Abstract
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.
Similar content being viewed by others
References
Al-Rasby, S.N., 1991. Solution techniques in nonlinear structural analysis.Computer and Structures,40(4):985–993.
Baltoz, J.L., Dhatt, G., 1979. Incremental displacement algorithms for nonlinear problems.International Journal for Numerical Methods in Engineering,14: 1262–1266.
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.
Bergan, P.G., Soreide, T.H., 1978. Solution of Large Displacement and Instability Problems Using the Current stiffness Parameter.In: Finite Element in Nonlinear Mechanics, Tapir press, p. 647–669.
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.
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.
Crisfield M.A., 1981. A fast incremental/iterative solution procedure that handles snap-through.Computer and Structures,13:55–62.
Crisfield, M.A., 1983. An arc-length method including line searches and accelerations.International Journal for Numerical Methods in Engineering,19:1269–1289.
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.
Fafard, M., Massicotte, B., 1993. Geometrical interpretation of the arc-length method.Computer and Structures,46(4):603–615.
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.
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.
Foster, S., 1992. An application of the arc-length method involving concrete cracking.International Journal for Numerical Methods in Engineering,33: 269–285.
Fried, I., 1984. Orthogonal trajectory accession to the non-linear equilibrium curve.Computer Methods in Applied Mechanics and Engineering,47:283–298.
Hellweg, H.B., Crisfield, M.A., 1998. A new arc-length method for handling sharp snap-backs.Computer and Structures,66(5):705–709.
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.
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.
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.
May, I.M., Duan, Y., 1997. A local arc-length procedure for strain softening.Computer and Structures,64(1–4):297–303.
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.
Riks, E., 1972. The application of Newton's method to the problem of elastic stability.Journal of Applied Mechanics,39:1060–1065.
Riks, E., 1979. An incremental approach to the solution of snapping and buckling problems.International Journal of Solids and Structures,15:529–551.
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.
Teng, J.G., Luo, Y.F., 1998. A user-controlled arc-length method for convergence to predefined deformation states.Communications in Numerical Methods in Engineering,14:51–58.
Wright, E.W., Gaylord, E.H., 1968. Analysis of unbraced multistory steel rigid frames.International Journal of Structural Division ASCE,94:1143–1163.
Wempner, G.A., 1971. Discrete approximation related to nonlinear theories of solids.International Journal of Solids and Structures,7:1581–1599.
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the State Education Commission Foundation for Scholars Returned from Overseas, China
Rights and permissions
About this article
Cite this article
Memon, BA., Su, Xz. Arc-length technique for nonlinear finite element analysis. J. Zheijang Univ.-Sci. 5, 618–628 (2004). https://doi.org/10.1631/jzus.2004.0618
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/jzus.2004.0618