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Application of Fuzzy Set Theory in Mechanics of Composite Materials

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Soft Computing in Textile Sciences

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 108))

Abstract

The field of composites mechanics, engineering and technology is relatively young, and the test methods and measurements techniques are not yet fully developed. The modeling of their mechanical properties is even further behind the experimental investigations. The study and application of composite materials is a truly interdisciplinary endeavor that has been enriched by contributions from chemistry, physics, material science and manufacturing engineering. Since numerous possibilities exist in combining constituents to form a composite there are many factors that can affect the global homogenized mechanical properties of composite materials, their behavior under different boundary and loading conditions, and their final failure. In fiber composites, both the fibers and the matrix retain their original physical and chemical identities, yet together they produce a combination of mechanical properties that cannot be achieved with either of the constituents acting alone, due to the presence of an interface between these two constituents. Thus, proper characterization of composites, whether it is for chemical, physical or mechanical properties, is extremely difficult because most interfaces are buried inside the material.

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References

  1. Taylor N.W. (1947), Mechanism of fracture of glass and similar brittle solids, J. Appl. Physics, 18, pp. 943–954.

    Article  Google Scholar 

  2. Stuart D.A. and Anderson O.L. (1952), Dependence of ultimate strength of glass under constant load and temperature, ambient atmosphere, and time, J. Amer. Ceram. Soc., 36, pp. 416–424.

    Article  Google Scholar 

  3. Charles R.J. (1958), Static fatigue of glass. I, Journal of Applied Physics, 29, pp. 1549–1553.

    Article  Google Scholar 

  4. Charles R.J. (1958), Static fatigue of glass. II, Journal of Applied Physics, 29, pp. 1554–1560.

    Article  Google Scholar 

  5. Mould R.E. and Southwick R.D. (1959), Strength and static fatigue of abraded glass under controlled ambient conditions, J. Amer. Ceram. Soc., 42, Part I, pp. 542–581, Part II, pp. 582–607.

    Article  Google Scholar 

  6. Charles R.J. and Hillig W.B. (1961), The kinetics of glass failure by stress corrosion, published as part of the Symposium on the Mechanical Strength of Glass and Ways of Improving It, Union Scientifique Continentale du Verre.

    Google Scholar 

  7. Kies J.A. (1964), The strength of glass fibers and the failure of filament wound pressure vessels, NRL Report 6034, U. S. Naval Research Laboratory.

    Google Scholar 

  8. Schmitz G.K. and Metcalfe A.G. (1965), Characterization of flaws on glass fibers, Proc. 20th Anniversary Technical Conference, The Society of the Plastics Industry.

    Google Scholar 

  9. Schmitz G.K. and Metcalfe A.G. (1966), Stress-corrosion of E-glass fibers, I&EC Product Res. & Dev., 5, pp. 1–6.

    Article  Google Scholar 

  10. Elishakoff I. (1983), Probabilistic methods in the theory of structures, John Wiley & Sons, New York.

    MATH  Google Scholar 

  11. Rao S.S. and Sawyer P. (1995), Fuzzy finite element approach for the analysis of imprecisely defined system, AIAA Journal, 33, no. 12, pp. 2364–2370.

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  13. McNeill F.M. and Thro E. (1996), Fuzzy logic: a practical approach, AP Professional, Fuzzy Logic CD-Rom Library, Electrographics Electronic Imaging, East Lansing, Michigan, USA.

    Google Scholar 

  14. Cox E. (1996), The fuzzy systems handbook, AP Professional, Fuzzy Logic CD-Rom Library, Electrographics Electronic Imaging, East Lansing, Michigan, USA.

    Google Scholar 

  15. Tsoukalas L.H. and Uhrig R.E. (1997), Fuzzy and neural approaches in engineering, A Wiley-Interscience Publication: John Wiley and Sons, New York, USA.

    Google Scholar 

  16. Dubois and Prade (1996), Fuzzy sets and system: theory and applications, AP Professional, Fuzzy Logic CD-Rom Library, Electrographics Electronic Imaging, East Lansing, Michigan, USA.

    Google Scholar 

  17. Zadeh L.A. (1996), Fuzzy sets and their application to cognitive and decision process, AP Professional, Fuzzy Logic CD-Rom Library, Electrographics Electronic Imaging, East Lansing, Michigan, USA.

