Skip to main content
SpringerLink
Log in

Monte Carlo techniques in computational stochastic mechanics

  • Published:
Archives of Computational Methods in Engineering Aims and scope Submit manuscript

Summary

A state of the art on simulation methods in stochastic structural analysis is presented. The purpose of the paper is to review some of the different methods available for analysing the effects of randomness of models and data in structural analysis. While most of these techniques can be grouped under the general name ofMonte Carlo methods, the several published algorithms are more suitable to some objectives of analysis than to others in each case. These objectives have been classified into the foolowing cathegories: (1), TheStatistical Description of the structural scattering, a primary analysis in which the uncertain parameters are treated as random variables; (2) The consideration of the spatial variability of the random parameters, that must then be modelled as Random Fields (Stochastic Finite Elements); (3) The advanced Monte Carlo methods for calculating the usually very low failure probabilities (Reliability Analysis), and, (4), a deterministic technique that depart from the random nature of the above methods, but which can be linked with them in some cases, known as theResponse Surface Method. All of these techniques are critically examined and discussed. The concluding remarks point out some research needs in the field from the authors' point of view.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Adomian, G. (1983):Stochastic Systems, Academic Press, New York.

    MATH  Google Scholar 

  • Ang, A. H. S., and Tang, W. H. (1984):Probability Concepts in Engineering Planning and Design, Vol II, John Wiley and Sons, New York.

    Google Scholar 

  • Ang, G. L., Ang, A. H. S. and Tang, W. H. (1991): Optimal Importance Sampling Density Estimator,Journal of Engineering Mechanics, ASCE, 118(6), 1146–1163.

    Article  Google Scholar 

  • Araujo, J. M. and Awruch, A. M. (1994): On Stochastic Finite Elements for Structural Analysis,Computers and Structures, 52(3), 461–469.

    Article  MATH  Google Scholar 

  • Arnbjerg-Nielsen, T., and Bjerager, P. (1988): Finite Element Reliability Method with Improved Efficiency by Sensitivity Analysis,Computational Probabilistic Methods, ASME, AMD-Vol. 93, edited by Liu, Belytschko, Lawrence and Cruce, 15–25.

  • Augusti, G., Baratta, A., and Casciatti, F. (1984):Probabilistic Methods in Structural Engineering, Chapman and Hall, London.

    MATH  Google Scholar 

  • Aumeier, S. E., Lee, J. C., Akeasu, A. Z. (1996): Probabilistic Techniques using Monte Carlo Sampling for Multi—component System Diagnostics,Proceedings of the International Conference on Mathematics and Computations, Reactor Physics and Environmental Analyses, 103–112. La Grange Park.

  • Ayyub, B. M., and Haldar, A. (1984): Practical Structural Reliability Techniques,Journal of Engineering Mechanics, ASCE, 110(8), 1707–1724.

    Google Scholar 

  • Ayyub, B. M., and Chia, C. Y. (1992): Generalized Conditional Expectation for Structural Reliability Assessment,Structural Safety, 11, 131–146.

    Article  Google Scholar 

  • Bazant, Z. P. and Liu, K. L. (1985): Random Creep and Shrinkage in Structures: Sampling,Journal of Structural Engineering, ASCE, 111(5), 1113–1134.

    Google Scholar 

  • Bharucha-Reid, A. T. (1959): On Random Operator Equations in Banach Space,Bull. Acad. Polon. Sci., Ser. Sci. Math. Astr. Phys., Vol. 7, 561–564.

    MATH  MathSciNet  Google Scholar 

  • Bjerager, P., and Krenk, S. (1987): Sensitivity Measures in Structural Reliability Analysis,Proc. of 1st IFIP Working Conference on Reliability and Optimization on Structural Systems, edited by P. Thoft-Christensen, Springer Verlag, 459–470.

  • Bjerager, P. (1988): Probability Integration by Directional Simulation,Journal of Engineering Mechanics, ASCE, 114(8), 1285–1302.

    Google Scholar 

  • Bjerager, P. (1991): Methods for Structural Reliability Computations, inReliability Problems: General Principles and Applications in Mechanics of Solids and Structures, edited by Casciatti, F. and Roberts, J. B., Springer-Verlag, New York.

    Google Scholar 

  • Box, G. E. P., and Draper, N. R. (1987):Empirical Model-Building and Response Surfaces, John Wiley and Sons, New York.

    MATH  Google Scholar 

  • Bratley, P., Fox, B. L., Schrage, L. E. (1987):A Guide to Simulation, Springer Verlag, New York.

    Google Scholar 

  • Breitung, K. (1984): Asymptotic Approximation for Multinormal Integrals,Journal of Engineering Mechanics, ASCE, 110(3), 357–366.

