Abstract
Stochastic structural mechanics deals with the analysis of random phenomena occurring in structural systems or components. There are two major categories of structural uncertainties which involve spatial correlation and which consequently require the treatment as random fields. These are:
-
Material properties such as modulus of elasticity or strength
-
Geometrical properties such as shape or thickness of structural components. The outcome of the stochastic structural analyses is significantly affected by the appropriate treatment of the random properties in the context of the Finite Element method.
The paperwill provide an overviewof random field representation as appropriate for the stochastic finite element method (cf. Matthies and Bucher, 1999). This includes integral representation models as well a point representation models. In addition, conditional random fields as required in the presence of pointwise deterministic information (e.g. from measurements) are introduced.
Example applications illustrate these concepts and discuss the numerical implications of random field modeling. These applications involve static and dynamic problems which arise in system identification (Macke and Bucher, 2000; Bucher et al., 2003) as well as dynamic stability issues due to geometrical imperfections of shells (Most et al., 2004).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arnold, L. and P. Imkeller (1994). Fürstenberg-Khasminskii formulas for Lyapunov exponents via anticipative calculus. Technical Report Report Nr. 317, Institut für dynamische Systeme, University of Bremen.
Bathe, K.-J. (1996). Finite Element Procedures. Englewood Cliffs: Prentice Hall.
Brenner, C. E. and C. Bucher (1995). A contribution to the SFE-based reliability assessment of nonlinear structures under dynamic loading. Probabilistic Engineering Mechanics 10, 265–273.
Bucher, C. (2001). Stabilization of explicit time integration by modal reduction. In W. A. Wall, K.-U. Bletzinger, and K. Schweizerhof (Eds.), Proceedings, Trends in Computational Mechancics. Barcelona: CINME.
Bucher, C., O. Huth, and M. Macke (2003). Accuracy of system identification in the presence of random fields. In A. DerKiureghian, S. Madanat, and J. Pestana (Eds.), Applications of Statistics and Probability in Civil Engineering, pp. 427–433. Millpress.
Ditlevsen, O. (1991). Random field interpolation between point by point measures properties. In Proceedings of I. Int. Conference on Computational Stochastic Mechanics, pp. 801–812. ComputationalMechanics Publications.
Ghanem, R. and P. D. Spanos (1991). Stochastic Finite Elements — A Spectral Approach. New York/Berlin/Heidelberg: Springer.
Krützig, W. (1989). Eine einheitliche statische und dynamische Stabilitütstheorie für Pfadverfolgungsalgorithmen in der numerischen Festkörpermechanik. Z. angew. Math. Mech. 69-7, 203–213.
Lin, Y.-K. and G.-Q. Cai (1995). Probabilistic Structural Dynamics. New York: McGraw-Hill.
Macke, M. and C. Bucher (2000). Conditional random fields for finite elements based on dynamic response. In M. Deville and R. Owens (Eds.), Proc. 16th IMACS World Congress on Scientific Computation, Applied Mathematics and Simulation, Lausanne, Switzerland, August 21–25, 2000.
Matthies, H. G. and C. Bucher (1999). Finite Elements for Stochastic Media Problems. Comput. Methods Appl. Mech. Engrg. 168, 3–17.
Matthies, H. G., C. E. Brenner, C. G. Bucher, and C. G. Soares (1997). Uncertainties in Probabilistic Numerical Analysis of Structures and Solids — Stochastic Finite Elements. Struct. Safety 19, 283–336.
Most, T., C. Bucher, and Y. Schorling (2004). Dynamic stability analysis of nonlinear structures with geometrical imperfections under random loading. Journal of Sound and Vibration (1–2)(276), 381–400.
Schorling, Y. and C. Bucher (1999). Stochastic stability of structures with random imperfections. In B. F. J. Spencer and E. A. Johnson (Eds.), Stochastic Structural Dynamics, pp. 343–348. Rotterdam/Brookfield: Balkema.
Soong, T.-T. and M. Grigoriu (1992). Random Vibrations of Mechanical and Structural Systems. Englewood Cliffs: Prentice Hall.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this paper
Cite this paper
Bucher, C. (2006). Applications Of Random Field Models In Stochastic Structural Mechanics. In: Pandey, M., Xie, WC., Xu, L. (eds) Advances in Engineering Structures, Mechanics & Construction. Solid Mechanics and Its Applications, vol 140. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4891-2_39
Download citation
DOI: https://doi.org/10.1007/1-4020-4891-2_39
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-4890-6
Online ISBN: 978-1-4020-4891-3
eBook Packages: EngineeringEngineering (R0)