Uncertain structural design based on nonlinear fuzzy analysis

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 84, Issue 10-11, 2004, Pages 740-753

  Beer, Michael ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

level optimization; Fuzzy clustering; Fuzzy numbers; Fuzzy structural analysis; Uncertain structural design

Indexed keywords

EID: 9544243681     PISSN: 00442267     EISSN: None     Source Type: Journal    
DOI: 10.1002/zamm.200410154     Document Type: Conference Paper

References (38)

1. H. O. Madsen, S. Krenk, and N. C. Lind, Methods of Structural Safety (Prentice-Hall, Englewood Cliffs, New Jersey, 1986).
2. G. Wright (ed.), Subjective Probability (Wiley, Chichester, 1994).
3. K. Stange, Bayes-Verfahren, Schätz- und Testverfahren bei Berücksichtigung von Vorinformationen (Springer-Verlag, Berlin, Heidelberg, New York, 1977).
4. G. Alefeld and J. Herzberger, Einführung in die Intervallrechnung, in: Reihe Informatik ,12, edited by K. H. Böhling, U. Kulisch, and H. Maurer (Bibliografisches Institut AG, Zürich, 1974).
5. Y. Ben-Haim and I. Elishakoff, Convex Models of Uncertainty in Applied Mechanics (Elsevier, Amsterdam, 1990).
6. Z. Pawlak, Rough sets. Theoretical aspects of reasoning about data (Kluwer Academic Publishers, Dordrecht, Netherlands 1991).
7. H. Bandemer and S. Gottwald, Einführung in FUZZY-Methoden. Wissenschaftliche Taschenbücher Mathematik/Physik, Band 305 (Akademie-Verlag, Berlin, 1989).
8. V. Krätschmer, A unified approach to fuzzy random variables, Fuzzy Sets Syst. 123, 1-9 (2001).
9. T. Kapitaniak, Chaos for Engineers: Theory, Applications, and Control. 2nd revised edition, (Springer-Verlag, Berlin, Heidelberg, New York, 2000).
10. I. Elishakoff, Whys and Hows in Uncertainty Modelling, Probability, Fuzziness and Anti-Optimization (Springer-Verlag, Wien, New York, 1999).
11. G. I. Schnëller (ed.), A state-of-the-art report on computational stochastic mechanics, Probab. Eng. Mech. 12(4), 197-321 (1997).
12. O. Dessombz, F. Thouverez, J.-P. Lainé, and L. Jézéquel, Analysis of mechanical systems using interval computations applied to finite elements methods, J. Sound Vib. 239(5), 949-968 (2001).
13. Y. Ben-Haim, Robust Reliability in the Mechanical Sciences (Springer-Verlag, Berlin, Heidelberg, New York, 1996).
14. Li Bing, Zhu Meilin, and Xu Kai, A practical engineering method for fuzzy reliability analysis of mechanical structures, Reliab. Eng. Syst. Saf. 67, 311-315 (2000).
15. R. C. Penmetsa and R. V. Grandhi, Efficient estimation of structural reliability for problems with uncertain intervals, Comput. Struct. 80(12), 1103-1112 (2002).
16. J. B. Kadane, E. Moreno, M. E. Perez, and L. R. Pericchi, Applying non-parametric robust Bayesian analysis to non-optionated judicial neutrality, J. Stat. Plan. Inf. 102, 425-439 (2002).
17. A. K. Noor, J. H. Starnes Jr., and J. M. Peters, Uncertainty analysis of stiffened composite panels, Compos. Struct. 51, 139-158 (2001).
18. F. Tonon and A. Beraardini, A random set approach to the optimization of uncertain structures, Comput. Struct. 68(6), 583-600 (1998).
19. W. Dong and H. C. Shah, Vertex method for computing fuzzy variables, Fuzzy Sets Syst. 24, 65-78 (1987).
20. M. Savoia, Structural reliability analysis through fuzzy number approach, with application to stability, Comput. Struct. 80(12), 1087-1102 (2002).
21. A. Muc and P. Kedziora, A fuzzy set analysis for a fracture and fatigue damage response of composite materials, Compos. Struct. 54, 283-287 (2001).
22. A. Bonarini and G. Bontempi, A qualitative simulation approach for fuzzy dynamical models, ACM Trans. Model. Comput. Simul. 4, 285-313 (1994).
23. D. Moens and D. Vandepitte, Frequency response analysis of uncertain damped structures using the Fuzzy Finite Element Method: In: Fifth World Congress on Computational Mechanics, Vienna 2002, Doc. 80170, edited by A. H. Mang, F. G. Rammerstorfer, and J. Eberhardsteiner, pp. 1-10.
24. M. Hanss, The transformation method for the simulation and analysis of systems with uncertain parameters, Fuzzy Sets Syst. 130, 277-289 (2002).
25. Th. Fetz, M. Oberguggenberger, J. Jager, D. Koll, G. Krenn, H. Lessmann, and R. F. Stark, Fuzzy models in geotechnical engineering and construction management, Special Issue on Fuzzy Modeling, Comput.-Aided Civ. Infrastruct. Eng. 14, 93-106 (1999).
26. B. Möller, W. Graf, and M. Beer, Fuzzy structural analysis using α-level optimization, Comput. Mech. 26(6), 547-565 (2000).
27. M. Beer, Fuzziness und Fuzzy-Zufälligkeit bei der Sicherheitsbeurteilung von Tragwerken, Veröffentlichungen des Lehrstuhls für Statik, TU Dresden, Heft 5 (2002).
28. R. Viertl, Statistical Methods for Non-Precise Data (CRC Press, Boca Raton, New York, London, Tokyo, 1996).
29. R. Schneider, Stochastische Analyse und Simulation des nichtlinearen Verhaltens ebener Stabtragwerke mittels M-N-Q-Interaktionsmodell, Veröffentlichungen des Lehrstuhls für Statik, TU Dresden, Heft 2 (2001).
30. H. Müller, W. Graf, R. Schneider, and E. Stanoev, Zum nichtlinearen mechanischen Verhalten von seilvorgespannten Stahlbeton-Stabtragwerken, in: Proceedings of the 6. Fachtagung Baustatik-Baupraxis BB6, Weimar, 1996, pp. 1-20.
31. B. Möller, W. Graf, and R. Schneider, Determination of the failure probability with implicite limit state function (Doc. 331), in: Proceedings of the European Conference on Computational Mechanics, Munich, 1999, edited by W. Wunderlich and E. Stein, CD-ROM, pp. 1-20.
32. L. A. Zadeh, Fuzzy sets, Inf. Contr. 8, 338-353 (1965).
33. K.-L. Lai and B. M. Ayyub, Generalized uncertainty in structural reliability assessment, Civ. Eng. Syst. 11, 81-110 (1994).
34. F. Höppner, F. Klawonn, R. Kruse, and T. Runkler, Fuzzy cluster analysis: Methods for Classification, Data Analysis, and Image Recognition (Wiley, Chichester, Weinheim 1999).
35. L. Kaufmann and P. J. Rousseeuw, Finding groups in data: An introduction to Cluster analysis, 3.ed. (Wiley, Chichester, Weinheim 1990).
36. H. Timm, Fuzzy-Clusteranalyse: Methoden zur Exploration von Daten mit fehlenden Werten sowie klassifizierten Daten, Dissertation, Magdeburg (2002).
37. H. Rommelfanger, Entscheiden bei Unscharfe (Springer-Verlag, Berlin, Heidelberg, 1988).
38. H.-J. Zimmermann, Fuzzy Set Theory and its Applications (Kluwer Academic Publishers, Boston, London, 1992).