Assessment of the flat-top stable GFEM for free vibration analysis

Silva, Ivan Assing da; Machado, Roberto Dalledone; Arndt, Marcos; Weinhardt, Paulo de Oliveira

doi:10.1016/j.camwa.2022.04.012

Cited by 5 publications

(2 citation statements)

References 24 publications

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“…] n j dΓ (23) and W (1,2) is the interaction strain energy: W (1,2) = 𝜎 (1) ij 𝜀 (2) ij = 𝜎 (2) ij 𝜀 (1) ij . The Interaction Integral of Equation ( 23) can be rewritten as an equivalent domain form by the multiplication of the integrand by a smooth weight function q and further application of the Divergence Theorem:…”

Section: Ijmentioning

confidence: 99%

“…To overcome the ill-conditioning problems, Babuška and Banerjee 15 proposed a modification to the G/XFEM, called Stable Generalized Finite Element Method (SGFEM). SGFEM and its variations have been applied to several problems of fracture mechanics, [16][17][18][19][20][21] interfaces, 22 dynamics 23 and to handle cohesive crack propagation simulations. 24 Another disadvantage of G/XFEM may be the imposition of boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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A novel application of recovered stresses in stress intensity factors extraction methods for the generalized/extended finite element method

Lins,

Fonseca,

Barros

2023

Numerical Meth Engineering

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SummaryAn efficient improvement to compute Stress Intensity Factors (SIFs) in two‐dimensional fracture mechanics problems solved by Generalized/eXtended Finite Element Method and Stable Generalized Finite Element Method is proposed. A stress field obtained by a recovery procedure based on a locally weighted projection of the approximate stresses, is used in the formulation of two energy‐based SIFs extraction methods: the Contour Integral Method (CIM) and the Interaction Integral strategy. The accuracy and the path independence feature of the proposed approach are investigated in three numerical examples, considering crack opening modes I and II, different crack orientations and the presence of holes. The results demonstrate that the recovered stresses significantly improve the accuracy of the CIM and ensure a notable decrease in SIFs variation for different integration paths. On the other hand, an equivalent impact is not observed for the Interaction Integral strategy.

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