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TECHNICAL PAPERS

A Method for the Validation of Predictive Computations Using a Stochastic Approach

[+] Author and Article Information
Manuel Pellissetti

Institut für Mechanik, Universität Innsbruck, Technikerstrasse 13, 6020 Innsbruck, Austriae-mail: Manuel.Pellissetti@uibk.ac.at

Roger Ghanem

The Johns Hopkins University, Department of Civil Engineering, 3400 N. Charles St., Baltimore, Maryland 21218, USAe-mail: ghanem@jhu.edu

J. Offshore Mech. Arct. Eng 126(3), 227-234 (Sep 20, 2004) (8 pages) doi:10.1115/1.1782915 History: Received December 02, 2002; Revised August 01, 2003; Online September 20, 2004
Copyright © 2004 by ASME
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References

Ghanem, Roger G., and Spanos, Pol D. 1991, Stochastic Finite Elements: A Spectral Approach. Springer-Verlag, Berlin, Germany.
Ghanem,  R., and Red-Horse,  J., 1999, Propagation of Uncertainty in Complex Physical Systems Using a Stochastic Finite Element Approach. Physica D, 133(1–4), pp. 137–144.
Ghanem,  Roger G., 1999, Ingredients for a General Purpose Stochastic Finite Elements Implementation. Computer Methods in Applied Mechanics and Engineering, 168, pp. 19–34.
Loeve, M., 1977, Probability Theory. Springer-Verlag, New York, 4th edition,
Cameron,  R. H., and Martin,  W. T., 1947, The Orthogonal Development of Non-linear Functionals in Series of Fourier-Hermite Functionals. Ann. Math., 48(2), pp. 385–392.
Kleiber, M., Antunez, H., Hien, T. D., and Kowalczyk, P., 1997, Parameter Sensitivity in Nonlinear Mechanics: Theory and Finite Element Computations. John Wiley & Sons Ltd.
Spanos,  P. D., and Roger,  Ghanem, 1989, Stochastic Finite Element Expansion for Random Media. J. Eng. Mech., 115(5), pp. 1035–1053.

Figures

Grahic Jump Location
Euler-Bernoulli beam, schematic and FE-mesh
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Top: mean α0(x) and modes of fluctuation αi(x),i>0, of the Gaussian bending rigidity (exponential covariance function, σ=0.1,b=0.1); left vertical axis: mean (i=0, thick solid line); right vertical axis: modes of fluctuation (i>0, thin lines with markers); Bottom: realizations α(x) of the rigidity
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Sensitivity ∂uJj/∂αNl of displacement coefficients uJj to variation of material coefficient αNl,N=2,l=0; support condition 1
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Sensitivity ∂uJj/∂αNl of displacement coefficient uJj,J=11,j=4, to variation of material coefficients αNl; support condition 1
Grahic Jump Location
Sensitivity ∂uJj/∂αNl of displacement coefficients uJj to variation of material coefficient αNl,N=6,l=2; support condition 2
Grahic Jump Location
Sensitivity ∂uJj/∂αNl of displacement coefficient uJj,J=6,j=6, to variation of material coefficients αNl; support condition 2
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RMS-error of P-C coefficients at node 11, due to variability in mean estimator (COV=5%), support condition 2; second order P-C
Grahic Jump Location
RMS-error of P-C coefficients at node 11, due to variability in mean estimator (COV=5%), support condition 2; second order P-C
Grahic Jump Location
RMS-error of P-C coefficients at node 6, due to variability in variance estimator (COV=10%), support condition 2; first order P-C
Grahic Jump Location
RMS-error of P-C coefficients at node 6, due to variability in variance estimator (COV=10%), support condition 2; second order P-C

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