Elaboração de algoritmo para análise não linear geométrica de treliças tridimensionais associado a técnica de comprimento de arco de Ricks-Wepner

Abstract

Geometric nonlinearity means that trusses do not behave in the same way when subjected to large displacements or deformations, significantly affecting the geometry of the structure and, consequently, its resistance. In this situation, the relationship between displacement and deformation is no longer linear, requiring a formulation that can specifically describe this behavior. Along the equilibrium path, several critical points typically emerge, such as the load limit point (snap-through), the displacement limit point (snap-back), and the structural failure point. Among these, the snap-through and snap-back phenomena are particularly significant, as they are directly associated with structural instability and must therefore be identified to enable the design of more efficient trusses. In this context, a geometrically nonlinear analysis algorithm is proposed, based on the positional formulation of the finite element method, employing the Newton-Raphson numerical procedure, the Green-Lagrange strain measure, and the arc-length continuation technique to ensure convergence. This algorithm allows for the computation of the equilibrium path for various truss configurations in both two and three dimensions. The results obtained from its implementation were satisfactory, confirming the effectiveness of the proposed approach and highlighting that the appropriate choice of strain measure is crucial for accurately capturing nonlinear behavior. Furthermore, it was observed that the computational cost of the code is directly influenced by the way in which the programmer implements it.