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Well-conditioning global–local analysis using stable generalized/extended finite element method for linear elastic fracture mechanics

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Abstract

Using the locally-enriched strategy to enrich a small/local part of the problem by generalized/extended finite element method (G/XFEM) leads to non-optimal convergence rate and ill-conditioning system of equations due to presence of blending elements. The local enrichment can be chosen from polynomial, singular, branch or numerical types. The so-called stable version of G/XFEM method provides a well-conditioning approach when only singular functions are used in the blending elements. This paper combines numeric enrichment functions obtained from global–local G/XFEM method with the polynomial enrichment along with a well-conditioning approach, stable G/XFEM, in order to show the robustness and effectiveness of the approach. In global–local G/XFEM, the enrichment functions are constructed numerically from the solution of a local problem. Furthermore, several enrichment strategies are adopted along with the global–local enrichment. The results obtained with these enrichments strategies are discussed in detail, considering convergence rate in strain energy, growth rate of condition number, and computational processing. Numerical experiments show that using geometrical enrichment along with stable G/XFEM for global–local strategy improves the convergence rate and the conditioning of the problem. In addition, results shows that using polynomial enrichment for global problem simultaneously with global–local enrichments lead to ill-conditioned system matrices and bad convergence rate.

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Acknowledgments

The authors wish to express their sincere appreciation to Prof. C.A. Duarte for his constructive comments on the numerical results. The authors also gratefully acknowledge the important support of the Brazilian research agencies CNPq (National Council for Scientific and Technological Developments - Grants 486959/2013-9 and 309005/2013-2) and CAPES (Coordination for the Improvement of Higher Education Personnel).

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  1. Graduate Program in Structural Engineering (PROPEEs), School of Engineering, Federal University of Minas Gerais (UFMG), Belo Horizonte, MG, Brazil

    Mohammad Malekan & Felicio Bruzzi Barros

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  1. Mohammad Malekan
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  2. Felicio Bruzzi Barros
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Correspondence to Felicio Bruzzi Barros.

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Malekan, M., Barros, F.B. Well-conditioning global–local analysis using stable generalized/extended finite element method for linear elastic fracture mechanics. Comput Mech 58, 819–831 (2016). https://doi.org/10.1007/s00466-016-1318-7

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