Arc-length technique for nonlinear finite element analysis

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.

[1]  A. Chulya,et al.  An improved automatic incremental algorithm for the efficient solution of nonlinear finite element equations , 1987 .

[2]  Siegfried F. Stiemer,et al.  Improved arc length orthogonality methods for nonlinear finite element analysis , 1987 .

[3]  G. Wempner.  Discrete approximations related to nonlinear theories of solids , 1971 .

[4]  Chang Sun Hong,et al.  An improved arc-length method for postbuckling analysis of composite cylindrical panels , 1994 .

[5]  David Murray,et al.  An incremental solution technique for unstable equilibrium paths of shell structures , 1995 .

[6]  E. Riks.  The Application of Newton's Method to the Problem of Elastic Stability , 1972 .

[7]  Shyh-Rong Kuo,et al.  Tracing postbuckling paths of structures containing multi‐loops , 1995 .

[8]  M. Crisfield.  An arc‐length method including line searches and accelerations , 1983 .

[9]  C. T. Morley,et al.  Arc-Length Method for Passing Limit Points in Structural Calculation , 1992 .

[10]  Isaac Fried,et al.  Orthogonal trajectory accession to the nonlinear equilibrium curve , 1984 .

[11]  Ekkehard Ramm,et al.  Strategies for Tracing the Nonlinear Response Near Limit Points , 1981 .

[12]  A. B. Sabir,et al.  The applications of finite elements to large deflection geometrically nonlinear behaviour of cylindrical shells , 1972 .

[13]  I. M. May,et al.  A LOCAL ARC-LENGTH PROCEDURE FOR STRAIN SOFTENING , 1997 .

[14]  Fan Zhiliang.  A study of variable step-length incremental/iterative methods for nonlinear finite element equations , 1994 .

[15]  E. Riks.  An incremental approach to the solution of snapping and buckling problems , 1979 .

[16]  J. G. Teng,et al.  A user‐controlled arc‐length method for convergence to predefined deformation states , 1998 .

[17]  Erasmo Carrera,et al.  A study on arc-length-type methods and their operation failures illustrated by a simple model , 1994 .

[18]  M. A. Crisfield,et al.  A new arc-length method for handling sharp snap-backs , 1998 .

[19]  B. Massicotte,et al.  Geometrical interpretation of the arc-length method , 1993 .

[20]  David R. Owen,et al.  A new criterion for determination of initial loading parameter in arc-length methods , 1996 .

[21]  P. Bergan,et al.  Solution techniques for non−linear finite element problems , 1978 .

[22]  E. Whitman Wright,et al.  Analysis of Unbraced Multistory Steel Rigid Frames , 1968 .

[23]  Stephen J. Foster,et al.  An application of the arc length method involving concrete cracking , 1992 .

[24]  Gouri Dhatt,et al.  Incremental displacement algorithms for nonlinear problems , 1979 .

[25]  M. Crisfield.  A FAST INCREMENTAL/ITERATIVE SOLUTION PROCEDURE THAT HANDLES "SNAP-THROUGH" , 1981 .