References


  1. Köylüoglu, U., Çakmak, A., and Nielsen, S., "Interval Algebra to Deal with Pattern Loading and Structural Uncertainties", Journal of Engineering Mechanics, Vol.121, No.11, 1995, pp.1149-1157.
  2. Mullen, R. and Muhanna, R., "Bounds of Structural Response for All Possible Loading Combinations", Journal of Structural Engineering, Vol.125, No.1, 1999, pp.98-106.
  3. Dessombz, O., Thouverez, F., Laîné, J.-P., and Jézéquel, L., "Analysis of Mechanical Systems Using Interval Computations Applied to Finite Element Methods", Journal of Sound and Vibration, Vol.~239, No.5, 2001, pp.949-968.
  4. Rao, S. and Sawyer, P., "Fuzzy Finite Element Approach for the Analysis of Imprecisely Defined Systems", AIAA Journal, Vol.~33, No.12, 1995, pp.2364-2370.
  5. Cherki, A., Plessis, G., Lallemand, B., Tison, T., and Level, P., "Fuzzy Behavior of Mechanical Systems with Uncertain Boundary Conditions", Computer Methods in Applied Mechanics and Engineering, Vol.189, 2000, pp.863-873.
  6. Chen, L. and Rao, S., "Fuzzy Finite-Element Approach for the Vibration Analysis of Imprecisely-Defined Systems", Finite Elements in Analysis and Design, Vol.27, 1997, pp.69-83.
  7. Wasfy, T. and Noor, A., "Application of Fuzzy Sets to Transient Analysis of Space Structures", Finite Elements in Analysis and Design, Vol.29, 1998, pp.153-171.
  8. Moens, D. and Vandepitte, D., "Fuzzy Finite Element Method for Frequency Response Function Analysis of Uncertain Structures", AIAA Journal, Vol.40, No.1, 2002, pp.126-136.
  9. Valliappan, S. and Pham, T., "Elasto-Plastic Finite Element Analysis with Fuzzy Parameters", International Journal for Numerical Methods in Engineering, Vol.38, 1995, pp.531-548.
  10. Fetz, T., Jäger, J., Köll, D., Krenn, G., Lessmann, H., Oberguggenberger, M., and Stark, R., "Fuzzy Models in Geotechnical Engineering and Construction Management", Computer-Aided Civil and Infrastructure Engineering, Vol.14, 1999, pp.93-106.
  11. Wasfy, T. and Noor, A., "Finite Element Analysis of Flexible Multibody Systems with Fuzzy Parameters", Computer Methods in Applied Mechanics and Engineering, Vol.160, 1998, pp.223-243.
  12. Dixit, U. and Dixit, P., "A Finite Element Analysis of Flat Rolling and Application of Fuzzy Set Theory", International Journal of Machine Tools and Manufacture, Vol.36, No.8, 1996, pp.947-969.
  13. Akpan, U., Koko, T., Orisamolu, I., and Gallant, B., "Fuzzy Finite Element Analysis of Smart Structures", Smart Materials and Structures, Vol.10, 2001, pp.273-284.
  14. Rao, S. and Liu, Q., "Fuzzy approach to the mechanics of fiber-reinforced composite materials", AIAA Journal, Vol.42, No.1, 2004, pp.159-167.
  15. Oberkampf, W., DeLand, S., Rutherford, B., Diegert, K., and Alvin, K., "A New Methodology for the Estimation of Total Uncertainty in Computational Simulation", Proceedings of the $40^{th}$ AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA-99-1612, 1999, pp. 3061-3083.
  16. Klir, G. and Folger, T., Fuzzy Sets, Uncertainty and Information, Prentice Hall, Englewood Cliffs, 1988.
  17. Miller, I. and Freund, J., Probability and Statistics for Engineers, Prentice Hall, Englewood Cliffs, 1985.
  18. Haldar, A. and Mahadevan, S., Reliability Assessment Using Stochastic Finite Element Analysis, John Wiley & Sons, New York, 2000.
  19. Freudenthal, A., "Fatigue Sensitivity and Reliability of Mechanical Systems, especially Aircraft Structures", WADD Technical Report 61-53, 1961.
  20. Moore, R., Interval Analysis, Prentice Hall, Englewood Cliffs, 1966.
  21. Zadeh, L., "Fuzzy sets", Information and Control, Vol.8, 1965, pp.338-353.
  22. Dubois, D. and Prade, H., Fuzzy Sets and Systems: Theory and Applications, Academic Press, Orlando, 1980.
  23. Dubois, D. and Prade, H., Possibility Theory. An Approach to Computerized Processing of Uncertainty, Plenum Press, New York, 1988.
  24. Driankov, D., Hellendoorn, H., and Reinfrank, M., An Introduction to Fuzzy Control, Springer-Verlag, Berlin, 1996.
  25. Zadeh, L., "Fuzzy Sets as a Basis for a Theory of Possibility", Fuzzy Sets and Systems, Vol.1, 1978, pp.3-28.
  26. Lodwick, W. and Jamison, K., "Interval Methods and Fuzzy Optimization", International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol.5, No.3, 1997, pp.239-249.
  27. Fang, J., Smith, S., and Elishakoff, I., "Combination of Anti-Optimization and Fuzzy-Set-Based Analysis for Structural Optimization under Uncertainty", Mathematical Problems in Engineering, Vol.4, 1998, pp.187-200.