    Article  Google Scholar 

  • Brenner, Ch. E., and Bucher, Ch. (1995): A contribution to the SFE-based Reliability Assessment of Nonlinear Structures Under Dynamic Loading,Probabilistic Engineering Mechanics, 10, 265–273.

    Article  Google Scholar 

  • Bucher, C. G. (1988): Adaptive Sampling: An Iterative Fast Monte-Carlo Procedure,Structural Safety, 5(2), 119–126.

    Article  Google Scholar 

  • Bucher, C. G., Pradlwarter, H. J. and Schuëller, G. I. (1991): Computational Stochastic Structural Analysis (COSSAN)Structural Dynamics: Recent Advances (G. I. Schuëller, editor), Springer Verlag, Berlin.

    Google Scholar 

  • Bucher, C. G., Brenner, C. E. (1992): Stochastic Response of Uncertain Systems,Archive of applied Mechanics, 62(8), 507–516.

    MATH  Google Scholar 

  • Casciatti, F. and Faravelli, L. (1990)Fragility Analysis of Complex Structural Systems Research Studies Press Ltd., Taunton, England.

    Google Scholar 

  • Casciatti, F. (1991): Safety Index, Stochastic Finite Elements and Expert Systems inReliability Problems: General Principles and Applications in Mechanics of Solids and Structures, edited by Casciatti, F., and Roberts, J. B., Springer-Verlag, New York.

    Google Scholar 

  • Chang, T. P., Chang, H. C. (1994): Stochastic Dynamic Finite Element Analysis of a Non Uniform Beam,International Journal of Solids and Structures, 3195), 587–597.

    Article  Google Scholar 

  • Chinchalkar, S., Taylor, D. L. (1991): Parallel Stochastic Finite Element Analysis on Distributed Memory Multiprocessors, inHigh Performance Computing II, 345–356. North Holland, Amsterdam.

    Google Scholar 

  • Cruse, T. A., Wu, Y. T., Dias, S., and Rajagopal, K. R. (1988): Probabilistic Structural Analysis Methods and Applications,Computers and Structures, 30(1/2), 163–170.

    Article  MathSciNet  Google Scholar 

  • Der Kiureghian, A. (1985): Finite Element Based Reliability Analysis of Frame Structures,Structural Safety and Reliability, edited by Konishi, Ang and Shinozuka, ICOSSAR, Kobe, Japan, Vol. I, 395–404.

    Google Scholar 

  • Der Kiureghian, A., and Liu, P. L. (1986): Structural Reliability under Incomplete Probability Information,Journal of Engineering Mechanics, ASCE, 112(1), 85–104.

    Google Scholar 

  • Der Kiureghian, A., and Lin, H. Z., and Hwang, S. J. (1987): Second Order Reliability Approximations.Journal of Engineering Mechanics, ASCE, 113(8), 1208–1225.

    Google Scholar 

  • Der Kiureghian, A., and Ke, J. B. (1987): The Stochastic Finite Element Method in Structural Reliability.Probabilistic Engineering Mechanics, 3(2), 83–91.

    Article  Google Scholar 

  • Der Kiureghian, A. (1988): Measures of Structural Safety under Imperfect States of Knowledge,Journal of structural Engineering, ASCE.

  • Der Kiureghian, A. and Ke, J. B. (1988): The Stochastic Finite Element Method in Structural Reliability,Probabilistic Engineering Mechanics, 3(2), 83–91.

    Article  Google Scholar 

  • Der Kiureghian, A., and De Stefano, M. (1990): An Efficient Algorithm for Second-Order Reliability Analysis, Report No. UCB 90/20, Department of Civil Engineering, University of California at Berkeley, Berkeley, California.

    Google Scholar 

  • Ditlevsen, O., and Bjerager, P. (1986): Methods of Structural Systems Reliability,Structural Safety, 3, 195–229.

    Article  Google Scholar 

  • Ditlevsen, O., Bjerager, P., Olesen, R., and Hasofer, A. M. (1988): Directional Simulation in Gaussian Processes,Probabilistic Engineering Mechanics, 3(4), 207–217.

    Article  Google Scholar 

  • Dolinski, K. (1983): First-Order Second Moment Approximation in Reliability of Structural Systems: Critical Review and Alternative Approach.Structural Safety, 1, 211–231.

    Article  Google Scholar 

  • Enevoldsen, I., Faber, M. H., and Sorensen, J. D. (1994): Adaptive Response Surface Techniques in Reliability Estimation,Structural Safety and Reliability, ed by Schuëller, Shinozuka and Yao, Balkema, Rotterdam, 1257–1264.

    Google Scholar 

  • Enevoldsen, I., Faber, M. H., and Sorensen, J. D. (1994): Adaptive Response surface Techniques in Reliability Estimation.Structural Safety and Reliability. II, 1257–1265. Balkema, Rotterdam.

