Improving the accuracy of XFEM crack tip fields using higher order quadrature and statically admissible stress recovery

By Q. Xiao, B. Karihaloo. 2006

151 citations recorded by the source corpus.

Subfields: Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ae2ed03543722ede1d36255a4be9698eadeb2d5f

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In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

Optimal convergence analysis for the extended finite element method (2011, methodology): “Keywords: extended finite element method, error estimates, stress intensity factors.”
Strain smoothing in FEM and XFEM (2010, unknown): “This is also the subject of recent work on derivative recovery [106] and a posteriori error estimation in XFEM [20,16,34].”
Equivalent polynomials for quadrature in Heaviside function enriched elements (2015, background): “…papers explicitly devoted to this problem and having the word ”quadrature” in their title are, in chronological order [11], where the concept of equivalent polynomials was introduced and [12], where the relation between quadrature rules and the accuracy of XFEM crack tip ﬁelds was studied.”
Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method (2010, methodology): “[49] as well as Xiao and Karihaloo [50] use DECUHR [51], an adaptive integration scheme based on nonuniform subdivision of elements for integration of singular functions.”
Accurate recovery-based upper error bounds for the extended finite element framework (2010, methodology): “[10] propose an approach based on the use of the Moving Least Squares (MLS) technique adapted to the XFEM framework and the use of statically admissible basis functions to obtain a recovered stress field that improves the accuracy of the stresses obtained by XFEM.”
A posteriori error estimation for extended finite elements by an extended global recovery (2008, methodology): “Some remarkable works has been performed on a posteriori error estimation for the GFEM [29–31], and a first step taken in [32] to improve crack tip fields in the XFEM by statically admissible stress recovery.”
The extended/generalized finite element method: An overview of the method and its applications (2010, methodology): “In [200], standard polynomial basis functions are employed for the MLS approximation.”
Integration of singular enrichment functions in the generalized/extended finite element method for three‐dimensional problems (2009, background): “…q 2008 John Wiley & Sons, Ltd. Received 12 August 2008; Revised 30 October 2008; Accepted 17 November 2008 KEY WORDS: GFEM/X-FEM; BEM; weakly singular integration; mapping method; branch functions; generalized FEM; extended FEM; boundary element method; fracture; singular enrichment functions”
Strict and effective bounds in goal‐oriented error estimation applied to fracture mechanics problems solved with XFEM (2010, background): “Even though sources of discretization errors have been identified (see [23, 24]) and error estimation has been addressed in several papers (e.”
Enhanced blending elements for XFEM applied to linear elastic fracture mechanics (2009, background): “Because there are discontinuous and singular functions in XFEM approximations, several studies have paid particular attention to numerical integration techniques [2, 8, 10, 19, 28].”
Derivative recovery and a posteriori error estimate for extended finite elements (2007, methodology): “Other partition of unity enriched finite element methods are the generalized finite element method (GFEM) [37, 38] and Nitsche’s method [22], although the latter’s kinematics is identical to that of the XFEM [5].”
Generalized Duffy transformation for integrating vertex singularities (2009, background): “Many recent studies have tackled the issue of numerical integration of singularities within partition of unity finite element methods [49–53].”