An exact solution for the static and dynamic analysis of FE discretized uncertain structures

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 21-24, 2007, Pages 2390-2400

  Falsone, G ^a   Ferro, G ^a  

^a UNIVERSITY OF MESSINA   (Italy)

Author keywords

Dynamic analysis; Exact probabilistic analysis; Static analysis; Stochastic finite element; Uncertain structures

Indexed keywords

DEFORMATION; DYNAMIC ANALYSIS; FINITE ELEMENT METHOD; PROBABILITY; STATIC ANALYSIS; STOCHASTIC MODELS; UNCERTAINTY ANALYSIS;

EXACT PROBABILISTIC ANALYSIS; POINT-DISCRETIZATION METHOD; UNCERTAIN STRUCTURES;

STRUCTURAL ANALYSIS;

DEFORMATION; DYNAMIC ANALYSIS; FINITE ELEMENT METHOD; PROBABILITY; STATIC ANALYSIS; STOCHASTIC MODELS; STRUCTURAL ANALYSIS; UNCERTAINTY ANALYSIS;

EID: 33947681302     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.12.003     Document Type: Article

References (27)

1. Zadeh L.A. Fuzzy sets as basis for a theory of possibility. Fuzzy Sets Syst. 1 (1978) 3-28
2. Rao S.S., and Savyer J.P. A fuzzy finite element approach for the analysis of imprecisely-defined systems. AIAA J. 33 (1995) 2264-2370
3. De Lima B.S.L.P., and Ebecken N.F.F. A comparison of models for uncertainty analysis by the finite element method. Finite Elem. Anal. Des. 34 (2000) 211-232
4. Moens D., and Vandepitte D. A survey of non-probabilistic uncertainty treatment in finite element analysis. Comput. Methods Appl. Mech. Engrg. 194 (2005) 1527-1555
5. Akpan U.O., Koko T.S., Orisamolu I.R., and Gallant B.K. Practically fuzzy finite element analysis of structures. Finite Elem. Anal. Des. 38 (2001) 93-111
6. Papadrakakis M., and Kotsopoulos A. Parallel solution method for stochastic finite element analysis using Monte-Carlo simulation. Comput. Methods Appl. Mech. Engrg. 168 (1999) 305-320
7. Liu K.L., Mani A., and Belytschko T. Finite element methods in probabilistic mechanics. Probab. Engrg. Mech. 2 4 (1987) 201-213
8. Ghanem R.G., and Spanos P.D. Stochastic Finite Elements: A Spectral Approach (1991), Springer-Verlag, NY
9. Matthies H.G., Brenner C.E., Bucher C.G., and Soares C.G. Uncertainties in probabilistic numerical analysis of structures and solids - stochastic finite elements. Struct. Safety 19 3 (1997) 283-336
10. B. Sudret, A. DerKiureghian, Stochastic finite element methods and reliability: a state-of-the-art report, Technical Report UCB/SEMM-2000/08, Department of Civil and Environmental Engineering, University of California, Berkeley, 2000.
11. Schueller G.I. Computational stochastic mechanics - recent advances. Comput. Struct. 79 (2001) 2225-2234
12. Noh H.-C. A formulation for stochastic finite element analysis of plate structures with uncertain Poisson's ratio. Comput. Methods Appl. Mech. Engrg. 193 (2004) 4847-4873
13. 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
14. S. Nakagiri, T. Hisada, Stochastic finite element method applied to structural analysis with uncertain parameters, in: Proceedings of the International Conference on Finite Element Methods, Aechen, Germany, 1982, pp. 206-211.
15. Elishakoff I., Ren Y.J., and Shinozuka M. Improved finite element method for stochastic structures. Chaos Solitons Fractals 5 5 (1995) 833-846
16. Impollonia N., and Muscolino G. Static and dynamic analysis of non-linear uncertain structures. Meccanica 37 (2002) 179-192
17. Van den Nieuwenhof B., and Coyette J.-P. Modal approaches for the stochastic finite element analysis of structures with material and geometric uncertainties. Comput. Methods Appl. Mech. Engrg. 192 (2003) 3705-3729
18. Yamazaki F., Shinozuka M., and Dasgupta G. Neumann expansion for stochastic finite element analysis. J. Engrg. Mech. 114 8 (1988)
19. Spanos P.D., and Ghanem R. Stochastic finite element expansion for random media. J. Engrg. Mech. 115 5 (1989)
20. Chakraborty S., and Dey S.S. A stochastic finite element dynamic analysis of structures with uncertain parameters. Int. J. Mech. Sci. 40 11 (1998) 1071-1087
21. Ghanem R.G., and Spanos P.D. Polynomial chaos in stochastic finite elements. J. Appl. Mech. 57 1 (1990) 197-202
22. Falsone G., and Impollonia N. A new approach for the stochastic analysis of finite element modelled structures with uncertain parameters. Comput. Methods Appl. Mech. Engrg. 191 (2002) 5067-5085
23. Falsone G., and Ferro G. A method for the dynamical analysis of FE discretized uncertain structures in the frequency domain. Comput. Methods Appl. Mech. Engrg. 194 (2005) 4544-4564
24. Li C.C., and Der Kiureghian A. Optimal discretization of random fields. J. Engrg. Mech. 119 6 (1993) 1136-1154
25. Der Kiureghian A., and Ke J.-B. The stochastic finite element method in structural reliability. Probab. Engrg. Mech. 3 2 (1988) 83-91
26. Vanmarcke E.H., and Grigoriu M. Stochastic finite element analysis of simple beams. J. Engrg. Mech. 109 5 (1983) 1203-1214
27. Liu K.L., Belytschko T., and Mani A. Random field finite elements. Int. J. Numer. Methods Engrg. 24 10 (1986) 1831-1845