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On the Smoothed eXtended Finite Element Method for Continuum [PDF]
, 2009 In this paper, we combine the strain smoothing technique proposed by Liu et al [1] coined as the smoothed finite element method (SFEM) to partition of unity methods, namely the extended finite element method (XFEM) [2] to give birth to the smoothed extended finite element method (SmXFEM) [3].
Natarajan, Sundararajan +3 more
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Extended finite element method for three-dimensional crack modelling [PDF]
International Journal for Numerical Methods in Engineering, 2000 International audienceAn extended finite element method (X‐FEM) for three‐dimensional crack modelling is described. A discontinuous function and the two‐dimensional asymptotic crack‐tip displacement fields are added to the finite element approximation to
N Sukumar, T Belytschko, Nicolas Moes
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hp‐adaptive extended finite element method
International Journal for Numerical Methods in Engineering, 2011SUMMARYThis paper discusses higher‐order extended finite element methods (XFEMs) obtained from the combination of the standard XFEM with higher‐order FEMs. Here, the focus is on the embedding of the latter into the partition of unity method, which is the basis of the XFEM.
Byfut, Andreas, Schröder, Andreas
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Extended finite element method for quasi‐brittle fracture
International Journal for Numerical Methods in Engineering, 2003AbstractA methodology for the simulation of quasi‐static cohesive crack propagation in quasi‐brittle materials is presented. In the framework of the recently proposed extended finite element method, the partition of unity property of nodal shape functions has been exploited to introduce a higher‐order displacement discontinuity in a standard finite ...
MARIANI, STEFANO, PEREGO, UMBERTO
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An extended finite element method for coupled Darcy–Stokes problems
International Journal for Numerical Methods in Engineering, 2022AbstractIn this article, we propose an extended finite element method to deal with coupled Darcy–Stokes problems with straight or curved interfaces. A mixed approximate form is presented based on Brezzi‐Douglas‐Marini finite element space and piecewise constant function space for Darcy equations, and a mixed approximate form is shown based on piecewise
Pei Cao, Jinru Chen
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Numerical aspects of the eXtended Finite Element Method
PAMM, 2005AbstractThe eXtended Finite Element Method (XFEM) is a very efficient way to reduce mesh dependencies when analysing crack growth. Displacements and stresses around the crack tip are calculated using additional shape functions which span the analytical displacement field around a crack tip.In this paper the following numerical aspects of the XFEM are ...
Markus Peters, Klaus Hackl
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Efficient Implementation of Extended Finite Element Method
Volume 2: 32nd Computers and Information in Engineering Conference, Parts A and B, 2012Extended finite element method (or XFEM) locally enriches the finite element solution using a priori known analytical solution. XFEM has been used extensively in fracture mechanics to compute stress concentration at crack tips. It is a mesh independent method that allows crack to be represented as an equation instead of using the mesh to approximate it.
Vishal Hotwani, Ashok V. Kumar
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The Extended Finite Element Method
2014This chapter discusses level-set topology optimization methods where the governing state equations are discretized by the Extended Finite Element Method (XFEM). In contrast to conventional methods that map the level-set function into a density distribution of a fictitious material, the XFEM allow preserving the crisp geometry information of level-sets ...
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Appliance of the Extended Finite Element Method in Geomechanics
71st EAGE Conference and Exhibition incorporating SPE EUROPEC 2009, 2009Crack propagation weakens the integrity of a structure, e.g., of rock mass and may eventually lead to failure of a whole structure. Since physical experiments to study the complex nature of rock mass behaviour and related fracturing are often not ...
A. Byfut +3 more
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An Integration Scheme of Extended Finite Element Method
Applied Mechanics and Materials, 2011A simple integration scheme is presented for numerical integration in the extended finite element method(XFEM). In this scheme, the integral domain of common triangular mesh is converted to that of standard triangular mesh and the integral domain of standard triangular mesh is converted to that of quadrilateral mesh.
Lin Sheng Li, Chang Jun Qiu, Lan Li
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