.org/10.1016/S0045-7825(02)00354-7
  3. Babuska, I. and Oden, J.T. (2004), 'Verification and validation in computational engineering and science: Basic concepts', Comput. Meth. Appl. Mech. Eng., 193(36-38), 4057-4066 https://doi.org/10.1016/j.cma.2004.03.002
  4. Benjamin, J.R. and Cornell, C.A. (1970), Probability, Statistics, and Decision for Civil Engineers, McGraw Hill, New York, NY
  5. Bharrucha-Reid, A. (1959), 'On random operator equations in banach space', Bull. Acad. Polon. Sci., Ser. Sci. Math. Astr. Phys., 7, 561-564
  6. Calvi, A. (2005), 'Uncertainty-based loads analysis for spacecraft: Finite element model validation and dynamic responses', Comput. Struct., 83(14), 1103-1112 https://doi.org/10.1016/j.compstruc.2004.11.019
  7. Capiez-Lernout, E., Pellissetti, M., Pradlwarter, H., Schueller, G.I. and Soize, C. (2006), 'Data and model uncertainties in complex aerospace engineering systems', J Sound Vib., 295(3-5), 923-938 https://doi.org/10.1016/j.jsv.2006.01.056
  8. Esnault, P. and Klein, M. (1996), 'Factors of safety and reliability - Present guidelines & future aspects', In: Proc. of the Conf. on Spacecraft Structures, Materials & Mechanical Testing, SP-386, European Space Agency, Nordwijk, The Netherlands, 109-119
  9. Ewins, D.J. (2000), Modal Testing : Theory, Practice, and Application, 2nd Edition, Research Studies Press, Baldock
  10. Freudenthal, A.M. (1947), 'The safety of structures', Transaction of ASCE, 112, 125-180
  11. Ghanem, R. and Spanos, P. (1991), Stochastic Finite Elements: A Spectral Approach, Springer Verlag, Berlin
  12. Kleiber, M. and Hien, T. (1992), The Stochastic Finite Element Method: Basic Perturbation Technique and Computer Implementation, John Wiley & Sons Ltd
  13. Klein, M., Schueller, G.I., Deymarie, P., Macke, M., Courrian, P. and Capitanio, R.S. (1994), 'Probabilistic approach to structural factors of safety in aerospace', In: Proc. of the Int. Conf. on Spacecraft Structures and Mechanical Testing, Cepadues-Editions, Paris, France, 679-693
  14. Liu, W., Belytschko, T. and Mani, A. (1986), 'Probabilistic finite elements for nonlinear structural dynamics', Comput. Meth. Appl. Mech. Eng., 56, 61-81 https://doi.org/10.1016/0045-7825(86)90136-2
  15. Menezes, R. and Schueller, G.I. (1997), 'On structural reliability assessment considering mechanical model uncertainties', In: H. Natke, Y. Ben-Haim (Eds.), Uncertainty: Models and Measures, Vol. 99 of Mathematical Research Series, Akademie Verlag, 173-186
  16. Moreno, C. (1998), 'Integral - service module structure mathematical model description', Tech. Rep. INT- TNCAS-1002, 1st edition, CASA Space Division, Madrid, Spain
  17. Moller, B. and Beer, M. (2004), Fuzzy-Randomness - Uncertainty in Civil Engineering and Computational Mechanics, Springer-Verlag
  18. Notarnicola, M., Paron, A., Tizzani, L. and Evans, E. (1998), 'Integral - structural mathematical model description and dynamic analysis results', Tech. Rep. INT-TN-Al-0089, Issue 2, Alenia Aerospazio Space Division, Turin, Italy
  19. Oden, J.T., Belytschko, T., Babuska, I. and Hughes, T.J.R. (2003), 'Research directions in computational mechanics', Comput. Meth. Appl. Mech. Eng, 192(7-8), 913-922 https://doi.org/10.1016/S0045-7825(02)00616-3
  20. Oxfort, M. (1997), 'Integral-plm payload module structure fern description', Tech. Rep. INT-RP-OCW-0002, 2nd edition, Oerlikon-Contraves BU Space, Zurich-Seebach, Switzerland
  21. Pellissetti, M.F. and Schueller, G.I. (2006), 'On general purpose software in structural reliability', Structural Safety, 28(1-2), 3-16 https://doi.org/10.1016/j.strusafe.2005.03.004
  22. Pellissetti, M.F, Pradlwarter, H.J. and Schueller, G.I. (2006a), 'Relative importance of uncertain structural parameters, Part II: Applications', Computational Mechanics, published online, DOI 10.1007/s00466-006-0128-8
