Using fuzzy numbers in fatigue reliability estimation

Using fuzzy numbers in fatigue reliability estimation

Tomasz Bednarek1,2, Piotr Prokopowicz2, Włodzimierz Sosnowski1,2

1Institute of Fundamental Technological Research, PAN, Warsaw, Poland.
2Kazimierz Wielki University, Bydgoszcz, Poland.

DOI:

https://doi.org/10.7494/cmms.2009.1.0206

Abstract:

Increasing safety requirements of structures induces necessity of taking into consideration the random nature of variables in the fatigue design. Fatigue analysis of real structures in connection with probabilistic analysis needs a big computational effort. In this paper a new approach and methodology to fatigue analysis of structures using fuzzy numbers are presented. The method has been developed. A new efficient tool of fatigue analysis was created. The calculation of fatigue life using fuzzy numbers set is illustrated with analysis of hydraulic cylinders. Local fatigue approach is used at critical locations on hydraulic cylinders. The purpose of the probabilistic design is to estimate the probability of failure for critical locations on hydraulic cylinder.

Cite as:

Bednarek, T., Prokopowicz, P., Sosnowski, W., (2009). Using fuzzy numbers in fatigue reliability estimation. Computer Methods in Materials Science, 9(1), 43 – 48. https://doi.org/10.7494/cmms.2009.1.0206

Article (PDF):

Keywords:

Fuzzy numbers, Fatigue analysis, Fatigue reliability

References:

Chaboche, J.L., Continuum damage mechanics and its application to structural lifetime prediction, Rech. Aerosp, 4, 1987, 37–54.

Dubois, D., Prade, H., Operations on fuzzy numbers, Int. J. System Science, 9, 1978, 576-578.

Klir, G.J., Fuzzy arithmetic with requisite constraints, Fuzzy Sets and Systems, 91, 1997, 165-175.

Kosiński, W., Prokopowicz, P., Algebra liczb rozmytych, Matematyka Stosowana: matematyka dla społeczeństwa, 5 (46), 2004, 37-63 (in Polish).

Kosiński, W., Prokopowicz, P., Fuzziness – representation of dynamic changes, using ordered fuzzy numbers arithmetic, New dimensions in fuzzy logic nd related technologies, vol I, Proc. of the 5th EUSFLAT Conference (eds) Martin Stepnicka, Vilem Novak, Ulrich Bodenhofer, University of Ostrava, Ostrava, 2007, 449-456

Kosiński, W., P. Prokopowicz, P., Ślęzak, D., Ordered fuzzy number, Bulletin of the Polish Academy of Sciences, Ser. Sci. Math., 51 (3), 2003, 327-338.

Luccioni, B., Oller, S., Danesi, R., Coupled plastic-damaged model. Comp. Meth. Appl. Mech. Eng., 129, 1996, 81–89

Marczewska, I., Bednarek, T., Marczewski, A., Sosnowski, W., Jakubczak, H, Rojek, J., Practical fatigue analysis of hydraulic cylinders and some design recommendation, Int. Journal of Fatigue, 28/12, 2006, 1739-1751.

Oller, S., Salomón, O., Onate, E., A continuum mechanics model for mechanical fatigue analysis, Computational Materials Science, 32(2), 2005, 175–195.

Zadeh, L.A., Fuzzy sets, Information and Control, 8 (1965), 1965, 338-353

Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning, Part I, Information Sciences, 8, 1975, 199-249.