Método Dos Elementos Finitos Generalizados Aplicado a Problemas De Fratura Elástica Em 3d

Santos, K. F.; Barros, Felício Bruzzi; Pitangueira, Roque Luiz da Silva

doi:10.20906/cps/cilamce2017-0237

Cited by 1 publication

(4 citation statements)

References 13 publications

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“…In accordance with Gupta et al [46] and Santos [39], two global-local cycles are enough to provide a convergent solution for the local problem. Therefore, only the results of the second cycle are presented here.…”

Section: Numerical Examplessupporting

confidence: 60%

“…In general, few cycles in the global-local process are necessary until the convergence of results is achieved. In this work, the energy norm was used to evaluate the convergence of the results and just two cycles were enough to achieve a good approximation [39].…”

Section: Global-local Techniquementioning

confidence: 99%

“…Since the global mesh adopted here is not uniform, the Jacobians of the transformation from the global element to the respective local elements are not constant, but they have the same order of magnitude. After a convergence test, the penalty parameter used was 1.25E10 [39].…”

Section: Numerical Examplesmentioning

confidence: 99%

“…In a recent version, the G/XFEM was implemented for several analysis models and any dimensions in Alves et al [37]. The expansion of the INSANE system to perform analysis considering the global-local strategy, according to Duarte and Kim [18], Kim et al [19], was also contemplated by Malekan et al [38] for the case of twodimensional problems and extended to three-dimensional problems in Santos [39].…”

Section: Introductionmentioning

confidence: 99%

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SGFEM: a numerical investigation of the two-scale simulation of 3D elastic fracture

Santos¹,

Barros²

2020

J Braz. Soc. Mech. Sci. Eng.

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The Generalized/eXtended Finite Element Method (G/XFEM) is applied as a very useful tool in the resolution of complex structural models using an effective approach to represent the existence of cracks and other micro-defects. This is an unconventional formulation of the Finite Element Method (FEM), in that there is an expansion of the approximate solution field from the use of enrichment functions associated with the nodes. Enrichment functions can be singular functions derived from analytic deductions, polynomial functions or even functions resulting from other solution processes, such as the global-local strategy. The Stable Generalized Finite Method (SGFEM) is a variation of the G/XFEM with a simple modification in its enrichment functions, reducing the condition number of the stiffness matrix as well as the approximate error in the so-called blending elements. Considering this under the global-local strategy, the solution quality and the conditioning of the stiffness matrix in 3D linear fracture problems are investigated here. The crack surface is described by the Heaviside discontinuous functions and singular/crack front functions on a local scale. The solution of the local problem is used to enrich the approximation in the global domain, which may cause bad conditioning of the resulting system of equations and poor approximation errors in the solution. In order to overcome this problem, its projection into the linear polynomial space, according to the SGFEM strategy, is subtracted from the enrichment. Numerical examples, with different load and crack configurations, of linear elastic fracture mechanics are employed. Differently from other works, the meshes of the two scales are kept constant. Only the number of nodes associated with the local enrichment functions is changing. The impact on the accuracy and conditioning of the analysis is assessed, and the importance of using the SGFEM strategy is highlighted.

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Section: Numerical Examplessupporting

confidence: 60%

Section: Global-local Techniquementioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%