  28. Moens, D. and Vandepitte, D., "An Interval Finite Element Approach for the Calculation of Envelope Frequency Response Functions", International Journal for Numerical Methods in Engineering Vol.61, No.14, 2004, pp.2480-2507.
  29. Civanalar, M. and Trussell, H., "Constructing Membership Functions Using Statistical Data", Fuzzy Sets and Systems, Vol.18, 1986, pp.1-13.
  30. Dubois, D. and Prade, H., "Random Sets and Fuzzy Interval Analysis", Fuzzy Sets and Systems, Vol.42, 1991, pp.87-101.
  31. Shafer, G., A Mathematical Theory of Evidence, Princeton University Press, Princeton, 1976.
  32. Moens, D. and Vandepitte, D., "A Survey of Non-Probabilistic uncertainty treatment in Finite Element Analysis", Computer Methods in Applied Mechanics and Engineering, 2005, in press.
  33. Dong, W. and Shah, H., "Vertex Method for Computing Functions of Fuzzy Variables", Fuzzy Sets and Systems, Vol.24, 1987, pp.65-78.
  34. Hanss, M., "The extended transformation method for the simulation and analysis of fuzzy-parameterized models", International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol.11, No.6, 2003, pp.711-727.
  35. Donders S., Vandepitte D., Van de Peer J., Desmet W., "Assessment of uncertainty on structural dynamic responses with the short transformation method", Journal of Sound and Vibration, 2005, in press
  36. Shary, S., "Algebraic Approach in the 'Outer Problem' for Interval Linear Equations", Reliable Computing, Vol.3, 1997, pp.103-135.
  37. Chen, S., Qiu, Z., and Song, D., "A New Method for Computing the Upper and Lower Bounds on Frequencies of Structures with Interval Parameters", Mechanics Research Communications, Vol.22, No.5, 1995, pp.431-439.
  38. El Gebeily, M., Abu-Baker, Y., and Elgindi, M., "The Generalized Eigenvalue Problem for Tridiagonal Symmetric Interval Matrices", International Journal on Control, Vol.72, No.6, 1999, pp.531-535.
  39. Manson, G., "Sharper eigenproblem estimates for uncertain multi degree of freedom systems", Proceedings of IMAC XXI CDrom, Orlando, Florida, USA, February 2003, 8 pages.
  40. Moens, D., "A Non-Probabilistic Finite Element Approach for Structural Dynamic Analysis with Uncertain Parameters", PhD thesis, K.U.Leuven, Leuven, 2002.
  41. Ross, T. and Parkinson, W., "Fuzzy set theory, fuzzy logic, and fuzzy systems", Fuzzy Logic and Probability Applications: Bridging the Gap, chap.2, SIAM, Philadelphia, ASA, Alexandria, VA, 2002, pp. 29-53.
  42. Zadeh, L., "Concept of A Linguistic Variable and Its Application to Approximate Reasoning .1", Information Sciences, Vol.8, No.3, 1975, pp.199-249.
  43. Ross, T., Sellers, K., and Booker, J., "Considerations for using fuzzy set theory and probability theory", Fuzzy Logic and Probability Applications: Bridging the Gap, chap.5, SIAM, Philadelphia, ASA, Alexandria, VA, 2002, pp. 87-104.
  44. Salita, M., "Shuttle disasters: a common cause?" Aerospace America, No.4, 2004, pp.41-43.
  45. Ben Haim, Y., "A Non-Probabilistic Measure of Reliability of Linear Systems based on Expansion of Convex Models", Structural Safety, Vol.17, 1995, pp.91-109.
  46. Zingales, M. and Elishakoff, I., "Anti-Optimization Versus Probability in an Applied Mechanics Problem: Vector Uncertainty", Transactions of the ASME, Journal of Applied Mechanics, Vol.67, 2000, pp.472-483.
  47. Ferrari, P. and Savoia, M., "Fuzzy Number Theory to Obtain Conservative Results with respect to Probability", Computer Methods in Applied Mechanics and Engineering, Vol.160, 1998, pp.205-222.
  48. Ross, T., Sellers, K., and Booker, J., "Introduction", Fuzzy Logic and Probability Applications: Bridging the Gap, chap.1, SIAM, Philadelphia, ASA, Alexandria, VA, 2002, pp.3-27.
  49. Kwakernaak, H., "Fuzzy Random Variables - I. Definitions and Theorems", Information Sciences, Vol.15, 1978, pp.1-29.
  50. Möller, B. and Beer, M., Fuzzy Randomness - Uncertainty in Civil Engineering and Computational Mechanics, Springer Verl., Berlin, 2004.
  51. Elishakoff, I. and Colombi, P., "Combination of Probabilistic and Convex Models of Uncertainty when Scarce Knowledge is Present on Acoustic Excitation Parameters", Computer Methods in Applied Mechanics and Engineering, Vol.104, 1993, pp.187-209.
  52. Ditlevsen, O., "Narrow Reliability Bounds for Structural Systems", Journal of Structural Mechanics, Vol.7, No.4, 1979, pp.453-472.
  53. Cui, W. and Blockley, D.I., "On the Bounds for Structural System Reliability", Structural Safety, Vol.9, 1991, pp.247-259.