Nonlinear analysis of static and dynamic stability of spatial truss structures using the positional Finite Element Method

Resumo

In order to ensure stuctural safety, in addition to checking for strength, structures must also be analyzed for stability, as structural collapse can occur due to material rupture or instability. The study of local or global stability loss in a structure is conducted considering geometric nonlinearity, where the structure's equilibrium is always satisfied in its deformed configuration. One way to study structural instability is by using numerical methods such as the Finite Element Method (FEM) based on positions. Positional FEM relies on the change in the body's configuration through an initial and current mapping system. This characteristic considers geometric nonlinearity. In this context, this work aims to apply positional FEM with a total Lagrangian reference system for the analysis of instability in spatial truss structures. The equilibrium equation system will be solved using the Newton-Raphson method, and dynamic behavior will be considered using the Newmark method. The expected results include nonlinear equilibrium curves, structure responses over time, natural frequencies, and vibration modes.