INCREMENTAL AND ITERATIVE METHODS WITH FOURTH ORDER OF CONVERGENCE FOR THE NONLINEAR ANALYSIS OF RETICULATE STRUCTURES

Abstract

The nonlinear behavior of a structure can be described by its equilibrium path in displacement versus load space, which is obtained iteratively by solving a series of linear problems. The nonlinear solution is obtained iteratively by solving a series of linear problems. Currently, analysis procedures have attracted much attention due to computational efficiency, analysis cost, feasibility and applicability. In this context, this paper proposes two incremental and iterative procedures with fourth order of convergence, in order to find the approximate solution of the system of nonlinear equations that describes the structural problem. Static analyzes of two problems with geometric nonlinear behavior – a beam and a column – are performed with the free program Scilab. The structures are discretized with the Corrotational formulation of the Finite Element Method. Connections are simulated using a null-length connection element. Equilibrium paths are obtained using the Linear Arc-Length path-following technique. The computational efficiency of the implemented methods is compared with the standard Newton-Raphson incremental procedure. As a conclusion, one of the proposed algorithms was able to obtain the approximate solution of the problems with fewer accumulated iterations and shorter processing time.