Exact response probability density functions of some uncertain structural systems

• Autorzy: Falsone, G. , Laudani, R.
• Konferencja: Solid Mechanics Conference (SolMech 2018) (41 ; 27–31.08. 2018 ; Warsaw, Poland)
• Języki publikacji: EN

Abstrakty

EN

This paper has the goal of defining a class of uncertain structural systems for which it is possible to consider an approach able to give the exact response in terms of the probability density function (PDF). The uncertain structures have been identified in the discretized statically determined ones and the approach has been identified in the coupling of the approximated principal deformation modes method (APDM) and of the probability transformation method (PTM). The first one gives the explicit relationships between the response variables and the uncertainty ones, that are exact when the structures are statically determined. The second method allows to determine the explicit relationship between the PDFs of the response and of the uncertainty variables. The results of some applications have confirmed the goodness of these choices and that the proposed approach gives always exact results for both correlated and uncorrelated uncertainty random variables.

Słowa kluczowe

EN

uncertain systems; exact response; probability density function; principal deformation modes; probability transformation method

• Czasopismo: Archives of Mechanics
• Rocznik: 2019
• Tom: Vol. 71, nr 4-5
• Strony: 315--336
• Opis fizyczny: Bibliogr. 30 poz.

Twórcy

autor

Falsone, G.

• Dipartimento di Ingegneria, Università degli studi di Messina, C. da Di Dio, 98166 Messina

autor

Laudani, R.

• Dipartimento di Ingegneria, Università degli studi di Messina, C. da Di Dio, 98166 Messina, Italy,

Bibliografia

• 1. K.L. Liu, A. Mani, T. Belytschko, Finite element methods in probabilistic mechanics, Probability Engineering Mechanics, 2, 4, 201–213, 1987.
• 2. G.I. Schueller, C.G. Bucher, U. Bourgund, W. Ouyporpraset, On efficient computational schemes to calculate structural failure probabilities, [in:] Stochastic Structural Mechanics, Y.K. Lin, G.I. Schueller [eds.], Springer, Berlin, 1987.
• 3. R. Ghanem, P. Spanos, Stochastic Finite Elements: A Spectral Approach, Springer, New York, 1991.
• 4. H.G. Matthies, C.E. Brenner, C.G. Bucher, C.G. Soares, Uncertainties in probabilistic numerical analysis of structures and solids – stochastic finite elements, Structural Safety, 19, 3, 283–336, 1997.
• 5. B. Sudret, A. DerKiureghian, Stochastic finite element methods and reliability: a state-of-the-art report, Technical Report UCB/SEMM-2000/08, Department of Civil and Environmental Engineering, University of California, Berkeley, 2000.
• 6. G.I. Schueller, Computational stochastic mechanics – recent advances, Computers & Structures, 79, 2225–2234, 2001.
• 7. L.D. Lutes, S. Sarkani, Random Vibration Analysis of Structural and Mechanical System, Burlingthon, 2004.
• 8. G.I. Schueller, H.J. Pradlwarter, Uncertain linear systems in dynamics: retrospective and recent developments by stochastic approaches, Engineering Structures, 31, 11, 2507–2517, 2009.
• 9. G. Falsone, An extension of the Kazakov relationship for non-Gaussian random variables and its use in the non-linear stochastic dynamics, Probabilistic Engineering Mechanics, 20, 1, 45–56.
• 10. M. Papadrakakis, V. Papadopoulos, Robust and efficient methods for stochastic finite element analysis using Monte Carlo simulation, Computer Methods in Applied Mechanics and Engineering, 134, 3–4, 325–340, 1996.
• 11. J.E. Hurtado, A.H. Barbat, Monte Carlo techniques in computational stochastic mechanics, Archives of Computational Methods in Engineering, 5, 1, 3–29, 1998.
• 12. M. Kleiber, T.D. Hien, The Stochastic Finite Element Method, John Wiley, Chichester, 1992.
• 13. M. Shinozuka, F. Yamazaki, Stochastic finite element analysis: an introduction, [in:] Stochastic Structural Dynamics: Progress in Theory and Applications, S.T. Ariaratnam, G.I. Schueller, I. Elishakoff [eds.], Elsevier Applied Science, London, 1998.
• 14. I. Elishakoff, Y.J. Ren, M. Shinozuka, Improved finite-element method for stochastic problems, Chaos Solitons & Fractals, 55, 5, 833–846, 1998.
• 15. M. Kaminski, Generalized perturbation-based stochastic finite element method in elastostatics, Computer & Structures, 85, 586–594, 2007.
• 16. M. Kaminski, On iterative scheme in determination of the probabilistic moments of the structural response in the stochastic perturbation-based finite element method, International Journal for Numerical Methods in Engineering, 104, 11, 1038–1060, 2015.
• 17. R.G. Ghanem, R.M. Kruger, Numerical solution of spectral stochastic finite element systems, Computer Methods in Applied Mechanics and Engineering, 129, 289–303, 1996.
• 18. M.F. Pellissetti, R.G. Ghanem, Iterative solution of systems of linear equations arising in the context of stochastic finite elements, Advanced Engineering Software, 31, 607–616, 2000.
• 19. R.V. Field, M. Grigoriu, On the accuracy of the polynomial chaos approximation, Probabilistic Engineering Mechanics, 19, 65–80, 2004.
• 20. A. Doostan, R.G. Ghanem, J. Red-Horse, Stochastic model reduction for chaos representations, Computer Methods in Applied Mechanics and Engineering, 196, 3951–3966, 2007.
• 21. S.K. Sachdeva, P.B. Nair, A.J. Keane, Comparative study of projection schemes for stochastic finite element analysis, Computer Methods in Applied Mechanics and Engineering, 195, 19–22, 2371–2392, 2006.
• 22. S. Adhikari, C.S. Manohar, Dynamic analysis of framed structures with statistical uncertainties, International Journal for Numerical Methods in Engineering, 44, 8, 1157–1178, 1999.
• 23. F. Yamazaki, M. Shinozuka, G. Dasgupta, Neumann expansion for stochastic finite element analysis, Journal of Engineering Mechanics, 114, 8, 1335–1354, 1988.
• 24. N. Metropolis, S. Ulam, The Monte Carlo method, Journal of American Statistical Association, 44, 335–341, 1949.
• 25. H. Kahn, Use of different Monte Carlo sampling techniques, [in:] Symposium on Monte Carlo methods, M.A. Mayer [ed.], Wiley, New York, pp. 146–190, 1956.
• 26. G. Falsone, N. Impollonia, A new approach for the stochastic analysis of finite element modelled structures with uncertain parameters, Computer Methods in Applied Mechanics and Engineering, 191, 44, 5067–5085, 2002.
• 27. G. Falsone, N. Impollonia, About the accuracy of a novel response surface method for the analysis of finite element modelled uncertain structures, Probabilistic Engineering Mechanics, 19, 1, 53–63, 2004.
• 28. G. Falsone, D. Settineri, Explicit solutions for the response probability density function of linear systems subjected to random static loads, Probabilistic Engineering Mechanics, 33, 86–94, 2013.
• 29. G. Falsone, D. Settineri, Explicit solutions for the response probability density function of nonlinear transformations of static random inputs, Probabilistic Engineering Mechanics, 33, 79–85, 2013.
• 30. A. Papoulis, S.U. Pillai, Probability, Random Variables and Stochastic Processes, 4th ed. McGraw-Hill, Boston, 2002.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).

Identyfikatory

DOI

10.24423/aom.3109