    Google Scholar 

  18. Kosko B. (1991), Neural networks and fuzzy systems, Prentice Hall, Englewood Cliffs, NJ.

    Google Scholar 

  19. CD-ROM (1996), AP Professional, Fuzzy Logic CD-Rom Library, Electrographics Electronic Imaging, East Lansing, Michigan, USA.

    Google Scholar 

  20. Mathematica® (1995), Fuzzy logic pack, Wolfram Research, Inc., Champaign, Illinois.

    Google Scholar 

  21. Lallemand B., Plessis G., Tison T., and Level P. (1999), Neumann expansion for fuzzy finite element analysis, Engineering Computations, pp. 572–583.

    Google Scholar 

  22. Skrzypczyk J. and Burczynski T. (1997), The fuzzy boundary element method, Proc. XIII PCCMM, Poznan, pp. 1195–1202.

    Google Scholar 

  23. Abdel-Tawab K. and Noor A.K. (1999), A fuzzy-set analysis for a dynamic thermoelasto-viscoplastic damage response, Computer and Structures, 70, pp. 91–107.

    Article  MATH  Google Scholar 

  24. Muc A. and Kedziora P. (2001), A fuzzy-set approach to failure analysis of composite structures, Mech. Composite Mat., (in print).

    Google Scholar 

  25. Szeliga E. and Witkowski M. (1999), Fuzzy Monte Carlo Method for the stability assessment, Proc. XIV PCCMM, Rzeszów, pp. 353–354.

    Google Scholar 

  26. Brown C.B. and Yao J.T.P. (1983), Fuzzy sets and structural engineering, ASCE Journal of Structural Engineering, 109, pp. 1211–1225.

    Article  Google Scholar 

  27. Valliappan S. and Pham T.D., Elasto-plastic finite element analysis with fuzzy parameters, International Journal for Numerical Methods in Engineering, 38, pp. 531–548.

    Article  Google Scholar 

  28. Loskiewicz-Buczak A. and Uhrig R.E. (1993), Neural network — fuzzy logic diagnosis system for vibration monitoring, Proceedings of ANNIE-93, Artificial Neural Networks in Engineering Conference, St. Louis, MO.

    Google Scholar 

  29. Kohonen T. (1990), The self-organizing map, Proceedings of the IEEE, 78, no. 9.

    Article  Google Scholar 

  30. Zimmermann H.J. (1976), Description and optimization of fuzzy systems, International Journal of General Systems, 2, no. 4, pp. 209–215.

    Article  MATH  Google Scholar 

  31. Verdegay J.L. (1982), Fuzzy mathematical programming, Fuzzy Information and Design Process (Edited by M. M. Gupta and E. Sanchez), North-Holland, Amsterdam.

    Google Scholar 

  32. Yazenin A.V. (1987), Fuzzy and stochastic programming, Fuzzy Sets Syst., 22, pp. 171–180.

    Article  MathSciNet  MATH  Google Scholar 

  33. Yeh Y.C. and Hsu D.S. (1988), Structural optimization with uncertainty factors, Twelfth National Conference on Theoretical and Applied Mechanics, Taipei, Taiwan, R.O.C., pp. 565–571.

    Google Scholar 

  34. Morton S.K. and Webber J.P.H. (1990), Uncertainty reasoning applied to the assessment of composite materials for structural design, Engineering Optimization, 16, pp. 43–77.

    Article  Google Scholar 

  35. Adali S. (1991), Fuzzy optimization of laminated cylindrical pressure vessels, Composite Structures, Elsevier Applied Science, London, pp. 249–260.

    Google Scholar 

  36. Norwich A.M. and Turksen I.B. (1984), A model for the measurement of membership and consequences of its empirical implementation, Fuzzy Sets and Systems, 12, no. 1, pp. 1–25.

    Article  MathSciNet  MATH  Google Scholar 

  37. Dombi J. (1993), Membership function as a evaluation, Fuzzy Sets and Systems, 35, no. 1, pp. 1–21.

    Article  MathSciNet  Google Scholar 

  38. Dong W. and Shah H.C. (1987), Vertex method for computing functions of fuzzy variables, Fuzzy Sets and Systems, 24, pp. 65–78.

    Article  MathSciNet  MATH  Google Scholar 

  39. Aboudi J. (1987), Closed form constitutive equations for metal matrix composites, International Journal Engineering Science, 25, no. 9, pp. 1229–1240.

    Article  MATH  Google Scholar 

  40. Aboudi, J., (1989), Micromechanical analysis of composites by method of cells , Appl. Mech. Rev., Vol. 42, No 7, pp. 193–221.

