Nonlinear formulations of 2D truss finite element for analysis of structures with large displacements

Abstract

The complete investigation of the equilibrium path of nonlinear structural systems is of great practical interest regarding your critical behavior, as in the analysis of buckling in truss bars. The study of structures with large displacements demands the creation of physical-mathematical models that accurately include loading and support conditions and, most importantly, model the rigidity and mechanical response of the structure. The objective of this article is to present a study of finite element formulations of bar for the nonlinear analysis of planar reticulated structures constituted by bi-articulated bars. The solution of the system of nonlinear equations, that describes the structural problem, is obtained by an iterative-incremental procedure based on the Potra-Pták method with order of cubic convergence. This procedure has two steps in the iterative cycle and is associated with the Minimum Standard for Residual Displacements path-following technique. A computational code with the free program Scilab is developed and the behavior of structures is described by curves in displacement-load space.