    Google Scholar 

  • Faber, M., and Rackwitz, R. (1988): Excursion Probabilities of Non-Homogeneous Gaussian Scalar Fields based on Maxima Considerations,Proc. of 2nd IFIP Working Conference on Reliability and Optimization on Structural Systems, edited by P. Thoft-Christensen, Springer Verlag.

  • Faravelli, L. (1988): Stochastic Finite Elements by Response Surface Techniques in Computational Probabilistic Methods,ASME-AMD, VOL.93 197–203.

    Google Scholar 

  • Faravelli, L. (1989): Response Surface Approach for Reliability Analysis,Journal of Engineering Mechanics, ASCE, 115(12), 2763–2781.

    Google Scholar 

  • Faravelli, L. (and Bigi, D. (1990): Stochastic Finite Elements for Crash Problems,Structural Safety, 8, 113–130.

    Article  Google Scholar 

  • Faravelli, L. (1993): Dynamic Analysis of Complex Structural Systems, inDynamic Motion Chaotic and Stochastic Behaviour, edited by Casciatti, Springer Verlag, New York.

    Google Scholar 

  • Faravelli, L. (1993): Dynamic Analysis of Complex Structural Systems, in:Dynamic Motion. Chaotic and Stochastic Behavior (F. Casciatti, editor), 301–324, Springer Verlag, Wien.

    Google Scholar 

  • Fenton, G. A. (1994): Error Evaluation of Three Random-Field Generators,Journal of Engineering Mechanics, ASCE, 120 (12), 2478–2497.

    Article  Google Scholar 

  • Fenton, G. A., and Vanmarcke, E. H. (1990): Simulation of Random Fields, via Local Average Subdivision,Journal of Engineering Mechanics, ASCE, 116(8), 1733–1949.

    Article  Google Scholar 

  • Fiessler, B., Neumann, H.J., and Rackwitz, R. (1979): Quadratic Limit States in Structural Reliability,Journal of Engineering Mechanics Division, ASCE, 105, 661–676.

    Google Scholar 

  • Florian, A. (1992): An Efficient Sampling Scheme: Updated Latin Hypercube Sampling,Probabilistic Engineering Mechanics, 7, 123–130.

    Article  Google Scholar 

  • Fujita, M., and Rackwitz, R. (1988): Updating First and Second Order Reliability Estimates by Importance Sampling,Structural Engineering and Earthquake Engineering, JSCE, 5(1), 31s-37s

    Google Scholar 

  • Fujita, M., Schall, G. and Rackwitz, R. (1987): Time Variant Component Reliabilities by FORM and SORM and Updating by Importance Sampling,Proc. of ICASP 5, Vancouver, Vol. 2, 520–527.

    Google Scholar 

  • Ghanern, R. G. and Spanos, P. D. (1991),Stochastic Finite Elements: A Spectral Approach Springer Verlag, New York.

    Google Scholar 

  • Ghanem, R. G. and Spanos, P. D. (1997): Spectral Techniques for Stochastic Finite Elements,Archives of Computational Methods in Engineering, 4(10) 63–100.

    MathSciNet  Google Scholar 

  • Gollwitzer, S., Zverev, A., Cuntze, R. and Grimmelt, M. (1994): Structural Reliability Applications in Acrospace Engineering.Structural Safety and Reliability.II 1265–1272 Balkema Rotterdam.

    Google Scholar 

  • Gollwitzer, S., and Rackwitz, R. (1988): An Efficient Numerical Solution to the Multinormal Integral,Probabilistic Engineering Mechanics, 3(2), 98–101.

    Article  Google Scholar 

  • Guoliang, J., Lin, C., Jiamei, D. (1993): Monte Carlo Finite Element Mothod of Structure Reliability Analysis,Reliability Engineering and System Safety, 40(1), 77–83.

    Article  Google Scholar 

  • Hall, P. (1992):The Bootstrap and the Edgeworth, Expansion Springer-Verlag, New York.

    Google Scholar 

  • Harbitz, A. (1983): Efficient and Accurate Probability of Failure Calculation by use of the Importance Sampling Technique.Proc. of ICASP4, Firenze, Italy, 825–836.

  • Harbitz, A. (1986): An Efficient Sampling Method for, Probability of Failure Calculation,Structural Safety, 3, 109–115.

    Article  Google Scholar 

  • Hasofer, A. M., and Lind, N. C. (1974): Exact and Invariant Second Moment Code Format.Journal of the Engineering Mechanics Division, ASCE, 100(EM1), 111–121.

    Google Scholar 

  • Hasselman, T. K. and Hart, G. C. (1972): Modal Analysis of Random Structural Systems,Journal of Engineering Mechanics, ASCE, 98 (EM3), 561–579.

