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References

  1. Binder, K. and Heermann, D. (1997). Monte Carlo Simulation in Statistical Physics, Springer Verlag, Berlin/Heidelberg.10.1007/978-3-662-03336-4
  2. Bjorck, A. (1996). Numerical Methods for Least Squares Problems, SIAM, Philadelphia, PA.10.1137/1.9781611971484
  3. Brandt, S. (1999). Data Analysis Statistical and Computational Methods for Scientists and Engineers, Springer-Verlag, New York, NY.
  4. Burczyński, T. (1995). Boundary element method in stochastic shape design sensitivity analysis and identification of uncertain elastic solids, Engineering Analysis with Boundary Elements15(2): 151–160.10.1016/0955-7997(95)00013-E
  5. Chakraverty, S. (2014). Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems, IGI Global, Hershey.10.4018/978-1-4666-4991-0
  6. Falsone, G. (2005). An extension of the Kazakov relationship for non-Gaussian random variables and its use in the non-linear stochastic dynamics, Probabilistic Engineering Mechanics20(1): 45–56.10.1016/j.probengmech.2004.06.001
  7. Feller, W. (1965). An Introduction to Probability Theory and Its Applications, Wiley, New York, NY.
  8. Grigoriu, M. (2000). Stochastic mechanics, International Journal of Solids and Structures37(1–2): 228–248.10.1016/S0020-7683(99)00088-8
  9. Hurtado, J. and Barbat, A. (1998). Monte-Carlo techniques in computational stochastic mechanics, Archives of Computer Methods in Engineering37(1): 3–30.10.1007/BF02736747
  10. Kamiński, M. (2005). Computational Mechanics of Composite Material, Springer-Verlag, London/New York, NY.
  11. Kamiński, M. (2013). The Stochastic Perturbation Method for Computational Mechanics, Wiley, Chichester.10.1002/9781118481844
  12. Kleiber, M. and Hien, T. (1992). The Stochastic Finite Element Method, Wiley, Chichester.
  13. Kwiatkowska, M., Norman, G., Sproston, J. and Wang, F. (2007). Symbolic model checking for probabilistic timed automata, Information and Computation205(7): 1027–1077.10.1016/j.ic.2007.01.004
  14. Kwiatkowska, M., Parker, D., Zhang, Y. and Mehmood, R. (2004). Dual-processor parallelisation of symbolic probabilistic model checking, 12th International Symposium Modeling, Analysis and simulation of Computer and Telecommunication Systems MASCOTS’04, Volendaam, The Netherlands, pp. 123–130.
  15. López, N., Nunez, M. and Rodriguez, I. (2006). Specification, testing and implementation relations for symbolic-probabilistic system, Theoretical Computer Science353(1–3): 228–248.10.1016/j.tcs.2005.10.047
  16. Melchers, R. (2002). Structural Reliability Analysis and Prediction, Wiley, Chichester.
  17. Moller, B. and Beer, M. (2004). Fuzzy Randomness. Uncertainty in Civil Engineering and Computational Mechanics, Springer-Verlag, Berlin/Heidelberg.10.1007/978-3-662-07358-2
  18. Nayfeh, A.H. (2000). Perturbation Method, Wiley-VCH Verlag GmbH, Weinheim.
  19. Peng, X., Geng, L., Liyan, W., Liu, G. and Lam, K. (1998). A stochastic finite element method for fatigue reliability analysis of gear teeth subjected to bending, Computational Mechanics21(3): 253–261.10.1007/s004660050300
  20. Sakata, S., Ashida, F., Kojima, T. and Zako, M. (2008). Three-dimensional stochastic analysis using a perturbation-based homogenization method for elastic properties of composite material considering microscopic uncertainty, International Journal of Solids and Structures45(3–4): 894–907.10.1016/j.ijsolstr.2007.09.008
  21. Schueller, G. (2007). On the treatment of uncertainties in structural mechanics and analysis, Computers and Structures85(5–6): 235–243.10.1016/j.compstruc.2006.10.009
  22. Shachter, R.D., D’Ambrosio, B. and Del Favero, B. (1990). Symbolic probabilistic inference in belief networks, Proceedings of the 8th National Conference on Artificial Intelligence AAAI-90, Boston, MA, USA, pp. 126–131.
  23. Shannon, C. (1948). A mathematical theory of communication, The Bell System Technical Journal27(4): 623–656.10.1002/j.1538-7305.1948.tb00917.x
  24. Sobczyk, K. and Spencer, B. (1992). Random Fatigue: From Data to Theory, Academic Press, Boston, MA.10.1016/B978-0-12-654225-7.50004-7
  25. Spanos, P. and Ghanem, R. (1991). Stochastic Finite Elements. A Spectral Approach, Springer-Verlag, Berlin/Heidelberg.
  26. To, C. and Kiu, M. (1994). Random responses of discretized beams and plates by the stochastic central difference method with time co-ordinate transformation, Computers and Structures53(3): 727–738.10.1016/0045-7949(94)90114-7
  27. Van Noortwijk, J. and Frangopol, D. (2004). Two probabilistic life-cycle maintenance models for deteriorating civil infrastructures, Probabilistic Engineering Mechanics19(4): 345–359.10.1016/j.probengmech.2004.03.002
  28. Wiggins, J. (1987). Option values under stochastic volatility. Theory and empirical evidence, Journal of Financial Economics19(2): 351–372.
  29. Zienkiewicz, O. and Taylor, R. (2005). Finite Element Method for Solid and Structural Mechanics, Elsevier, Amsterdam.
DOI: https://doi.org/10.1515/amcs-2015-0069 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 961 - 973
Submitted on: Oct 17, 2013
Published on: Dec 30, 2015
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2015 Marcin Kamiński, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.