Stochastic simulation of riser-sections with uncertain measured pressure loads and/or uncertain material properties

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 41-44, 2007, Pages 4250-4271

  Foo, Jasmine ^a   Yosibash, Zohar ^b   Karniadakis, George Em ^a  

^a BROWN UNIVERSITY   (United States)

^b BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Karhunen Lo ve (K L) expansion; p FEM; Polynomial chaos; Random fluid loads; Stochastic collocation; Uncertainty quantification

Indexed keywords

COMPUTER SIMULATION; ELASTIC DEFORMATION; ELASTIC MODULI; FINITE ELEMENT METHOD; GALERKIN METHODS; POLYNOMIALS; RANDOM VARIABLES;

GENERALIZED POLYNOMIAL CHAOS; P-FINITE ELEMENT SOLVER; SPECTRAL COLLOCATION FORMULATION;

MECHANICS;

COMPUTER SIMULATION; ELASTIC DEFORMATION; ELASTIC MODULI; FINITE ELEMENT METHOD; GALERKIN METHODS; MECHANICS; POLYNOMIALS; RANDOM VARIABLES;

EID: 34547591758     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.04.005     Document Type: Article

References (31)

1. Soong T., and Grigoriu M. Random Vibration of Mechanical and Structural Systems (1993), Prentice-Hall, Englewood Cliffs, NJ
2. Ghanem R.G., and Kruger R.M. Numerical solution of spectral stochastic finite element systems. Comput. Methods Appl. Mech. Engrg. 129 (1996) 289-303
3. Stefanou G., and Papadrakakis M. Stochastic finite element analysis of shells with combined random material and geometric properties. Comput. Methods Appl. Mech. Engrg. 193 (2004) 139-160
4. Anders M., and Hori M. Three-dimensional stochastic finite element method for elasto-plastic bodies. Int. J. Numer. Methods Engrg. 51 (2001) 449-478
5. Xiu D., and Karniadakis G. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24 2 (2002) 619-644
6. Wiener N. The homogeneous chaos. Am. J. Math. 60 (1938) 897-936
7. Ghanem R., and Spanos P. Stochastic Finite Elements: A Spectral Approach (1991), Springer, New York
8. Frauenfelder P., Schwab C., and Todor R.A. Finite elements for elliptic problems with stochastic coefficients. Comput. Methods Appl. Mech. Engrg. 194 (2005) 205-228
9. Babuska I., Tempone R., and Zouraris G.E. Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation. Comput. Methods Appl. Mech. Engrg. 194 12-16 (2005) 1251-1294
10. Matthies H.G., and Keese A. Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations. Comput. Methods Appl. Mech. Engrg. 194 (2005) 1295-1331
11. Xiu D., and Hesthaven J. High-order collocation methods for differential equations with random inputs. SIAM J. Sci. Comput. 27 (2005) 1118-1139
12. Sokolnikoff I.S. Mathematical Theory of Elasticity (1956), McGraw-Hill, New York
13. Szabó B.A., and Babuška I. Finite Element Analysis (1991), John Wiley & Sons, New York
14. Noel A., and Szabó B. Formulation of geometrically non-linear problems in the spatial reference frame. Int. J. Numer. Methods Engrg. 40 (1997) 1263-1280
15. C. Norberg, Pressure forces on a cylinder in cross flow, IUTAM Symposium on Bluff-Body Wakes, Dynamics and Instabilities, 7-11 September 1992.
16. Radovic M., Lara-Curzion E., and Riester L. Comparison of different experimental techniques for determination of elastic properties of solids. Mater. Sci. Engrg. A 368 (2004) 56-70
17. Jaynes E. Information Theory and Statistical Mechanics. Phys. Rev. 106 (1957) 620-630
18. Jaynes E. Information Theory and Statistical Mechanics, II. Phys. Rev. 108 (1957) 171-190
19. Cameron R.H., and Martin W.T. The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals. Ann. Math. 48 (1947) 385
20. Wan X., and Karniadakis G.E. Multi-element generalized polynomial chaos for arbitrary probability measures. SIAM J. Sci. Comput. 28 3 (2006) 901-928
21. Loéve M. Probability Theory II (1997), Springer, New York
22. I. Babuska, F. Nobile, R. Tempone, A stochastic collocation method for elliptic partial differential equations with random input data, SIAM J. Numer. Anal., submitted for publication.
23. Oksendal B. Stochastic Differential Equations. fifth ed. (1998), Springer
24. Wan X., and Karniadakis G.E. An adaptive multi-element generalized polynomial chaos method for stochastic differential equations. J. Comput. Phys. 209 2 (2005) 617-642
25. Maitre O.P.L., Njam H.N., Ghanem R.G., and Knio O.M. Multi-resolution analysis of Wiener-type uncertainty propagation schemes. J. Comput. Phys. 197 (2004) 502-531
26. M. Tatang, G. McRae, Direct treatment of uncertainty in models of reaction and transport, MIT Technical Reports.
27. A. Keese, H. Matthies, Numerical methods and Smolyak quadrature for nonlinear partial differential equations, Informatikbericht 2003-5, Technische Universitat Braunschweig.
28. Smolyak S. Quadrature and interpolation formulas for tensor products of certain classes of functions. Sov. Math. Dokl. 4 (1963) 240-243
29. Novak E., and Ritter K. High dimension integration of smooth functions over cubes. Numer. Math. 75 (1996) 79-97
30. Lucor D., Su C.-H., and Karniadakis G. Covariance kernal representations of multidimensional second-order stochastic processes. J. Comput. Phys. 217 1 (2006) 82-99
31. Ghanem R., and Doostan A. On the construction and analysis of stochastic models: characterization and propagation of the errors associated with limited data. J. Comput. Phys. 217 (2006) 63-81