    Google Scholar 

  • Hisada, T. and Nakagiri, S. (1985): Role of the Stochastic Finite Element Method in Structural Safety and Reliability,ICOSSAR '85, International Conference on Structural Safety and Reliability, 1, 385–392.

    Google Scholar 

  • Hohenbichler, M., and Rackwitz, R. (1981): Non normal Dependent Vectors in Structural Reliability,Journal of Engineering Mechanics Division, ASCE, 107, 1227–1238.

    Google Scholar 

  • Hohenbichler, M., and Rackwitz, R. (1986a): Sensitivity and Importance Measures in Structural Reliability,Civil Engineering Systems, 3(4), 203–209.

    Article  Google Scholar 

  • Hohenbichler, M., and Rackwitz, R. (1986b): Asymptotic Crossing Rate of Gaussian Vector Processes into Intersections of Failure Domains,Probabilistic Engineering Mechanics, I(3), 177–179.

    Article  Google Scholar 

  • Hohenbichler, M., Gollwitzer, S., Kruse, W., and Rackwitz, R.: New Light on First-and Second-Order Reliability Methods,Structural Safety, 4, 267–284.

  • Hohenbichler, M., and Rackwitz, R. (1988): Improvement of Second Order Reliability Estimates by Importance Sampling,Journal of Engineering Mechanics, ASCE, 114(12), 2195–2199.

    Google Scholar 

  • Hong, H. P. and Lind, N. C. (1996): Approximate reliability analysis using normal polynomial and simulation results,Structural Safety, 18:329–339.

    Article  Google Scholar 

  • Hoshiya, M. (1994): Conditional Simulation of a Stochastic Field.Structural Safety and Reliability. I, 349–354. Balkema, Rotterdam.

    Google Scholar 

  • Igusa, T., and Der Kiureghian, A. (1988); Response of Uncertain Systems to Stochastic Excitation,Journal of Engineering Mechanics, ASCE, 114(5).

  • Iman, R. L. and Canover, W. J. (1980): Small Sample Sensitivity Analysis Techniques for Computer Models with an Application to Risk Assessment,Communications in Statistics, Theory and Methods, A9 (17), 1749–1842.

    Article  Google Scholar 

  • Johnson, N. L., S. Kotz and N. Balakrishnan (1994):Continuous Univariate Distributions, 2nd. edition. John Wiley, New York.

    MATH  Google Scholar 

  • Kameda, H. and Morikawa, H. (1994): Conditional Stochastic Processes for Conditional Random Fields,Journal of Engineering Mechanics, ASCE, 120(4), 855–875.

    Article  Google Scholar 

  • Karamchandani, A. (1987): Structural System Reliability Analysis Methods, Report 83, John A. Blume Earthquake Engineering Center, Stanford University.

  • Karamchandani, A., Bjerager, P., and Cornell, C. A. (1988): Methods to Estimate Parametric Sensitivity in Structural Reliability Analysis,Probabilistic Engineering Mechanics, ASCE, edited by P.D. Spanos, 86–89.

  • Karamchandani, A., Bjerager, P., and Cornell, C. A. (1989): Adaptive Importance Sampling,Proceedings, 5th International Conference on Structural Safety and Reliability, San Francisco, California, August 7–11, 1989.

  • Kasutki, S. and Frogonpol, D. M. (1994): Hypersphere Division Method for Structural Reliability,Journal of Engineering Mechanics, ASCE, 120(11), 2405–2442.

    Article  Google Scholar 

  • Kim, S. H. and Na, S. W. (1997): Response Surface Method using Vector Projected Sampling Points.Structural Safety, 19:3–19.

    Article  Google Scholar 

  • Kleiber, M. and Hien, T. D. (1992),The Stochastic Finite Element Method, John Wiley and Sons, New York.

    MATH  Google Scholar 

  • Kolassa, J. E. (1997):Series Approximation Methods in Statistics, 2nd, edition. Springer-Verlag, New York.

    MATH  Google Scholar 

  • Law, A. and Kelton, W. D. (1991):Simulation Modeing and Analysis McGraw Hill, Singapore.

    Google Scholar 

  • Lepage, G. P. (1980): VEGAS: An Adaptive Multidimensional Integration Program. Publication CLNS-80/447. Cornell University.

  • Li, C. C. and Der Kiureghian, A. (1993): Optimal Discretization of Random Fields,Journal of Engineering Mechanics, ASCE, 119 (6), 1136–1154.

    Article  Google Scholar 

  • Li, Y. and Kareem, A. (1993): Simulation of Multivariate Random Processes: Hybrid DFT and Digital Filtering Approach,Journal of Engineering Mechanics, 119 (5), 1078–1098.

