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An improved time integration scheme based on uniform cubic B-splines and its application in structural dynamics

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Abstract

A time integration algorithm for structural dynamic analysis is proposed by uniform cubic B-spline functions. The proposed algorithm is successfully used to solve the dynamic response of a single degree of freedom (SDOF) system, and then is generalized for a multiple-degree of freedom (MDOF) system. Stability analysis shows that, with an adjustable algorithmic parameter, the proposed method can achieve both conditional and unconditional stabilities. Validity of the method is shown with four numerical simulations. Comparison between the proposed method and other methods shows that the proposed method possesses high computation accuracy and desirable computation efficiency.

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References

  1. Wilson, E. L., Farhoomand, I., and Bathe K. J. Nonlinear dynamic analysis of complex structures. Earthquake Engineering and Structural Dynamics, 1, 241–252 (1972)

    Article  Google Scholar 

  2. Chung, J. and Hulbert G. M. A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. Journal of Applied Mechanics, 60, 371–375 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bathe, K. J. Conserving energy and momentum in nonlinear dynamics: a simple implicit time integration scheme. Computers and Structures, 85, 437–445 (2007)

    Article  MathSciNet  Google Scholar 

  4. Liu, T., Zhao, C., Li, Q., and Zhang, L. An efficient backward Euler time-integration method for nonlinear dynamic analysis of structures. Computers and Structures, 106/107, 20–28 (2012)

    Article  Google Scholar 

  5. Dokainish, M. A. and Subbaraj, K. A survey of direct time-integration methods in computational structural dynamics I: explicit methods. Computers and Structures, 32, 1371–1386 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  6. Mullen, R. and Belytschko, T. An analysis of an unconditionally stable explicit method. Computers and Structures, 16, 691–696 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  7. Chung, J. and Lee, J. M. A new family of explicit time integration methods for linear and non-linear structural dynamics. International Journal for Numerical Methods in Engineering, 37, 3961–3976 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  8. Subbaraj, K. and Dokainish, M. A. A survey of direct time-integration methods in computational structural dynamics II: implicit methods. Computers and Structures, 32, 1387–1401 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bathe, K. J. and Noh, G. Insight into an implicit time integration scheme for structural dyanmics. Computers and Structures, 98/99, 1–6 (2012)

    Article  Google Scholar 

  10. Rougier, E., Munjiza, A., and John, N. W. M. Numerical comparison of some explicit time integration schemes used in DEM, FEM/DEM and molecular dynamics. International Journal for Numerical Methods in Engineering, 61, 856–879 (2004)

    Article  MATH  Google Scholar 

  11. Xie, Y. M. An assessment of time integration schemes for non-linear equations. Journal of Sound and Vibration, 192, 321–331 (1996)

    Article  Google Scholar 

  12. Hulbert, G. M. and Chung, J. Explicit time integration algorithms for structural dynamics with optimal numerical dissipation. Computer Methods in Applied Mechanics and Engineering, 137, 175–188 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  13. Chang, S. Y. and Liao, W. I. An unconditionally stable explicit method for structural dynamics. Journal of Earthquake Engineering, 9, 349–370 (2005)

    Google Scholar 

  14. Noh, G., Ham, S., and Bathe, K. J. Performance of an implicit time integration scheme in the analysis of wave propagations. Computers and Structures, 123, 93–105 (2013)

    Article  Google Scholar 

  15. Noh, G. and Bathe, K. J. An explicit time integration scheme for the analysis of wave propagations. Computers and Structures, 129, 178–193 (2013)

    Article  Google Scholar 

  16. Rostami, S., Shojaee, S., and Moeinadini, A. A parabolic acceleration time integration method for structural dynamics using quartic B-spline functions. Applied Mathematical Modelling, 36, 5162–5182 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. Wen, W. B., Jian, K. L., and Luo, S. M. An explicit time integration method for structural dynamics using septuple B-spline functions. International Journal for Numerical Methods in Engineering, 97, 629–657 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  18. Wen, W. B., Luo, S. M., and Jian, K. L. A novel time integration method for structural dynamics utilizing uniform quintic B-spline functions. Archive of Applied Mechanics, 85, 1743–1759 (2015)

    Article  Google Scholar 

  19. Wen, W. B., Jian, K. L., and Luo, S. M. 2D numerical manifold method based on quartic uniform B-spline interpolation and its application in thin plate bending. Applied Mathematics and Mechanics (English Edition), 34, 1017–1030 (2013) DOI 10.1007/s10483-013-1724-x

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. College of Engineering, Peking University, Beijing, 100871, China

    Weibin Wen & Daining Fang

  2. Beijing Institute of Technology, Beijing, 100081, China

    Hongshuai Lei, Shengyu Duan & Daining Fang

  3. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, School of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, China

    Kai Wei

  4. Key Laboratory of Applied Mechanics, Department of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University, Beijing, 100084, China

    Baosheng Xu

Authors
  1. Weibin Wen
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  2. Hongshuai Lei
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  3. Kai Wei
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  4. Baosheng Xu
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  5. Shengyu Duan
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  6. Daining Fang
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Corresponding author

Correspondence to Kai Wei.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11602004 and 11602081) and the Fundamental Research Funds for the Central Universities (No. 531107040934)

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Wen, W., Lei, H., Wei, K. et al. An improved time integration scheme based on uniform cubic B-splines and its application in structural dynamics. Appl. Math. Mech.-Engl. Ed. 38, 889–908 (2017). https://doi.org/10.1007/s10483-017-2207-8

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  • DOI: https://doi.org/10.1007/s10483-017-2207-8

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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