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Archive of Applied Mechanics

, Volume 89, Issue 4, pp 699–711 | Cite as

Hybrid uncertain analysis for random convex response of structures with a mixture of random and convex properties

  • Yongwei Han
  • Zhaopu Guo
  • Zhongmin DengEmail author
Original
  • 92 Downloads

Abstract

This paper presents a new numerical algorithm named hybrid Neumann Lagrange method for static analysis of structural systems with a mixture of random and convex variables. The random variables are used to treat the uncertain parameters with sufficient statistical information, whereas the convex variables are used to describe the uncertain parameters with limited information. The expressions for expectation and variance of random convex structural displacements are developed based on the Neumann series theory. Then the first-order Taylor series and the Lagrange multiplier method are employed to determine the upper and lower bounds of these probabilistic characters of the structural responses. By comparing with the results of Monte Carlo simulation, numerical examples are given to verify the effectiveness of the proposed method.

Keywords

Random convex responses Random variables Convex variables Neumann series Lagrange multiplier method 

Notes

Acknowledgements

This research was supported by the National Natural Science Foundation of China (11772018).

References

  1. 1.
    Moens, D., Vandepitte, D.: A survey of non-probabilistic uncertainty treatment in finite element analysis. Comput. Methods Appl. Eng. 194(12), 1527–1555 (2005)CrossRefzbMATHGoogle Scholar
  2. 2.
    Feng, Y.T., Li, C.F., Owen, D.R.J.: A direct Monte Carlo solution of linear stochastic algebraic system of equations. Finite Elem. Anal. Des. 46(6), 462–473 (2010)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Kamiński, M., Lauke, B.: Uncertainty in effective elastic properties of particle filled polymers by the Monte Carlo simulation. Compos. Struct. 123, 374–382 (2015)CrossRefGoogle Scholar
  4. 4.
    Jablonka, A.: Stochastic sensitivity analysis for structural dynamics systems via the second-order perturbation. Arch. Appl. Mech. 86, 1913–1926 (2016)CrossRefGoogle Scholar
  5. 5.
    Füssl, J., Kandler, G., Eberhardsteiner, J.: Application of stochastic finite element approaches to wood-based products. Arch. Appl. Mech. 86, 89–110 (2016)CrossRefGoogle Scholar
  6. 6.
    Ngah, M.F., Young, A.: Application of the spectral stochastic finite element method for performance prediction of composite structures. Compos. Struct. 78(3), 447–456 (2007)CrossRefGoogle Scholar
  7. 7.
    Zakian, P., Khaji, N.: A novel stochastic-spectral finite element method for analysis of elastodynamic problems in the time domain. Meccanica 51(4), 893–920 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Gao, W., Zhang, N., Ji, J.C.: A new method for random vibration analysis of stochastic truss structures. Finite Elem. Anal. Des. 45(3), 190–199 (2009)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Deng, Z.M., Guo, Z.P., Zhang, X.J.: Interval model updating using perturbation method and Radial Basis Function neural networks. Mech. Syst. Signal Process. 84, 699–716 (2017)CrossRefGoogle Scholar
  10. 10.
    Degrauwe, D., Lombaert, G., Roeck, G.D.: Improving interval analysis in finite element calculations by means of affine arithmetic. Comput. Struct. 88(3–4), 247–254 (2010)CrossRefGoogle Scholar
  11. 11.
    Moore, R.E.: Methods and Applications of Interval Analysis. Prentice-Hall, London (1979)CrossRefzbMATHGoogle Scholar
  12. 12.
    Rao, S.S., Berke, L.: Analysis of uncertain structural systems using interval analysis. AIAA J. 35, 727–735 (1997)CrossRefzbMATHGoogle Scholar
  13. 13.
    Qiu, Z.P., Chen, S.H., Song, D.: The displacement bound estimation for structures with an interval description of uncertain parameters. Commun. Numer. Methods Eng. 12, 1–11 (1997)CrossRefzbMATHGoogle Scholar
  14. 14.
    Jiang, C., Zhang, Q.F., Han, X., Qian, Y.H.: A non-probabilistic structural reliability analysis method based on a multidimensional parallelepiped convex model. Acta Mech. 225(2), 383–395 (2014)CrossRefGoogle Scholar
  15. 15.
    Ben-Haim, Y., Elishakoff, I.: Convex Models of Uncertainties in Applied Mechanics. Elsevier, Amsterdam (1990)zbMATHGoogle Scholar
  16. 16.
    Ben-Haim, Y.: Convex models of uncertainty in radial pulse buckling of shells. J. Appl. Mech. 60(3), 683–688 (1993)CrossRefzbMATHGoogle Scholar
  17. 17.
    Elishakoff, I., Elisseeff, P.: Non-probabilistic convex-theoretic modeling of scatter in material properties. AIAA J. 32, 843–849 (1994)CrossRefzbMATHGoogle Scholar
  18. 18.
    Xia, B.Z., Yu, D.J.: Response analysis of acoustic field with convex parameters. J. Vib. Acoust. 136(4), 041017 (2014)CrossRefGoogle Scholar
  19. 19.
    Deng, Z.M., Guo, Z.P., Zhang, X.J.: Non-probabilistic set-theoretic models for transient heat conduction of thermal protection systems with uncertain parameters. Appl. Therm. Eng. 95, 10–17 (2016)CrossRefGoogle Scholar
  20. 20.
    Oberkampf, W.L., Helton, J.C., Joslyn, C.A., et al.: Challenge problems: uncertainty in system response given uncertain parameters. Reliab. Eng. Syst. Saf. 85(1–3), 11–19 (2005)Google Scholar
  21. 21.
    Gao, W., Song, C.M., Tin-Loi, F.: Probabilistic interval analysis for structures with uncertainty. Struct. Saf. 32(3), 191–199 (2010)CrossRefGoogle Scholar
  22. 22.
    Gao, W., Wu, D., Song, C.M., Tin-Loi, F., Li, X.J.: Hybrid probabilistic interval analysis of bar structures with uncertainty using a mixed perturbation Monte-Carlo method. Finite Elem. Anal. Des. 47(7), 643–652 (2011)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Xia, B.Z., Yu, D.J., Liu, J.: Hybrid uncertain analysis for structural-acoustic problem with random and interval parameters. J. Sound Vib. 332(11), 2701–2720 (2013)CrossRefGoogle Scholar
  24. 24.
    Wang, C., Qiu, Z.P.: Hybrid uncertain analysis for steady-state heat conduction with random and interval parameters. Int. J. Heat Mass Transf. 80, 319–328 (2015)CrossRefGoogle Scholar
  25. 25.
    Penmetsa, R.C., Grandhi, R.V.: Efficient estimation of structural reliability for problems with uncertain intervals. Comput. Struct. 80(12), 1103–1112 (2002)CrossRefGoogle Scholar
  26. 26.
    Adduri, P.R., Penmetsa, R.C.: Systems reliability analysis for mixed uncertain variables. Struct. Saf. 227(7), 1441–1453 (2009)Google Scholar
  27. 27.
    Karanki, D.R., Kushwaha, H.S., Verma, K.A., Ajit, S.: Uncertainty analysis based on probability bounds (p-box) approach in probabilistic safety assessment. Risk Anal. 29(5), 662–675 (2009)CrossRefGoogle Scholar
  28. 28.
    Luo, Y., Kang, Z., Li, A.: Structural reliability assessment based on probability and convex set mixed model. Comput. Struct. 87(21–22), 1408–1415 (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of AstronauticsBeihang UniversityBeijingPeople’s Republic of China
  2. 2.Beijing Power Machinery InstituteBeijingPeople’s Republic of China

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