Análise comparativa da formulação “exata” de elementos pela teoria de Timoshenko com o software de elementos finitos MASTAN2 para problemas de instabilidade de colunas e pórticos

Abstract

One of the usual strategies used to solve geometrically nonlinear problems is the use of the Finite Element Method, discretizing the structure for satisfactory results. The process of choosing the mesh refinement (discretization) is defined according to the analyst's experience. Therefore, engineering students or recent graduates often do not have the necessary knowledge to appropriately choose the degree of discretization of the structure, resulting in unrealistic results or an exaggerated increase in the computational cost for this analysis. Timoshenko's beam theory, considered more realistic, considers shear deformation, in addition to deformation resulting from bending, unlike Euler-Bernoulli beam theory. The two-cycle iterative method, using the "exact" element as a basis, proves simpler for non-linear analyses compared to traditional methods like Newton-Raphson and other iterative strategies, as its result is independent of the degree of structure discretization. Thus, the objective of this work is to perform a comparative analysis using the two-cycle iterative method with the consideration of shear distortion using the Matlab software, with the non-linear analysis software MASTAN2, using traditional methods. The results demonstrate the efficiency of the two-cycle iterative method, with no discretization, compared against results from MASTAN2 using discretization.