Uncertainty propagation in finite deformations - A spectral stochastic Lagrangian approach

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 19-22, 2006, Pages 2289-2312

  Acharjee, Swagato ^a   Zabaras, Nicholas ^a  

^a School of Chemical and Molecular Engineering   (United States)

Author keywords

Finite deformations; Karhunen Lo ve (KL) expansion; Spectral stochastic finite element method (SSFEM); Uncertainty propagation

Indexed keywords

COMPUTATIONAL METHODS; ELASTIC MODULI; ELASTOPLASTICITY; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; MONTE CARLO METHODS; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES; STRESSES;

DEFORMATION ANALYSIS; FINITE DEFORMATIONS; STOCHASTIC LAGRANGIAN APPROACH; UNCERTAINTY PROPAGATION;

DEFORMATION;

COMPUTATIONAL METHODS; DEFORMATION; ELASTIC MODULI; ELASTOPLASTICITY; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; MONTE CARLO METHODS; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES; STRESSES;

EID: 33644607578     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.05.005     Document Type: Article

References (22)

1. R. Ghanem P.D. Spanos Stochastic Finite Elements: A Spectral Approach 1999 Springer-Verlag New York
2. R.V. Field Jr. M. Grigoriu On the accuracy of the polynomial chaos approximation Probab. Engrg. Mech. 19 2004 65-80
3. B.J. Debusschere H.N. Najm A. Matta O.M. Knio R.G. Ghanem Protein labeling reactions in electrochemical microchannel flow: Numerical simulation and uncertainty propagation Phys. Fluids 15 2003 2238-2250
4. R. Ghanem Probabilistic characterization of transport in heterogeneous porous media Comput. Methods Appl. Mech. Engrg. 158 1998 199-220
5. R. Ghanem A. Sarkar Mid-frequency structural dynamics with parameter uncertainty Comput. Methods Appl. Mech. Engrg. 191 2002 5499-5513
6. R. Ghanem Higher order sensitivity of heat conduction problems to random data using the spectral stochastic finite element method ASME J. Heat Transfer 121 1999 290-299
7. D. Xiu G.E. Karniadakis Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos Comput. Methods Appl. Mech. Engrg. 191 2002 4927-4948
8. D. Xiu G.E. Karniadakis Modeling uncertainty in flow simulations via generalized polynomial chaos J. Comput. Phys. 187 2003 137-167
9. D. Xiu G.E. Karniadakis A new stochastic approach to transient heat conduction modeling with uncertainty Int. J. Heat Mass Transfer 46 2003 4681-4693
10. B.N. Velamur Asokan N. Zabaras Stochastic inverse heat conduction using a spectral approach Int. J. Numer. Methods Engrg. 60 2004 1569-1593
11. B.N. Velamur Asokan N. Zabaras Variational multiscale stabilized FEM formulations for transport equations: Stochastic advection-diffusion and incompressible stochastic Navier-Stokes equations J. Comput. Phys. 202 2005 94-133
12. M. Anders M. Hori Stochastic finite element method for elasto-plastic body Int. J. Numer. Methods Engrg. 46 1999 1897-1916
13. B. Moran M. Ortiz C.F. Shih Formulation of implicit finite-element methods for multiplicative finite deformation plasticity Int. J. Numer. Methods Engrg. 29 1990 483-514
14. S. Resnick Adventures in Stochastic Processes 1992 Birkhauser Boston
15. D. Xiu G.E. Karniadakis The Wiener-Askey polynomial chaos for stochastic differential equations SIAM J. Sci. Comput. 24 2002 619-644
16. B. Debusschere H. Najm P. Pebay O. Knio R. Ghanem O. Le Maître Numerical challenges in the use of polynomial chaos representations for stochastic processes SIAM J. Sci. Comput. 26 2004 134-153
17. R.L. Iman W.J. Conover Small sample sensitivity analysis techniques for computer models, with a application to risk assessment Commun. Statist. A9 1980 1749-1842
18. J. Shi, R. Ghanem, Nonlocal modeling of materials with random subscale interactions, in: Proceedings of the 16th ASCE Engineering Mechanics Conference, July 16-18, 2003, University of Washington, Seattle.
19. J. Fish K. Shek Finite deformation plasticity for composite structures: computational models and adaptive strategies Comput. Methods Appl. Mech. Engrg. 172 1999 145-174
20. J. Bonet A.J. Burton A simple orthotropic, transversely isotropic hyperelastic constitutive equation for large strain computations Comput. Methods Appl. Mech. Engrg. 162 1998 151-164
21. B.N. Velamur Asokan N. Zabaras Using stochastic analysis to capture unstable equilibrium in natural convection J. Comput. Phys. 208 2005 698-719
22. O.P. Le Maître O.M. Knio H.N. Najm R.G. Ghanem Uncertainty propagation using Wiener-Haar expansions J. Comput. Phys. 197 2004 28-57