    Article  Google Scholar 

  • Lin, H. Z. and Der Kiureghian, A. (1987): Second-Order System Reliability using Directional Simulation,Reliability and Risk Analysis in civil Engineering 2, ICASP. 5. edited byN.C. Lind, University of Waterloo, Ontario Canada, 930–936.

    Google Scholar 

  • Liu, P. L., and Der Kiureghian, A. (1988a): Reliability of Geometrically Nonlincar Structures,Probabilistic Engineering Mechanics, ASCE, edited, by P.D. Spanos, 164–167.

  • Liu, P. L., and Der Kureghian, A. (1988b): Optimization Algorithms for Structural Reliability,Computational Probabilistic Methods, ASCE,93, edited by Liu, Belytschko, Lawrence, and Cruce, 185–196.

    Google Scholar 

  • Liu, P. L. (1993): Selection of Random Field Mesh in Finite Element Reliability Analysis,Journal of Engineering Mechanics, ASCE, 119(4), 667–680.

    Article  Google Scholar 

  • Liu, W. K., Belytschko, T., and Mani, A. (1986): Random Field Finite Elements,Numerical Methods in Engineering 23, 1831–1845.

    Article  MATH  MathSciNet  Google Scholar 

  • Liu, W. K., Mani, A., and Belytschko, T. (1987): Finite Element Methods in Probabilistic Mechanics,Probabilistic Engineering Mechanics 2(4), 201–213.

    Article  Google Scholar 

  • Liu, W. K., Besterfield, G. H. and Belytschko, T. (1988): Variational Approach to Probabilistic finite Elements,Journal of Engineering Mechanics, ASCE, 114(12), 2115–2133.

    Google Scholar 

  • Lutes, L. D., Shahram, S., and Jin, S. (1996): Efficiency and Accuracy in Simulation of random Fields,Probabilistic Engineering Mechanics, 11, 73–86.

    Article  Google Scholar 

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

    Google Scholar 

  • Madsen, H. O. (1987): Model Updating in Reliability Theory,Reliability and Risk Analysis in Civil Engineering 1, ICASP 5, edited by N. C. Lind, University of Waterloo, Ontario, Canada, 564–577.

    Google Scholar 

  • Madsen, H. O. and Moghtaderi-Zadeh, M. (1987): Reliability of Plates under Combined Loading,Proceedings, Marine Structural Reliability Symposium, SNAME, Arlington, Virginia, 185–191.

  • Madsen, H. O., and Tvedt, L. (1988): Efficient Methods in Time Dependent Reliability,Probabilistic Engineering Mechanics, ASCE, edited by P. D. Spanos, 432–435.

  • Madsen, H. O. (1988): Omission Sensitivity Factors,Structural Safety, 5, 35–45.

    Article  MathSciNet  Google Scholar 

  • Madsen, H. O. and Tvedt, L. (1990): Methods for Time-Dependent Reliability and Sensitivity Analysis, Journal of Engineering Mechanics, ASCE, 116(10), 2118–2135.

    Article  Google Scholar 

  • Maltz, F. H. and Hitzl, D. L. (1979): Variance Reduction in Monte-Carlo Computations Using Multi-Dimensional Hermite Polynomials,Journal of Computational Physics, 32, 345–376.

    Article  MATH  MathSciNet  Google Scholar 

  • Mantoglou, A. and Wilson, J. L. (1981): Simulation of Random Fields with the Turning Bands Method,Rep. No 264, Deptartment of Civil Engineering, MIT, Cambridge, Mass.

    Google Scholar 

  • Marek, P., Gustar, M. and Anagnos, T. (1996):Simulation—Based Reliability Assessment for Structural Engineers. CRC Press, Boca Raton.

    Google Scholar 

  • McKay, M. D., Beckman, R. J. and Conover, W. J. (1979): A Comparison of Three Methods for Selecting Values of input Variables in the Analysis of Output from a Computer Code,Technometrics, 21(n2).

  • Melehers, R. E. (1987):Structural Reliability, Analysis and Prediction, Ellis Horwood Series in Civil Engineering, Halsted Press, England.

    Google Scholar 

  • Melchers, R. E. (1987): Structural System Reliability Assessment Using Directional Simulation,Structural Safety, 16, 23–37.

    Article  Google Scholar 

  • Mignolet, M. P. and Spanos, P. D. (1992): Simulation of Homogeneous Two-Dimensional Random Fields: Part I-AR and ARMA Models,Journal of Applied Mechanics, 59, S260-S269.

    Google Scholar 

  • Muscolino, G. (1993): Response of Linear and Non-linear Structural Systems under Gaussian or Non-Gaussian Filtered Input, in:Dynamic Motion. Chaotic and Stochastic Behavior. (edited by F. Casciatti), 203–301, Springer Verlag, Wien.

