Structural Engineering and Mechanics

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An improved interval analysis method for uncertain structures

  • Wu, Jie (College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics) ;
  • Zhao, You Qun (College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics) ;
  • Chen, Su Huan (Department of Mechanics, Nanling Campus, Jilin University)
  • Received : 2004.08.31
  • Accepted : 2005.04.26
  • Published : 2005.08.20
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Abstract

Based on the improved first order Taylor interval expansion, a new interval analysis method for the static or dynamic response of the structures with interval parameters is presented. In the improved first order Taylor interval expansion, the first order derivative terms of the function are also considered to be intervals. Combining the improved first order Taylor series expansion and the interval extension of function, the new interval analysis method is derived. The present method is implemented for a continuous beam and a frame structure. The numerical results show that the method is more accurate than the one based on the conventional first order Taylor expansion.

Keywords

References

  1. Alefeld, G and Herzberger, J. (1983), Introductions to Interval Computations, Academic Press, New York
  2. Ben-Haim, Y. and Elishakoff, I. (1990), Convex Models of Uncertainty in Applied Mechanics, Elsevier Science Publishers, Amsterdam
  3. Chen, S.H., Lian H.D. and Yang, X.W. (2002), 'Interval displacement analysis for structures with interval parameters', Int. J. Numer. Meth. Eng., 53(2), 393-407 https://doi.org/10.1002/nme.281
  4. Chen, S.H. and Yang, X.W. (2000), 'Interval finite element method for beam structures', Finite Element in Analysis and Design, 34(1), 75-88 https://doi.org/10.1016/S0168-874X(99)00029-3
  5. Chen, S.H. and Lian H.D. (2002), 'Dynamic response analysis for structures with interval parameters', Struct. Eng. Mech., 13(3), 299-312 https://doi.org/10.12989/sem.2002.13.3.299
  6. Hansen, E. (1992), Global Optimization Using Interval Analysis, Marcel Dekker, New York
  7. Moore, R.E. (1979), Methods and Applications of Interval Analysis, SIAM, Philadelphia
  8. Qiu, Z.P. and Wang, X.J. (2003), 'Comparison of dynamic response of structures with uncertain-but-bounded parameters using non-probabilistic interval analysis method and probabilistic approach', Int. J. Solids Struct., 40, 5423-5439 https://doi.org/10.1016/S0020-7683(03)00282-8
  9. Qiu, Z.P. (2003), 'Comparison of static response of structures using convex models and interval analysis method', Int. J. Numer. Meth. Eng, 56(12), 1735-1753 https://doi.org/10.1002/nme.636

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