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Showing results 21 to 28 of 28
   Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework; ; Bordas, Stéphane  in International Journal for Numerical Methods in Engineering (2010), 83(3), 269-294 Partition of unity methods, such as the extended finite element method, allows discontinuities to be simulated independently of the mesh (Int. J. Numer. Meth. Engng. 1999; 45:601-620). This eliminates the ... [more ▼] Partition of unity methods, such as the extended finite element method, allows discontinuities to be simulated independently of the mesh (Int. J. Numer. Meth. Engng. 1999; 45:601-620). This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome re-meshing, as the discontinuity evolves. However, to compute the stiffness matrix of the elements intersected by the discontinuity, a subdivision of the elements into quadrature subcells aligned with the discontinuity is commonly adopted. In this paper, we use a simple integration technique, proposed for polygonal domains (Int. J. Numer. Meth. Engng 2009; 80(1):103-134. DOI: 10.1002/nme.2589) to suppress the need for element subdivision. Numerical results presented for a few benchmark problems in the context of linear elastic fracture mechanics and a multi-material problem show that the proposed method yields accurate results. Owing to its simplicity, the proposed integration technique can be easily integrated in any existing code. © 2010 John Wiley & Sons, Ltd. [less ▲] Detailed reference viewed: 273 (0 UL)On numerical integration of discontinuous approximations in partition of unity finite elements; Bordas, Stéphane ; in IUTAM Bookseries (2010), 19 This contribution presents two advances in the formulation of discontinuous approximations in finite elements. The first method relies on Schwarz-Christoffel mapping for integration on arbitrary polygonal ... [more ▼] This contribution presents two advances in the formulation of discontinuous approximations in finite elements. The first method relies on Schwarz-Christoffel mapping for integration on arbitrary polygonal domains [1]. When an element is split into two subdomains by a piecewise continuous discontinuity, each of these polygonal domains is mapped onto a unit disk on which cubature rules are utilized. This suppresses the need for the usual two-level isoparametric mapping. The second method relies on strain smoothing applied to discontinuous finite element approximations. By writing the strain field as a non-local weighted average of the compatible strain field, integration on the surface of the finite elements is transformed into boundary integration, so that the usual subdivision into integration cells is not required, an isoparametric mapping is not needed and the derivatives of the shape (enrichment) functions do not need to be computed. Results in fracture mechanics and composite materials are presented and both methods are compared in terms of accuracy and simplicity. The interested reader is referred to [1,6,13] for more details and should contact the authors to receive a version of the MATLAB codes used to obtain the results herein. © 2010 Springer Science+Business Media B.V. [less ▲] Detailed reference viewed: 234 (2 UL)Enriched finite elements (XFEM) for multi-crack growth simulations in orthotropic materials; ; et al Scientific Conference (2010) Detailed reference viewed: 147 (0 UL)XFEM modelling of delamination in composite materials; ; et al Scientific Conference (2010) Detailed reference viewed: 173 (0 UL)Modelling of crack growth behaviour in composite materials using the extended finite element method (XFEM); ; et al Scientific Conference (2010) Detailed reference viewed: 160 (0 UL)The smoothed extended finite element method for strong discontinuities; Bordas, Stéphane ; Scientific Conference (2009, June) Detailed reference viewed: 122 (0 UL)Numerical integration over arbitrary polygonal domains based on Schwarz-Christoffel conformal mapping; Bordas, Stéphane ; in International Journal for Numerical Methods in Engineering (2009), 80(1), 103-134 This paper presents a new numerical integration technique on arbitrary polygonal domains. The polygonal domain is mapped conformally to the unit disk using Schwarz-Christoffel mapping and a midpoint ... [more ▼] This paper presents a new numerical integration technique on arbitrary polygonal domains. The polygonal domain is mapped conformally to the unit disk using Schwarz-Christoffel mapping and a midpoint quadrature rule defined on this unit disk is used. This method eliminates the need for a two-level isoparametric mapping usually required. Moreover, the positivity of the Jacobian is guaranteed. Numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results. © 2009 John Wiley & Sons, Ltd. [less ▲] Detailed reference viewed: 273 (0 UL)The smoothed extended finite element method; Bordas, Stéphane ; et alin Proceedings of the 6th International Conference on Engineering Computational Technology (2008) This paper shows how the strain smoothing technique recently proposed by G.R.Liu [1] coined as smoothed finite element method (SFEM) can be coupled to partition of unity methods, namely extended finite ... [more ▼] This paper shows how the strain smoothing technique recently proposed by G.R.Liu [1] coined as smoothed finite element method (SFEM) can be coupled to partition of unity methods, namely extended finite element method (XFEM) [2] to give birth to the smoothed extended finite element method (SmXFEM), which shares properties both with the SFEM and the XFEM. The proposed method suppresses the need to compute and integrate the derivatives of shape functions (which are singular at the tip in linear elastic fracture mechanics). Additionally, integration is performed along the boundary of the finite elements or smoothing cells and no isoparametric mapping is required, which allows elements of arbitrary shape. We present numerical results for cracks in linear elastic fracture mechanics problems. The method is verified on several examples and comparisons are made to the conventional XFEM. © 2008 Civil-Comp Press. [less ▲] Detailed reference viewed: 223 (2 UL)
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