Engineering Applications of Stochastic Mechanics - Achievements and Prospects

  • G. I. Schuëller
Conference paper
Part of the Solid Mechanics and its Applications book series (SMIA, volume 47)


Various procedures of stochastic structural mechanics are discussed in view of their potential to be utilized for engineering applications. These procedures encompass direct and advanced Monte-Carlo simulation, response surface methodology, statistical equivalent linearization and hybrid methods. Subsequently, representative classes of areas of applications of these procedures are discussed i.e. stochastic structural analysis (systems reliability), stochastic fracture and fatigue analysis, stochastic Finite Elements and stochastic structural dynamics. Then the respective states of application of these methods in three selected fields of engineering i.e. aerospace, nuclear and offshore engineering are reviewed.

Finally some conclusions are drawn, particularly with respect to future prospects of stochastic mechanics in engineering practice.


Response Surface Methodology Monte Carlo Simulation Failure Probability Response Surface Methodology Stochastic Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    MAYER M.:“Die Sicherheit der Bauwerke”, J.Springer Verlag, Berlin, 1926 (in German).zbMATHGoogle Scholar
  2. [2]
    FREUDENTHAL A.M.:“Introductory Remarks”, in Structural Safety and Reliability, A.M. Freudenthal (ed.), Pergamon Press, Oxford, 1972, pp 5–9.Google Scholar
  3. [3]
    YANG J.N.:“Application of Reliability Methods to Fatigue, Quality Assurance and Maintenance” in Structural Safety and Reliability, G.I. Schuëller, M. Shinozuka and J.T.P. Yao (eds.), Balkema, Rotterdam, 1994, pp. 3 – 20.Google Scholar
  4. [4]
    EUROCODE 1: “Basis of Design and Actions on Structures”, 6th Draft, ENV 1991 – 1, CEN/TC250/N105, March 1993.Google Scholar
  5. [5]
    RUBINSTEIN R.Y.: “Simulation and the Monte Carlo Method”, J. Wiley, New York, 1981.zbMATHCrossRefGoogle Scholar
  6. [6]
    KAHN H.: “Use of Different Monte Carlo Sampling Techniques”, Symp. on Monte Carlo Methods, Ed. H.A. Mayer, Wiley, New York, USA, 1956, pp 146–190.Google Scholar
  7. [7]
    SCHUËLLER G.I., STIX R.: “A Critical Appraisal of Methods to Determine Failure Probabilities”, J. Structural Safety, 4, (1987), pp 293–309.CrossRefGoogle Scholar
  8. [8]
    PRADLWARTER H.J., SCHUËLLER G.I.: “On Advanced MCS Procedures in Stochastic Structural Dynamics”, to appear: Journal Nonlinear Mechanics, 1996Google Scholar
  9. [9]
    PRADLWARTER H.J., SCHUËLLER G.I., JEHLICKA P., STEINHILBER H.: “Structural Failure Probabilities of the HDR-Containment”, J. Nuclear Engineering and Design, 128, 1991, pp 237–246.CrossRefGoogle Scholar
  10. [10]
    SCHUËLLER G.I. and BUCHER C.G.: “Computational Stochastic Structural Analysis - A Contribution to the Software Development for the Reliability Assessment of Structures under Dynamic Loading”, Probabilistic Engineering Mechanics, Vol. 6, Nos. 3/4, 1991, pp 134–138.CrossRefGoogle Scholar
  11. [11]
    IWAN W.D. (1973): “A Generalization of the Concept of Equivalent Linearization” Int. J. Nonlinear Mechanics, 8, pp 279–298.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    PRADLWARTER H.J., SCHUËLLER G.I. and CHEN X.-W.: “Consideration of Non-Gaussian Response Properties by Use of Stochastic Equivalent Linearization”, Proc., Third International Conference on Recent Advances in Structural Dynamics, 18 –22 July 1988, Southampton, M.Petyt, H.F. Wolfe and C. Mei (eds.), Vol. II, pp. 737–752.Google Scholar
  13. [13]
    WEN Y.K. (1989): “Methods of Random Vibrations for Inelastic Structures”, Appl. Mech. Review, 42(2), pp 39–52.CrossRefGoogle Scholar
  14. [14]
