Contribuições para análise estática e dinâmica de estruturas treliçadas modeladas pelo método dos elementos finitos posicional

Abstract

Aiming to ensure safety, in addition to verifying structural strength, structures must also be analyzed for their stability, as structural collapse can occur due to material failure or instability. The study of local or global stability loss in a structure requires consideration of geometric nonlinear behavior, where equilibrium is satisfied in the deformed configuration of the structure. One approach to studying structural instability is through numerical methods, such as the Finite Element Method (FEM) based on positions. The positional FEM is grounded in the change of body configuration through an initial and current mapping system, which inherently considers geometric nonlinearity. In this context, the present work aims to apply the positional FEM with a total Lagrangian reference system in a computational code developed in the Python programming language, for static and dynamic analyses of truss structures. The main focus is on obtaining resonance curves and bifurcation diagrams. Python was chosen due to its wide application in engineering, characterized by its flexibility, the availability of versatile libraries, and the ease of replicating results. The resolution of the equilibrium equation system is performed using the Newton-Raphson method, while the dynamic behavior is addressed using the Newmark method. Aiming to validate the computational implementation, the model was compared with analytical solutions and numerical examples available in the literature. As outcomes, a planar truss and a spatial truss were thoroughly analyzed, yielding nonlinear equilibrium curves, time responses of the structure, natural frequencies, vibration modes, deformed configurations, resonance curves, and bifurcation diagrams. The results were satisfactory and revealed important characteristics of the structural behavior of the analyzed structures.