    Google Scholar 

  • Nakagiri, S. and Hisada, T. (1982): Stochastic Finite Element Method Applied to Structural Analysis with Uncertain Parameters,Proceedings of the International Conference on FEM, 206–211.

  • Nataf, A. (1962): Determination des distributions dont les marges sont donées.Comptes rendues de l'Academie des Sciences, Paris, 225, 42–43.

    MathSciNet  Google Scholar 

  • Paloheimo, E. and Hannus, M. (1974): Structural Design Based on Weighted Fractiles,Journal of the Structural Division, ASCE, 100(ST7), 1367–1378.

    Google Scholar 

  • Papadopoulos, V. and Papadrakakis, M., (1996): Efficient Solution Procedures for the Stochastic Analysis of Space Frames using the Monte Carlo Simulation.Developments in Computational Techniques for Structural Engineering (edited by Topping, B. H. V.), 61–70, Edinburgh.

  • Papoulis, A. (1991):Probability, Random Variables and Stochastic Processes, McGraw Hill, New York.

    Google Scholar 

  • Plantee, J. Y. and Rackwitz, R. (1989): Structural Reliability under Non-Stationary Gaussian Vector Process Loads,Proceedings of the Eighth International Conference on Offshore Mechanics and Arctic Engineering, The Hague, The Netherlands, 1989.

  • Ponslet, E., Maglaras, G., Haftka, R. T., Nikolaidis, E., and Sensharma, P. (1994): Analytical and Experimental Comparison of Probabilistic and Deterministic Optimization,American Institute of Aeronautics and Astronautics, 544–559.

  • Pulido, J. E., Jacobs, T. L., and Prates de Lima, E. C. (1992): Structural Reliability using Monte Carlo Simulation with Variance Reduction Techniques on Elastic—Plastic Structures,Computers and Structures, 43(3), 419–430.

    Article  Google Scholar 

  • Pradlwarter, H. J. and Schuëller, G. I. and Melnik-Melnikov, P. G. (1994): Reliability of MDOF-Systems,Probabilistic Engineering Mechanics, 9, 235–243.

    Article  Google Scholar 

  • Pradlwarter, H. J. and Schuëller, G. I. (1995): On Advanced Monte Carlo Simulation Procedures in Stochastic Structural Dynamics,Submitted to: Journal of Nonlinear Mechanics.

  • Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P. (1992):Numerical Recipes in FORTRAN, Cambridge University Press, Cambridge.

    MATH  Google Scholar 

  • Priestley, M. B. (1994):Spectral Analysis and Time Series, Academic Press, London.

    Google Scholar 

  • Rackwitz, R. (1982): Response Surfaces in Structural Reliability,Report 67, 1982, Institut fur Bauingenieurwesen III, Technical University of Munich, West Germany.

    Google Scholar 

  • Righetti, G. and Harrop-Williams, K. (1988): Finite Element Analysis of Random Soil Media,Journal of Geotechnical Engineering, 114(1), 59–75.

    Article  Google Scholar 

  • Ripley, B. D. (1987):Stochastic Simulation, John Wiley and Sons, New York.

    MATH  Google Scholar 

  • Ronold, K. O. (1989): Probabilistic Consolidation Analysis with Model Updating,Journal of Geotechnical Engineering, ASCE, 115(2).

  • Rubinstein, R. Y. (1981):Simulation and the Montecarlo Method, J. Wiley and Sons, New York.

    Google Scholar 

  • Santos, J. L. T., Siemaszko, A., Cardoso, J. M. B., and Barros, P. M. S. (1994): Interactive-Computer Aided Reliability Engineering,American Institute of Aeronautics and Astronautics, 581–589.

  • Schetzen, M. (1989):The Volterra and Wiener Theories and Nonlinear Systems. Krieger Publishing Company, Malabar, Florida.

    Google Scholar 

  • Schuëller, G. I. and Shinozuka, M. (eds.) (1987):Stochastic Methods in Structural Dynamics. Martinus Nijhoff Publishers, Dordrecht.

    MATH  Google Scholar 

  • Schuëller, G. I. and Stix, R. (1987): A Critical Appraisal of Methods to determine Failure Probabilities,Structural Safety, 4, 293–309.

    Article  Google Scholar 

  • Schuëller, G. I., Bucher, C. G., Bourgund, U. and Ouypornprasert, W. (1989): On Efficient Computational Schemes to Calculate Structural Failure Probabilities,Probabilistic Engineering Mechanics, 4(1), 10–18.

    Article  Google Scholar 

  • Schuëller, G. I., Bucher, C. G., and Pradlwarter, H. J. (1990): Computational Methods in Stochastic Structural Dynamics,Structural Dynamics, ed by Krätziget al., 599–636.

