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X-FEM in isogeometric analysis for linear fracture mechanics

Abstract : The extended finite element method (X-FEM) has proven to be an accurate, robust method for solving problems in fracture mechanics. X-FEM has typically been used with elements using linear basis functions, although some work has been performed using quadratics. In the current work, the X-FEM formulation is incorporated into isogeometric analysis to obtain solutions with higher order convergence rates for problems in linear fracture mechanics. In comparison with X-FEM with conventional finite elements of equal degree, the NURBS-based isogeometric analysis gives equal asymptotic convergence rates and equal accuracy with fewer degrees of freedom (DOF). Results for linear through quartic NURBS basis functions are presented for a multiplicity of one or a multiplicity equal the degree.
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Emmanuel de Luycker, David J. Benson, Ted Belytschko, Yuri Bazilevs, Ming Chen Hsu. X-FEM in isogeometric analysis for linear fracture mechanics. International Journal for Numerical Methods in Engineering, Wiley, 2011, 87 (6), pp.541-565. ⟨10.1002/nme.3121⟩. ⟨hal-01657905⟩



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