Acta Mechanica Sinica

, Volume 20, Issue 5, pp 541–550 | Cite as

Improvements on the arc-length-type method

  • Li Yuanqi
  • Shen Zuyan


Arc-length-type and energy-type methods are two main strategies used in structural nonlinear tracing analysis, but the former is widely used due to the explicitness and clarity in conception, as well as the convenience and reliability in calculation. It is very important to trace the complete load-deflection path in order to know comprehensively the characteristics of structures subjected to loads. Unfortunately, the nonlinear analysis techniques are only workable for tracing the limit-point-type equilibrium path. For the bifurcation-point-type path, most of them cannot secure a satisfactory result. In this paper, main arc-length-type methods are reviewed and compared, and the possible reasons of failures in tracing analysis are briefly discussed. Some improvements are proposed, a displacement perturbation method and a force perturbation method are presented for tracing the bifurcation-point-type paths. Finally, two examples are analyzed to verify the ideas, and some conclusions are drawn with respect to the arc-length-type methods.

Key Words

arc-length-type methods limit point bifurcation point displacement perturbation method force perturbation method 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Szilard R. Critical load post-buckling analysis by FEM using energy balancing technique.Computers & Structures, 1985, 20: 277–286MATHCrossRefGoogle Scholar
  2. 2.
    Zhou ZL, Murray DW. An incremental solution technique for unstable equilibrium paths of shell structures.Computers & Structures, 1994, 55(5): 749–759CrossRefGoogle Scholar
  3. 3.
    Hellweg HB, Crifield MA. A new arch-length method for handing sharp snap-backs.Computers & Structures, 1998, 66(5): 705–709MATHCrossRefGoogle Scholar
  4. 4.
    Souza Neto EA, Feng YT. On the determination of the path direction for arch-length methods in the presence of bifurcations and snap-backs.Computer Method in Applied Mechanics and Engineering, 1999, 179: 81–89MATHCrossRefGoogle Scholar
  5. 5.
    Carrera E. A study on arc-length-type methods and their operation failures illustrated by a simple model.Computers & Structures, 1994, 50(2): 217–229MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Fafard M, Massicotte B. Geometrical interpretation of the arc-length method.Computers & Structures, 1993, 46(4): 603–615MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Bellini PX, Chulya A. An improved automatic incremental algorithm for the efficient solution of nonlinear finite element equations.Computers & Structures, 1987, 26(1/2): 99–110MATHCrossRefGoogle Scholar
  8. 8.
    Shen ZY, Luo YF. Updating large rotations of space joints and revision technique for tracing the equilibrium path in analysis of reticulated shells. In: Symposiums on New Space Structures, Hangzhou: Zhejiang Univ, 1994. 144–150 (in Chinese)Google Scholar
  9. 9.
    Bergan PG, et al. Solution techniques for nonlinear finite element problems.International Journal of Numerical methods in Engineering, 1978, 12: 1677–1699MATHCrossRefGoogle Scholar
  10. 10.
    Feng YT, Peric D, Owen DRJ. A new criterion for determination of initial loading parameter in arc-length methods.Computers & Structures, 1996, 58 (3): 479–485MATHCrossRefGoogle Scholar
  11. 11.
    Meek JL, Loganathan S. Large displacement analysis of space-frame structures.Computer Methods in Applied Mech and Eng, 1989, 72: 57–75MATHCrossRefGoogle Scholar
  12. 12.
    Chrescielewski J, Schmiot R. A solution control method for nonlinear finite element post-buckling analysis of structures. In: ZS Gaspar ed. Post-Buckling of Elastic Structures Proceeding of the Euromech Colloquium, 1985Google Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 2004

Authors and Affiliations

  • Li Yuanqi
    • 1
  • Shen Zuyan
    • 1
  1. 1.Department of Building EngineeringTongji UniversityShanghaiChina

Personalised recommendations