  • Schuëller, G. I. and Bayer, V. (1996): Computational Procedures in Structural Reliability.Proceedings of the Second International Symposium on Uncertainty Modelling and Analysis, 152–159, IEEE Computers Society Press.

  • Shao S. and Murotsu, Y. (1994): Reliability of Complex Structural Systems using an Efficient Directional Simulation.Structural Safety and Reliability. III, 1529–1534. Balkema, Rotterdam.

    Google Scholar 

  • Shinozuka, M. (1964): Probability of Failure under Random Loading,Journal of Engineering Mechanics, ASCE, 90(5), 147–171.

    Google Scholar 

  • Shinozuka, M. and Lenoe, R. (1976): A Probabilistic Model for Spatial Distribution of Material Properties,Engineering Fracture Mechanics, 8, 217–227.

    Article  Google Scholar 

  • Shinozuka, M. (1983): Basic Analysis of Structural Safety,Journal of Structural Engineering, ASCE, 109(3), 721–740.

    Google Scholar 

  • Shinozuka, M. (1987a): Structural Response Variability,Journal of Engineering Mechanics, ASCE, 113(6), 825–842.

    Google Scholar 

  • Shinozuka, M. (1987b): Basic Issues in Stochastic Finite Element Analysis,Reliability and Risk Analysis in Civil Engineering,1, edited by N. C. Lind, University of Waterloo, Ontario, 506–519.

    Google Scholar 

  • Shinozuka, M. (1987c): Stochastic Fields and Their Digital Simulation, inStochastic Methods in Structural Dynamics, edited by Schuëller, G. I. and Shinozuka, M., Martinus Nijhoff Publishers, Dordrecht.

    Google Scholar 

  • Spanos, P. D. and Mignolet, M. P. (1992): Simulation of Homogeneous Two-Dimensional Random Fields: Part II-MA and ARMA Models,Journal of Applied Mechanics, 59, 270–277.

    Google Scholar 

  • Spanos, P. D., and Zeldin, B. A. (1994): Galerkin Sampling Method for Stochastic Mechanics Problems,Journal of Engineering Mechanics, ASCE, 120(5), 1091–1106.

    Article  Google Scholar 

  • Stubbs, N., Kim, J. T. and Topole, K. G. (1994): Experimental Determination of System Stochasticity.Structural Safety and Reliability. I, 369–374. Balkema, Rotterdam.

    Google Scholar 

  • Thoft-Christensen, P. and Murotsu, Y. (1986):Application of Structural Systems Reliability Theory, Springer Verlag, West Germany.

    MATH  Google Scholar 

  • Turk, G., Ramirez, M. R. and Corotis, R. B. (1994): Structural Reliability Analysis of Nonlinear systems,Structural Safety and Reliability, ed by Schuëller, Shinozuka and Yao, Balkema, Rotterdam, 1345–1352.

    Google Scholar 

  • Tvedt, L. (1988): Second Order Reliability by an Exact Integral,Proc. of 2nd IFIP Working Conference on Reliability and Optimization on Structural Systems, edited by P. Thoft-Christensen, Springer Verlag (in press).

  • Vanmarcke, E. (1983):Random Fields: Analysis and Synthesis, M.I.T. Press, Cambridge.

    Google Scholar 

  • Vanmarcke, E., Shinozuka, M. Nakagiri, S. Schuëller, G. I. and Grigoriu, M. (1986): Random Fields and Stochastic Finite Elements,Structural Safety, 3, 143–166.

    Article  Google Scholar 

  • Vanmarcke, E. (1994): Stochastic finite elements and experimental measurements.Probabilistic Engineering Mechanics, 9, 103–114.

    Article  Google Scholar 

  • Van Vinckenroy, G., De Wilde, W. P. (1993): Monte Carlo Techniques applied to Finite Element Modelling of Adhesively Bonded Joints,Computational Methods and Experimental Measurements (edited by C. A. Brebbia and G. M. Carlomagno), 2, 3–12.

    Google Scholar 

  • Veneziano, D., Casciatti, F. and Faravelli, L. (1983): Method of Seismic Fragility for Complicated Systems,Proceedings of 2nd Commitee on the Safety of Nuclear installations (CSNI): Specialist Meeting on Probabilistic Methods in Seismic Risk Assessment for NPP, Livermore, California.

  • Wang, G. S., and Ang, A. H. S. (1994): Adaptive Kernel Method for Evaluating Structural System Reliability.Structural Safety and Reliability. III, 1495–1500. Balkema, Rotterdam.

    Google Scholar 

  • Wen, Y. K. (1987): Approximate Methods for Nonlinear Time-Variant Reliability Analysis,Journal of Engineering Mechanics, ASCE, 113(12), 1826–1839.

