Fuzzy finite element analysis based on reanalysis technique

Structural Safety

Volumn 32, Issue 6, 2010, Pages 442-448

  Farkas, L ^a   Moens, D ^b   Vandepitte, D ^c   Desmet, W ^c  

^a LMS INTERNATIONAL   (Belgium)

^b Thomas More University College   (Belgium)

^c UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Fuzzy FE method; Krylov methods; Reanalysis; Static analysis; Uncertainty

Indexed keywords

ANALYTICAL GRADIENTS; BLACK BOX APPROACH; BLACK BOXES; DESIGN ENGINEERS; EXTERNAL INFLUENCES; FE ANALYSIS; FE METHOD; FUZZY APPROACH; FUZZY FINITE ELEMENT ANALYSIS; GAINING MOMENTUM; GLOBAL OPTIMISATION; INTERVAL ARITHMETIC; KRYLOV METHOD; NEW APPROACHES; NON-DETERMINISTIC APPROACH; NUMERICAL MODELING; NUMERICAL MODELS; OPTIMISATIONS; REANALYSIS; RELIABILITY ASSESSMENTS; STATIC STRUCTURAL ANALYSIS; UNCERTAINTY;

DESIGN; FINITE ELEMENT METHOD; GLOBAL OPTIMIZATION; OPTIMIZATION; RELIABILITY ANALYSIS; STATIC ANALYSIS; STRUCTURAL ANALYSIS;

UNCERTAINTY ANALYSIS;

EID: 77957348891     PISSN: 01674730     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.strusafe.2010.04.004     Document Type: Article

References (30)

1. Oberkampf W, Helton J, Sentz K. Mathematical representation of uncertainty. Non-deterministic approaches forum, AIAA 2001-1645; 2001.
2. Ross T.J., Booker J.M., Parkinson W.J. Fuzzy logic and probability applications: bridging the gap 2002, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA.
3. Schuëller G.I. Computational stochastic mechanics - recent advances. Comput Struct 2001, 79:2225-2234.
4. Elishakoff I. Possible limitations of probabilistic methods in engineering. ASME Appl Mech Rev 2000, 53:19-36.
5. Moens D., Vandepitte D. A survey of non-probabilistic uncertainty treatment in finite element analysis. Comput Methods Appl Mech Eng 2005, 194:1527-1555.
6. Klir G. Uncertainty and information measures for imprecise probabilities: an overview. In: Proceedings of the first international symposium on imprecise probabilities and their applications; 1999.
7. Möller B., Beer M. Fuzzy randomness - uncertainty in civil engineering and computational mechanics 2004, Springer, Berlin.
8. Shafer G. A mathematical theory of evidence 1976, Princeton University Press, Princeton.
9. Zadeh L. Fuzzy sets. Inform Control 1965, 8:338-353.
10. Rao S., Sawyer P. Fuzzy finite element approach for the analysis of imprecisely defined systems. AIAA J 1995, 33(12):2364-2370.
11. Muhanna R.L., Mullen R.L. Formulation of fuzzy finite element methods for mechanics problems. Comput Aided Civil Infrastruct Eng 1999, 14:107-117.
12. Moens D., Vandepitte D. Fuzzy finite element method for frequency response function analysis of uncertain structures. AIAA J 2002, 40(1):126-136.
13. Hanss M., Willner K. A fuzzy arithmetical approach to the solution of finite element problems with uncertain parameters. Mech Res Commun 2000, 27:257-272.
14. Rao S., Berke L. Analysis of uncertain structural systems using interval analysis. AIAA J 1997, 34(4):727-735.
15. Muhanna R.L., Mullen R.L. Uncertainty in mechanics problems interval-based approach. J Eng Mech - ASCE 2001, 127(6):557-566.
16. Dong W., Shah H.C. Vertex method for computing functions of fuzzy variables. Fuzzy Sets Syst 1987, 24:65-78.
17. Möller B., Graf W., Beer M. Fuzzy structural analysis using α-level optimization. Comput Mech 2000, 26:547-565.
18. Farkas L., Moens D., Vandepitte D., Desmet W. Application of fuzzy numerical techniques for product performance analysis in the conceptual and preliminary design stage. Comput Struct 2008, 86(10):1061-1079.
19. De Munck M., Moens D., Desmet W., Vandepitte D. A response surface based optimisation algorithm for the calculation of fuzzy envelope FRFs of models with uncertain properties. Comput Struct 2008, 86(10):1080-1092.
20. Saad Y. Iterative methods for sparse linear systems 1996, PWS.
21. Van der Vorst H. Iterative Krylov methods for large linear systems 2003, Cambridge University Press, Cambridge.
22. Zienkiewicz O.C., Taylor R.I. The finite element method 2000, Butterworth-Heinemann, Oxford.
23. Abu Kassim A.M., Tobbing B.H.V. Static reanalysis: a review. J Struct Eng 1987, 1113:1029-1045.
24. Barthelemy J.-F.M., Haftka R.T. Approximation concepts for optimum design - a review. Struct Optim 1993, 5:129-144.
25. Akgün M.A., Garcelon J.H., Haftka R.T. Fast exact linear and non-linear structural reanalysis and the Sherman-Morrison-Woodbury formulas. Int J Numer Methods Eng 2001, 50:1587-1606.
26. Kirsch U. A unified reanalysis approach for structural analysis, design, and optimization. Struct Multidiscip Optim 2003, 25:67-85.
27. Chipperfield K., Vance J.M., Fischer A. Fast meshless reanalysis using combined approximations, preconditioned conjugate gradient, and Taylor series. AIAA J 2006, 44(6):1325-1331.
28. Nair P.B. Equivalence between the combined approximation technique and Krylov subspace methods. AIAA J 2002, 40(5):1021-1023.
29. Kirsch U., Kocvara M., Zowe J. Accurate reanalysis for structures by a preconditioned conjugate gradient method. Int J Numer Methods Eng 2002, 55:233-251.
30. Ashby S.F., Holst M.J., Manteuffel A., Saylor P.E. The role of the inner product in stopping criteria for conjugate gradient iterations. Bit Numer Math 1999, 41(1):26-52.