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Stochastic Structural Mechanics pp 84–109Cite as

The stochastic finite element method in structural reliability

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Part of the book series: Lecture Notes in Engineering ((LNENG,volume 31))

Abstract

First-order reliability and finite element methods are used to develop a methodology for reliability analysis of structures with stochastically varying properties and subjected to random loads. Two methods for discretization of random fields are examined and the influence of the correlation length of random property or load fields on the reliability of example structures are investigated. It is found that the correlation length of load fields has significant influence on the reliability against displacement or stress limit-states. The correlation length of property fields is significant for displacement limit states, but may not be significant for stress limit states. Examples studied include a fixed ended beam with stochastic rigidity and a composite plate with stochastic elasticity.

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References

  1. A.H-S. Ang and W.H. Tang, Probability Concepts in Engineering Planning and Design-Volume II: Decision, Risk, and Reliability, J. Wiley & Sons, New York, N.Y., 1984.

    Google Scholar 

  2. J. Astill, C. J. Nosseir, and M. Shinozuka, “Impact Loading on Structures with Random Properties,” Journal of Structural Mechanics, vol. 1, no. 1, pp. 63–77, 1972.

    Article  Google Scholar 

  3. G. B. Baecher and T. S. Ingra, “Stochastic FEM in Settlement Predictions,” Journal of the Geotechnical Engineering Division, vol. 107, no. GT4, pp. 449-463, April 1981.

    Google Scholar 

  4. B. Cambou, “Application of First Order Uncertainty Analysis in the Finite Element Method in Linear Elasticity,” in Proceedings, Second International Conference on Applications of Statistics and Probability in Soil and Structural Engineering, Lond England, 1971.

    Google Scholar 

  5. B. A. Dendrou and E. N. Houstis, “Uncertainty Finite Element Dynamic Analysis,” Report CSD-TR 271, Department of Civil Engineering, Purdue University, West Lafayette, Indiana, July 1978.

    Google Scholar 

  6. A. Der Kiureghian, “Finite Element Methods in Structural Safety Studies,” in Proceedings, ASCE Symposium on Structural Safety Studies, pp. 40–52, Denver, CO, April–May, 1985.

    Google Scholar 

  7. A. Der Kiureghian, “Finite Element Based Reliability Analysis of Frame Structures,” in Proceedings, Fourth International Conference on Structural Safety and Reliability, vol. I, pp. 395-404, Kobe, Japan, May 1985.

    Google Scholar 

  8. A. Der Kiureghian, “Multivariate Distribution Models for Structural Reliability,” in Transactions, International Conference on Structural Mechanics in Reactor Technology, Lausanne, Switzerland, August, 1987.

    Google Scholar 

  9. A. Der Kiureghian, H.-Z. Lin, and S.-J. Hwang, “Second Order Reliability Approximations,” Journal of Engineering Mechanics, to appear.

    Google Scholar 

  10. A. Der Kiureghian and P-L. Liu, “Structural Reliability Under Incomplete Probability Information,” Journal of Engineering Mechanics, vol. 112, no. 1, pp. 85–104, January 1986.

    Article  Google Scholar 

  11. A. Der Kiureghian and R. L. Taylor, “Numerical Methods in Structural Reliability,” in Proceedings, Fourth International Conference on Applications of Statistics and Probability in Soil and Structural Engineering, pp. 769-784, Florence, Italy, June 1983.

    Google Scholar 

  12. K. Handa and K. Anderson, “Application of Finite Element Methods in the Statistical Analysis of Structures,” in Proceedings, Third International Conference on Structural Safety and Reliability, pp. 409-417, Trondheim, Norway, June 1981.

    Google Scholar 

  13. T. Hisada and S. Nakagiri, “Stochastic Finite Element Method Developed for Structural Safety and Reliability,” in Proceedings, Third International Conference on Structural Safety and Reliability, pp. 395-408, Trondheim, Norway, June 1981.

    Google Scholar 

  14. T. Hisada and S. Nakagiri, “Role of the Stochastic Finite Element Method in Structural Safety and Reliability,” in Proceedings, Fourth International Conference on Structural Safety and Reliability, Kobe, Japan, May 1985.

    Google Scholar 

  15. T. Hisada, S. Nakagiri, and M. Mashimo, “A Note on Stochastic Finite Element Method (Part 10) — On Dimensional Invariance of Advanced First-Order Second-Moment Reliability Index in Analysis of Continuum,” Seisan-Kenkyu, vol. 37, no. 3, pp. 111-114, Institute of Industrial Science, University of Tokyo, Tokyo, Japan, 1985.

