Análise não linear física e geométrica de treliças pelo método dos elementos finitos

Abstract

The behavior of trusses under large displacements and strains can be not exactly characterized when the nonlinear effects are disregarded during the structural analysis. Here, is developed a study about the physical (PNL) and geometrical nonlinearities (GNL) on these structures, considering them subjected to large displacements, rotations and strains, and is studied the influence of yielding in these analyses, using bilinear stress-strain relations. The stiffness matrix and internal forces vector are obtained employing the corotational kinematics description, the engineering strain, the Green strain, and the logarithmic strain. The equilibrium path is achieved applying incremental-iterative techniques, making use of the Newton-Raphson method, the modified Newton-Raphson method and the Riks-Wempner arc-length method with a divergencies corrector strategy based on a minimal linear increment. Ultimately, a MATLAB code is developed aiming to perform these nonlinear analysis, and seven examples are evaluated, using all the strain measures and the incremental- iterative methods presented. The results agree with values from others authors formulations, validating the code, that is able to obtain with great accuracy points on the equilibrium paths of trusses, furthermore, the arc-length can surpass all the critical points, they being snap-through or snap-back conditions. The displacements history is complex when the PNL and GNL effects are taken account, even for simple examples, showing the great difference between the linear and nonlinear structural analysis.