    BENAROYA H. and REHAK M (1988): “Finite Element Methods in Probabilistic Structural Analysis: A Selective Review”,Appl. Mech. Rev., 41(5), pp 201 – 213CrossRefGoogle Scholar
  15. [15]
    PRADLWARTER H.J., SCHUËLLER G.I.: “A Practical Approach to Predict the Stochastic Response of Many-DOF-Systems Modelled by Finite Elements”, in Nonlinear Stochastic Mechanics, N. Bellomo and F. Casciati (Eds.), Springer Verlag, Berlin, Heidelberg, 1992, pp. 427–437Google Scholar
  16. [16]
    NAESS A: “Prediction of Extreme Response of Nonlinear Structures by Extended Stochastic Linearization”, Probabilistic Engineering Mechanics, 10 (1995) pp 153–160.CrossRefGoogle Scholar
  17. [17]
    SCHUËLLER G.I.: “Current Trends in Systems Reliability”, Proc., 4th Int. Conference on Structural Safety and Reliability, (ICOSSAR’85), Kobe, Japan, I. Konishi, A.H.-S. Ang and M. Shinozuka (Ed.), IASSAR, New York, 1985, Volume I, pp. 139 – 148.Google Scholar
  18. [18]
    MUROTSU Y., OKADA H., GRIMMELT M.J., YONEZAWA M., TAGUCHI K.: “Automatic Generation of Stochastically Dominant Failure Modes of Frame Structures” J. Structural Safety, Vol. 2, 1984, pp 17 -25.CrossRefGoogle Scholar
  19. [19]
    YAO J.T.P., KOZIN F., WEN Y.-K., YANG J.-N., SCHUËLLER G.I. and DITLEVSEN O.: “Stochastic Fatigue, Fracture and Damage Analysis” J. Structural Safety, Vol. 3+4, 1986, pp. 231–267.CrossRefGoogle Scholar
  20. [20]
    SOBCZYK K. and SPENCER B.F.: “Random Fatigue: From Data to Theory” Academic Press, Boston, 1992.zbMATHGoogle Scholar
  21. [21]
    BOGDANOFF J.L. and KOZIN F.: “Probabilistic Models of Cumulative Damage”, John Wiley & Sons, New York, 1985.Google Scholar
  22. [22]
    OSWALD G.F., SCHUËLLER G.I.: “Reliability of Deteriorating Structures”, Int. Journ. Engineering Fracture Mechanics, Vol. 20, No. 3, pp. 479 - 488, 1984.CrossRefGoogle Scholar
  23. [23]
    MARSHALL W. (Ed.): “An Assessment of the integrity of PWR pressure vessels” United Kingdom Atomic Energy Authority UKAEA (Oct 1, 1976).Google Scholar
  24. [24]
    SCHUËLLER G.I., TSURUI A., NIENSTEDT J.: “On the Failure Probability of Pipings”, J. Nuclear Engineering and Design, 128, 1991, pp 201–206.CrossRefGoogle Scholar
  25. [25]
    DEODATIS G.: “Non-periodic Inspection of Fatigue- sensitive Structures by Bayesian Approach”, in Struct. Safety and Reliability, (Ed.): Schuëller G.I., Shinozuka M. and Yao J.T.P., Balkema, Rotterdam, 1994, pp 997–1004.Google Scholar
  26. [26]
    ROCHA M.M., SCHUËLLER G.I.: “Markov Chain Modelling of NDE-Techniques for Crack Inspection in Structural Components”, in Struct. Safety and Reliability, (Ed.): Schuëller G.I., Shinozuka M. and Yao J.T.P., Balkema, Rotterdam, 1994, pp 1117 – 1124.Google Scholar
  27. [27]
    BRENNER C.E.: “Ein Beitrag zur Zuverlässigkeitsanalyse von Strukturen unter Berücksichtigung von Systemunsicherheiten mit Hilfe der Methode der Stochastischen Finiten Elemente” (in German) Dissertation, University of Innsbruck, Innsbruck, Austria, 1995.Google Scholar
  28. [28]
    PRADLWARTER H.J., SCHUËLLER G.L: “Equivalent Linearization - A Suitable Tool to Analyse MDOF-Systems”, Probabilistic Engineering Mechanics, 8, 1993, pp. 115 – 126.CrossRefGoogle Scholar
  29. [29]
    LIN Y.K.: “Probabilistic Theory of Structural Dynamics”, McGraw-Hill, New York, 1967.Google Scholar
  30. [30]
    LIN Y.K. and CAI G.Q.: “Probabilistic Structural Dynamics - Advanced Theory and Applications” McGraw Hill, New York, 1995.Google Scholar
  31. [31]
    SCHUËLLER G.I.(Ed.): “Structural Dynamics - Recent Advances”, Springer-Verlag, Berlin, Heidelberg, 1991.zbMATHGoogle Scholar
  32. [32]
    SOONG T.T. and GRIGORIU M.: “Random Vibration of Mechanical and Structural Systems”, Prentice Hall, Englewood Cliffs, N.J., USA, 1993.Google Scholar