  23. Pellissetti, M.F., Schueller, G.I., Pradlwarter, H.J., Calvi, A., Fransen, S. and Klein, M. (2006b), 'Reliability analysis of spacecraft structures under static and dynamic loading', Comput. Struct., 84(21), 1313-1325 https://doi.org/10.1016/j.compstruc.2006.03.009
  24. Pradlwarter, H.J. (2006), 'Relative importance of uncertain structural parameters, Part I: Algorithm', Computational Mechanics, published online, DOI 10.1007/s00466-006-0127-9
  25. Pradlwarter, H.J., Pellissetti, M.F. and Schueller, G.I. (2005a), 'Sensitivity and uncertainty in complex FEmodels', In: G Augusti, G. I. Schueller, M. Ciampoli (Eds.), Proc. of the 9th Int. Conf on Structural Safety and Reliability (ICOSSAR '05), Millpress, Rotterdam, CD-ROM, Rome, Italy
  26. Pradlwarter, H.J., Pellissetti, M.F., Schenk, C.A., Schueller, G.I., Kreis, A., Fransen, S., Calvi, A. and Klein, M. (2005b), 'Realistic and efficient reliability estimation for aerospace structures', Comput. Meth. Appl. Mech. Eng, 194, 1597-1617 https://doi.org/10.1016/j.cma.2004.05.029
  27. Schueller, G.I. and Pradlwarter, H.J. (2006), 'Benchmark study on reliability estimation in higher dimensions of structural systems - An overview', Structural Safety, in press
  28. Schueller, G.I., Calvi, A., Pradlwarter, H.J., Fransen, S., Pellissetti, M.F., Klein, M. and Kreis, A. (2006), 'Uncertainty analysis of large structural systems', Comput. Meth. Appl. Mech. Eng, under review
  29. Schueller, G.I., Pradlwarter, H.J. and Koutsourelakis, P. (2004), 'A critical appraisal of reliability estimation procedures for high dimensions', Probabilistic Engineering Mechanics, 19(4), 463-474 https://doi.org/10.1016/j.probengmech.2004.05.004
  30. Schueller, G.I., Pradlwarter, H.J. and Koutsourelakis, P.S. (2003), 'A comparative study of reliability estimation procedures for high dimensions using FE analysis', In: G. Turkiyyah (Ed.), Electronic Proc. of the 16th ASCE Engineering Mechanics Conf., University of Washington, Seattle, USA
  31. Schueller, G.I., Pradlwarter, H.J., Beck, J., Au, S., Katafygiotis, L. and Ghanem, R. (2005), 'Benchmark study on reliability estimation in higher dimensions of structural systems - An overview', In: C. Soize, G.I. Schueller (Eds.), Structural Dynamics EURODYN 2005 - Proc. of the 6th Int. Conf. on Structural Dynamics, Millpress, Rotterdam, Paris, France, 717-722
  32. Simonian, S. (1987), 'Survey of spacecraft damping measurements: Applications to electrooptic jitter problems', In: The Role of Damping in Vibration and Noise Control, Vol. DE-Vol. 5 of ASME Publication, 287-292
  33. Soize, C. (2000), 'A nonparametric model of random uncertainties for reduced matrix models in structural dynamics', Probabilistic Engineering Mechanics, 15, 277-294 https://doi.org/10.1016/S0266-8920(99)00028-4
  34. Soize, C. (2001), 'Maximum entropy approach for modeling random uncertainties in transient elastodynamics', Journal of the Acoustical Society of America, 109, 1979-1996 https://doi.org/10.1121/1.1360716
  35. Soize, C. (2005), 'Random matrix theory for modeling uncertainties in computational mechanics', Comput. Meth. Appl. Mech. Eng., 194, 1333-1366 https://doi.org/10.1016/j.cma.2004.06.038
  36. Szekely, G.S., Teichert, W.H., Brenner, C.E., Pradlwarter, H.J., Klein, M. and Schueller, G.I. (1998), 'Practical procedures for reliability estimation of spacecraft structures and their components', J. AIAA, 36(8), 1509-1515 https://doi.org/10.2514/2.545
  37. Yamazaki, F., Shinozuka, M. and Dasgupta, G. (1988), 'Neumann expansion for stochastic finite element analysis', J. Eng. Mech., 114(8), 1335-1354 https://doi.org/10.1061/(ASCE)0733-9399(1988)114:8(1335)

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