Full Text:   <10080>

CLC number: TU31

On-line Access: 

Received: 2003-07-30

Revision Accepted: 2003-09-11

Crosschecked: 0000-00-00

Cited: 20

Clicked: 8688

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE A 2004 Vol.5 No.5 P.618~628


Arc-length technique for nonlinear finite element analysis

Author(s):  MEMON Bashir-Ahmed, SU Xiao-zu

Affiliation(s):  Department of Structural Engineering, Tongji University, Shanghai 200092, China

Corresponding email(s):   bashirmemon@sohu.com, xiaozub@online.sh.cn

Key Words:  Arc-length method, Nonlinear analysis, Finite element method, Reinforced concrete, Load-deflection path

Share this article to: More

MEMON Bashir-Ahmed, SU Xiao-zu. Arc-length technique for nonlinear finite element analysis[J]. Journal of Zhejiang University Science A, 2004, 5(5): 618~628.

@article{title="Arc-length technique for nonlinear finite element analysis",
author="MEMON Bashir-Ahmed, SU Xiao-zu",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Arc-length technique for nonlinear finite element analysis
%A MEMON Bashir-Ahmed
%A SU Xiao-zu
%J Journal of Zhejiang University SCIENCE A
%V 5
%N 5
%P 618~628
%@ 1869-1951
%D 2004
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2004.0618

T1 - Arc-length technique for nonlinear finite element analysis
A1 - MEMON Bashir-Ahmed
A1 - SU Xiao-zu
J0 - Journal of Zhejiang University Science A
VL - 5
IS - 5
SP - 618
EP - 628
%@ 1869-1951
Y1 - 2004
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2004.0618

Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load displacement response. The arc-length method serves the purpose well in principle, received wide acceptance in finite element analysis, and has been used extensively. However modifications to the basic idea are vital to meet the particular needs of the analysis. This paper reviews some of the recent developments of the method in the last two decades, with particular emphasis on nonlinear finite element analysis of reinforced concrete structures.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Al-Rasby, S.N., 1991. Solution techniques in nonlinear structural analysis.Computer and Structures,40(4):985-993.

[2] Baltoz, J.L., Dhatt, G., 1979. Incremental displacement algorithms for nonlinear problems.International Journal for Numerical Methods in Engineering,14:1262-1266.

[3] Bellini, P.X., Chulya, A., 1987. An improved automatic incremental algorithm for the efficient solution of nonlinear finite element equations.Computer and Structures,26(1-2):99-110.

[4] Bergan, P.G., Soreide, T.H., 1978. Solution of Large Displacement and Instability Problems Using the Current stiffness Parameter.In: Finite Element in NonlinearMechanics, Tapir press, p.647-669.

[5] Bergan, P.G., Horrigmoe, G., Krakeland, B., Soreide, T.H., 1978. Solution techniques for nonlinear finite element problems.International Journal for Numerical Methods in Engineering,12:1677-1696.

[6] Carrera, E., 1994. A study on arc-length type methods and their operation failures illustrated by a simple model.Computer and Structures,50(2):217-229.

[7] Crisfield, M.A., 1981. A fast incremental/iterative solution procedure that handles snapthrough.Computer and Structures,13:55-62.

[8] Crisfield, M.A., 1983. An arc-length method including line searches and accelerations.International Journal for Numerical Methods in Engineering,19:1269-1289.

[9] Fan, Z.L., 1994. A study of variable step-length incremental/iterative methods for nonlinear finite element equations.Computer and Structures,52(6):1269-1275.

[10] Fafard, M., Massicotte, B., 1993. Geometrical interpretation of the arclength method.Computer and Structures,46(4):603-615.

[11] Feng, Y.T., Peric, D., Owen, D.R.J., 1996. A new criterion for determination of initial loading parameter in arc-length methods.Computer and Structures,58(3):479-485.

[12] Forde, B.W.R., Stiemer, S.F., 1987. Improved arc-length orthogonality methods for nonlinear finite element analysis.Computer and Structures,27(5):625-630.

[13] Foster, S., 1992. An application of the arc-length method involving concrete cracking.International Journal for Numerical Methods in Engineering,33:269-285.

[14] Fried, I., 1984. Orthogonal trajectory accession to the non-linear equilibrium curve.Computer Methods in Applied Mechanics and Engineering,47:283-298.

[15] Hellweg, H.B., Crisfield, M.A., 1998. A new arc-length method for handling sharp snap-backs.Computer and Structures,66(5):705-709.

[16] Kuo, S.R., Yang, Y.B., 1995. Tracing post buckling paths of structures containing multi-loops.International Journal for Numerical Methods in Engineering,38:4053-4075.

[17] Kweon, J.H., Hong, C.S., 1994. An improved arc-length method for post-buckling analysis of composite cylindrical panels.Computer and Structures,53(3):541-549.

[18] Lam, W.F., Morley, C.T., 1992. Arc-length method for passing limit points in structural calculation.Journal of Structural Engineering,118(1):169-185.

[19] May, I.M., Duan, Y., 1997. A local arc-length procedure for strain softening.Computer and Structures,64(1-4):297-303.

[20] Ramm, E., 1981. Strategies for Tracing the Nonlinear Response near Limit Points.In:Nonlinear Finite Element Analysis in Structural Mechanics. Springer, New York, p.68-89.

[21] Riks, E., 1972. The application of Newton's method to the problem of elastic stability.Journal of Applied Mechanics,39:1060-1065.

[22] Riks, E., 1979. An incremental approach to the solution of snapping and buckling problems.International Journal of Solids and Structures,15:529-551.

[23] Sabir, B., Lock A.C., 1972. The Application of Finite Elements to the Large-deflection Geometrically Nonlinear Behavior of Cylindrical Shells. Proceedings of International Conference on Variational Mechanics. Southampton University, Session VII.

[24] Teng, J.G., Luo, Y.F., 1998.A user-controlled arc-length me-thod for convergence to predefined deformation states.Communications in Numerical Methods in Engineering,14:51-58.

[25] Wright, E.W., Gaylord, E.H., 1968. Analysis of unbraced multistory steel rigid frames.International Journal of Structural Division ASCE,94:1143-1163.

[26] Wempner, G.A., 1971. Discrete approximation related to nonlinear theories of solids.International Journal of Solids and Structures,7:1581-1599.

[27] Zhou, Z.L., Murray, D.W., 1994. An incremental solution technique for unstable equilibrium paths of shell structures.Computer and Structures,55(5):749-759.

Open peer comments: Debate/Discuss/Question/Opinion


Sandeep MS<sandeep.ms1986@gmail.com>

2016-01-22 12:46:09

Respected sir I am a research scholar from National Institute of Technology, Calicut, India. I was in search of procedure for doing arc length method to plot the full load deflection response of concrete. This paper will be very helpful for me. If possible please send me the paper.


2014-08-04 21:22:33

Thanks for the paper!!!!


2014-07-22 21:02:46

Arc length method is interesting.

Levon Shahinian@City College<sphere4000@gmail.com>

2014-05-07 22:25:43

Just learning about Arc length and was interested in reading your paper.
much appreciated!

georgios PApapostolou<giorgosp2005@hotmail.com>

2014-05-06 10:10:58

Hi, I am a graduate student at City College of New York and I am doing a project on Arc-Length Method. So, I think your journal will be very helpful



2014-05-03 15:02:58

I am interested to arc length tecnche


2014-04-10 15:52:58

thank you very much

DF@Columbia University<df2472@columbia.edu>

2013-08-22 04:21:38

Thank you!


2013-01-29 01:26:18

thanks so much for the paper

Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE