Avaliação do método de elementos finitos Híbrido-Trefftz em mecânica da fratura elástica linear bidimensional

Abstract

Finding analytical solutions to fracture mechanics problems is a complex or even impossible task in most cases, demanding numerical approximation methods, such as the Finite Elements Method (FEM) and the Boundary Elements Method (BEM). The pre sent work aims to evaluate the application of the Hybrid-Trefftz Finite Elements Method (HT-FEM) in the calculation of the stress intensity factor besides the displacement and fields in classic two-dimensional linear-elastic fracture mechanics problems, the crack on a infinite plate proposed by Westergaard (1939) and a thick tube with exterstress crack subjected to internal pressure. Although not widespread, HT-FEM, which is a hybrid between FEM and BEM, is effective in solving the proposed problems, achinal eving low error values and good convergence rates with hrefiniment and algebraic enrichment. The absence of area integrations in obtaining stiffness matrices allows a significant reduction in computational costs of integration and the insensitivity to mesh distortion allows to work easily with complex domains. In addition, HT-FEM shows good results when applied with the Virtual Crack Extension (VCE) method used to extract the stress intensity factor 𝐾𝐼, even if it works with area integrations. The changing in the VCE integration domain seems to have little influence on the obtained value for 𝐾𝐼, except when the internal vertices colapses on the crack tip, promoting a significant increase in the error.