    Article  Google Scholar 

  41. Aboudi, J., (1984), Effective behavior of inelastic fiber reinforced composites, International Journal Engineering Science, 22, pp.439–449.

    Article  MATH  Google Scholar 

  42. Aboudi, J., (1982), A continuum theory for fiber reinforced elastic-viscoplastic composites, International Journal Engineering Science, 20, pp.605–621.

    Article  MATH  Google Scholar 

  43. Byun J.H. and Chou T.W. (1995), Effect of yarn twist on the elastic property of composites, Proceedings of ICCM-10, Whistler, B. C., Canada, 4, pp. 293–299.

    Google Scholar 

  44. Muc A., Rys J., and Latas W. (1993), Limit load carrying capacity for spherical laminated shells under external pressure, Composite Structures, 25, pp. 295–303.

    Article  Google Scholar 

  45. Muc A. and Kedziora P. (2000), A fuzzy set analysis for a fatigue damage response of composite materials, Proceedings of International Conference ICCST/3, Durban, pp. 417–422.

    Google Scholar 

  46. Muc A. and Kedziora P. (2001), A description of infra-laminar cracks with the use of fuzzy sets, Composite Structures, (in print).

    Google Scholar 

  47. Fish J.C. and Lee S.W. (1988), Tensile strength of tapered composite structures, Proceedings of the AIAA/ASME/ASCE/AHS/ASC 29th Structures, Structural Dynamics and Materials Conference, Part I, AIAA Paper 88–2252.

    Google Scholar 

  48. Curry J.M., Johnson E.R., and Starnes J.H. (1992), Effect of dropped plies on the strength of graphite/epoxy laminates, AIAA J., 30, pp. 82–88.

    Article  Google Scholar 

  49. Winsom M.R. (1991), Delamination in tapered unidirectional glass/epoxy under static tension loading, Proceedings of the AIAA/ASME/ASCE/AHS/ ASC 32nd Structures, Structural Dynamics and Materials Conference, Part II, AIAA Paper 91–1142

    Google Scholar 

  50. Salpeker S.A., Raju I.S., and O’Brien T.K. (1988), Strain energy release rate analysis of delamination in tapered laminates subjected to tension loading, Proceedings of the American Society for Composites, 3rd Technical Conference, Technomic Publ.,

    Google Scholar 

  51. Trethewey B.R., Gillespie J.W., and Wilkins D.J. (1990), Interlaminar performance of tapered composite laminates, Proceedings of the American Society for Composites, 5th Technical Conference, Technomic Publ., Lancaster.

    Google Scholar 

  52. Kanninen M.F. and Popelar C.H. (1985), Advanced Fracture Mechanics, Oxford Engineering Science Series 15, Oxford University Press.

    MATH  Google Scholar 

  53. Bergmann H.W., Prinz R. (1989), Fatigue life estimation of graphite/epoxy laminates under consideration of delamination growth, Int. J. Num. Meth. Eng., 27, pp. 323–341.

    Article  Google Scholar 

  54. Russel A.J. and Street K.J. (1987), The effect of matrix toughness on delamination static and fatigue fracture under mode II shear loading of graphite composites, Toughened Composites, ASTM STP 937, American Society for Testing and Materials, Philadelphia.

    Google Scholar 

  55. Rao S.S. (1987), Multi-objective optimization of fuzzy structural systems, International Journal for numerical Methods in Engineering, 24, pp. 1157–1171.

    Article  MathSciNet  MATH  Google Scholar 

  56. Rao S.S. (1992), Fuzzy goal programming approach for structural optimization, AIAA Journal, 30, no. 5, pp. 1425–1432.

    Article  MATH  Google Scholar 

  57. Muc A. (1988), Optimal fiber orientations for simply -supported plates under compression, Composite Structures, 9, pp.161–172.

    Article  Google Scholar 

  58. Lee J., Harris B., Almond D.P., and Hammett F. (1997), Fiber composites fatigue-life determination, Composites: Part A, 28A, pp. 5–15.

    Google Scholar 

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Muc, A., Kedziora, P. (2003). Application of Fuzzy Set Theory in Mechanics of Composite Materials. In: Sztandera, L.M., Pastore, C. (eds) Soft Computing in Textile Sciences. Studies in Fuzziness and Soft Computing, vol 108. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1750-8_2

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  • DOI: https://doi.org/10.1007/978-3-7908-1750-8_2

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-2516-9

  • Online ISBN: 978-3-7908-1750-8

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