  33. [33]
    DAVENPORT A.G.: “The Application of Statistical Concepts to the Wind Loading of Structures”, Proc. Inst. Civ. Engrs., Vol 19, 1961, pp. 449 – 471.CrossRefGoogle Scholar
  34. [34]
    SCHUËLLER G.I., BUCHER C.G.: “Non-Gaussian Response of Systems Under Dynamic Excitation”, in Stochastic Structural Dynamics - Progress in Theory and Applications, S.T. Ariaratnam et al. (Ed.)., Elsevier Appl. Science Publ., Barking, Essex, Engl., pp 219 – 239, 1988.Google Scholar
  35. [35]
    GRIGORIU M.: “Applied Non-Gaussian Processes”, Prentice Hall, Englewood Cliffs, N.J. USA, 1995.zbMATHGoogle Scholar
  36. [36]
    SCHUËLLER G.I., PRADLWARTER HJ., PANDEY M.D: “Method for reliability assessment of nonlinear systems under stochastic loading - a review”, Proc. EURODYN‘93, Vol. 2, T. Moan et al. (Eds.), A.A. Balkema Publ., Rotterdam, The Netherlands, 1993, pp. 751–760.Google Scholar
  37. [37]
    DE MOLLERAT T., VIDAL C.: “Evaluation of Design and Tests Safety Factors”, Final Report of ESTEC Contract No. 6370/85/NL/PB, Cannes, 1986.Google Scholar
  38. [38]
    VIDAL C. DE MOLLERAT T., KLEIN M.: “Evaluation of Test and Design Factors”, Proc. International Conference on Spacecraft Structures and Mechanical Testing, Noordwijk, The Netherlands, 19–21 October 1988, ESA SP-289, 1989.Google Scholar
  39. [39]
    KLEIN M., SCHUËLLER G.I., DEYMARIE P., MACKE M., COURRIAN P., CAPITANIO R.S.: “Probabilistic Approach to Structural Factors of Safety in Aerospace”, Proc. International Conference on Spacecraft Structures and Mechanical Testing, Paris, France, Cèpadués-Editions, 1994, pp 679–693.Google Scholar
  40. [40]
  41. [41]
    PRADLWARTER H.J., DIEZ R., KLEIN M., SCHUËLLER G.I.: “On Engineering Tools for Numerical Evaluation of Structural Scatter and Reliability”, Proc. International Conference on Spacecraft Structures and Mechanical Testing, Paris, France, Cèpadués-Editions, 1994, pp 695 – 708.Google Scholar
  42. [42]
    REACTOR SAFETY STUDY, WASH 1400, Washington D.C., US.NRC, 1975Google Scholar
  43. [43]
    SCHUËLLER G.I. and ANG A.H-S.: “Advances in Structural Reliability”, J. Nuclear Engineering and Design, 134, 1992, pp. 121–140.CrossRefGoogle Scholar
  44. [44]
    LUCIA A.C., ARMAN G. and JOVANOVIC A.: “Fatigue Crack Propagation: Probabilistic Models and Experimental Evidence, Vol. M, SMIRT 9, F.H. Wittmann (ed.), Balkema, Rotterdam 1987, pp 313 – 320.Google Scholar
  45. [45]
    MOAN T.: “Reliability and Risk Analysis for Design and Operations Planning of Offshore Structures”, in: Structural Safety and Reliability, (Ed.): Schuëller G.I., Shinozuka and Yao J.T.P., Balkema, Rotterdam 1994, Vol I, pp 21 – 43.Google Scholar
  46. [46]
    FREUDENTHAL A.M. and GAITHER W.S.: “Design Criteria for Fixed Offshore Structures” Prepr., Offshore Technology Conf., pp. 623 – 646, Houston, Texas, 1969.Google Scholar
  47. [47]
    MARSHALL P.W.: “Risk Evaluations for Offshore Structures”, J. Struct. Div., Proc. ASCE, Dez. 1969.Google Scholar
  48. [48]
    BEA R.G.: “Selection of Environmental Criteria for Offshore Platform Design”, Prepr. 5th Ann. Offshore Tech. Conf., Houston, 1973, Paper No. 1839, pp 186 – 193.Google Scholar
  49. [49]
    PAYER H.G., HUPPMANN H.H., JOCHUM C., MADSEN H.O., NITTINGER K., SHIBATA H., WILD W. and WINGENDER H.-J.: “Plenary Panel Discussion: How Safe is safe enough?”, in Structural Safety and Reliability, G.I. Schuëller, M. Shinozuka and J.T.P. Yao, (Eds.), Balkema, Rotterdam, 1994, pp 57 – 74.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • G. I. Schuëller
    • 1
  1. 1.Institute of Engineering MechanicsUniversity of InnsbruckInnsbruckAustria

Personalised recommendations