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.     

Arc-length technique for nonlinear finite element analysis

INTRODUCTION Complete investigation of the nonlinear be-havior of structures must follow the equilibriumpath; identify and compute the singular points likelimit or bifurcation points, whose secondary bran-ches in the equilibrium path must be examined andfollowed. Several techniques to achieve the solu-tion pattern on the equilibrium path were presentedin literature. Load controlled Newton-Raphson me-thod was the earliest method in this regard; but itfails near the limit point. To overcom…