    Google Scholar 

  • Wen, Y. K. and Chen, H. C. (1987): On Fast Integration for Time Variant Structural Reliability,Probabilistic Engineering Mechanics, 2(3), 156–162.

    Article  Google Scholar 

  • Wiener, N. (1958):Nonlinear Problems in Random Theory, Technology Press of the Massachussets Institute of Technology and John Wiley and Sons Inc., New York.

    MATH  Google Scholar 

  • Winkler, G. (1995):Image Analysis, Random Fields and Dynamic Monte Carlo Methods. Springer Verlag, Berlin.

    MATH  Google Scholar 

  • Winterstein, S. R. and Cornell C. A. (1984): Load Combination and Clustering Effects,Journal of Structural Engineering, ASCE, 110, 2690–2708.

    Google Scholar 

  • Winterstein, S. R. and Bjerager, P. (1987): The Use of Higher Moments in Reliability Estimation,Reliability and Risk Analysis in Civil engineering 2, ICASP 5, edited by N. C. Lind, University of Waterloo, Ontario, Canada, 1027–1036.

    Google Scholar 

  • Winterstein, S. R. (1988): Nonlinear Vibration Models for Extremes and Fatigue,Journal of Engineering Mechanics, ASCE, 114(10), 1772–1790.

    Google Scholar 

  • Wirsching, P. H., Ortiz, K., and Lee, S. J. (1987): An Overview of Reliability Methods in Mechanical and Structural Desing,American Institute of Aeronautics and Astronautics, 260–266.

  • Wu, Y. T. and Wirsching, P. H. (1987): A New Algorithm for Structural Reliability Estimation,Journal of Engieering Mechanics, ASCE, 113, 1319–1336.

    Google Scholar 

  • Wu, Y. T., Burnside, O. H. and Crusc, T. A. (1989): Probabilistic Methods for Structural Response Analysis,Computational Mechanics of Probabilistic and Reliability Analysis, edited by Liu and Belytschko, Elme Press International, Lausanne, Switzerland.

    Google Scholar 

  • Yamazaki, F. and Shinozuka, M. (1986):Digital Generation of Non-Gaussian Stochastic Fields, Technical Report, Department of Civil Engineering, Columbia University, New York.

    Google Scholar 

  • Yamazaki, F. and Shinozuka, M. (1988): Digital Generation of Non-Gaussian Stochastic Fields,Journal of Engineering Mechanics, ASCE, 114(7), 1183–1197.

    Article  Google Scholar 

  • Yamazaki, F., Shinozuka, M. and Dasgupta, G. (1988): Neumann Expansion for Stochastic Finite Element Analysis,Journal of Engineering Mechanics, ASCE, 114(8), 1335–1354.

    Google Scholar 

  • Yamazaki, F. (1990): Simulation of Stochastic Fields by Statistical Preconditioning,Journal of Engineering Mechanics, ASCE, 116(2), 268–287.

    Article  MathSciNet  Google Scholar 

  • Yamazaki, F., and Shinozuka, M. (1990): Simulation of Stochastic Fields by Statistical Preconditioning,Journal of Engineering Mechanics, ASCE, 116(2), 268–287.

    Article  Google Scholar 

  • Yonezawa, M. and Okuda, S. (1994): An Improved Importance Sampling Density Estimation for Structural Reliability Assessment, inStructural Safety and Reliability, ICOSSAR '93, 3, 1501–1508. edited by Schuëller, G. I., Shinozuka, M. and Yao, J. T. P., A. A. Balkema, Rotterdam.

    Google Scholar 

  • Zhang, J. and Ellingwood, B. (1994): Orthogonal Series Expansions of Random Fields in Reliability Analysis,Journal of Engineering Mechanics, ASCE, 120(12), 2660–2678.

    Article  Google Scholar 

  • Zhu, W. Q. and Wu, W. Q. (1990): A Stochastic Finite Element Method for Real Eigenvalue Problems, inStochastic Structural Dynamics 2, edited by Elishakoff, I. and Lin, Y. K., Springer Verlag, New York.

    Google Scholar 

  • Ziha, K. (1995): Descriptive Sampling in Structural Safety,Structural Safety, 17, 33–41.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Facultad de Ingenicría y Arquitectura, Universidad Nacional de Colombia, Manizales, Colombia

    J. E. Hurtado

  2. Departmento de Resistencia de Materiales y Estructuras en la Ingeniería, Universidad Politécnica de Cataluña, 08034, Barcelona, España

    A. H. Barbat

Authors
  1. J. E. Hurtado
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. H. Barbat
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hurtado, J.E., Barbat, A.H. Monte Carlo techniques in computational stochastic mechanics. Arch Computat Methods Eng 5, 3–29 (1998). https://doi.org/10.1007/BF02736747

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02736747

Keywords

Search

Navigation