    Google Scholar 

  16. T. Hisada, S. Nakagiri, and T. Nagasaki, “Stochastic Finite Element Analysis of Uncertain Intrinsic Stresses Caused by Structural Misfits,” in Transactions, Seventh International Conference on Structural Mechanics in Reactor Technology, vol. M, pp. 199-206, Chicago, Illinois, August, 1983.

    Google Scholar 

  17. M. Hohenbichler and R. Rackwitz, “Non-Normal Dependent Vectors in Structural Safety,” Journal of the Engineering Mechanics Division, vol. 107, no. EM6, pp. 1227-1238, Dec. 1981.

    Google Scholar 

  18. T. Igusa and A. Der Kiureghian, “Response of Uncertain Systems to Stochastic Excitation,” Journal of Engineering Mechanics, to appear.

    Google Scholar 

  19. M. A. Lawrence, A Basis Random Variable Approach to Stochastic Structural Analysis, p. Thesis, submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Civil Engineering, University of Illinois, Urbana, Illinois, 1986.

    Google Scholar 

  20. P-L. Liu and A. Der Kiureghian, “Optimization Algorithms for Structural Reliability Analysis,” Report No. UCB/SESM-86/09, Department of Civil Engineering, Division of Structural Engineering and Structural Mechanics, University of California, Berkeley, Calif., July 1986.

    Google Scholar 

  21. W. K. Liu, T. Belytschko, and A. Mani, “Probabilistic Finite Elements for Nonlinear Structural Dynamics,” Computer Methods in Applied Mechanics and Engineering, no. 56, pp. 61-86, 1986.

    Google Scholar 

  22. H. O. Madsen, S. Krenk, and N. C. Lind, Methods of Structural Safety, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1986.

    Google Scholar 

  23. S. Nakagiri and T. Hisada, “A Note on Stochastic Finite Element Method (Part 6) — An Application in Problems of Uncertain Elastic Foundation,” Seisan-Kenkyu, vol. 35, no. 1, pp. 20–23, Institute of Industrial Science, University of Tokyo, Tokyo, Japan, January 1983.

    Google Scholar 

  24. M. Shinozuka and G. Dasgupta, “Stochastic Finite Element Methods in Dynamics,” in Proceedings, pp. 44–54, ASCE-EMD Specialty Conference on Dynamic Response of Structures, Los Angeles, March 1986.

    Google Scholar 

  25. M. Shinozuka and T. Nomoto, “Response Variability Due to Spatial Randomness,” Report No. CU-CEEM-MS-80-1, Department of Civil Engineering and Engineering Mechanics, Columbia University, August 1980.

    Google Scholar 

  26. E. Vanmarcke, Random Fields: Analysis and Synthesis, MIT Press, Cambridge, Mass., 1983.

    MATH  Google Scholar 

  27. E. Vanmarcke and M. Grigoriu, “Stochastic Finite Element Analysis of Simple Beams,” Journal of Engineering Mechanics, vol. 109, no. 5, pp. 1203–1214, October 1983.

    Article  Google Scholar 

  28. D. Veneziano, F. Casciati, and L. Faravelli, “Method of Seismic Fragility for Complicated Systems,” in Proceedings, Second CSNI Specialty Meeting on Probabilistic Methods in Seismic Risk Assessment for Nuclear Power Plants, Livermore, California, May 1983.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Civil Engineering, University of California, Berkeley, CA, 94720, USA

    Armen Der Kiureghian & Jyh-Bin Ke

Authors
  1. Armen Der Kiureghian
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  2. Jyh-Bin Ke
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Editor information

Editors and Affiliations

  1. College of Engineering, Center for Applied Stochastics Research, Florida Atlantic University, P. O. Box 3091, Boca Raton, FLA, 33431, USA

    Y. K. Lin (Schmidt Chair in Engineering) (Schmidt Chair in Engineering)

  2. Institute of Engineering Mechanics, University of Innsbruck, Technikerstraße 13, A-6020, Innsbruck, Austria

    G. I. Schuëller

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© 1987 Springer-Verlag Berlin Heidelberg

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Der Kiureghian, A., Ke, JB. (1987). The stochastic finite element method in structural reliability. In: Lin, Y.K., Schuëller, G.I., Spanos, P. (eds) Stochastic Structural Mechanics. Lecture Notes in Engineering, vol 31. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83254-3_5

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  • DOI: https://doi.org/10.1007/978-3-642-83254-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18463-8

  • Online ISBN: 978-3-642-83254-3

  • eBook Packages: Springer Book Archive

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