Journal ArticleDOI
On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)
Stéphane Bordas,Stéphane Bordas,Sundararajan Natarajan,Pierre Kerfriden,Pierre Kerfriden,Charles E. Augarde,D. Roy Mahapatra,Timon Rabczuk,Stefano Dal Pont +8 more
TLDR
In this article, Chen et al. extended the strain smoothing to higher order elements and investigated numerically in which condition strain-smoothing is beneficial to accuracy and convergence of enriched finite element approximations.Abstract:
By using the strain smoothing technique proposed by Chen et al. (Comput. Mech. 2000; 25: 137-156) for meshless methods in the context of the finite element method (FEM), Liu et al. (Comput. Mech. 2007; 39(6): 859-877) developed the Smoothed FEM (SFEM). Although the SFEM is not yet well understood mathematically, numerical experiments point to potentially useful features of this particularly simple modification of the FEM. To date, the SFEM has only been investigated for bilinear and Wachspress approximations and is limited to linear reproducing conditions. The goal of this paper is to extend the strain smoothing to higher order elements and to investigate numerically in which condition strain smoothing is beneficial to accuracy and convergence of enriched finite element approximations. We focus on three widely used enrichment schemes, namely: (a) weak discontinuities; (b) strong discontinuities; (c) near-tip linear elastic fracture mechanics functions. The main conclusion is that strain smoothing in enriched approximation is only beneficial when the enrichment functions are polynomial (cases (a) and (b)), but that non-polynomial enrichment of type (c) lead to inferior methods compared to the standard enriched FEM (e.g. XFEM). Copyright (C) 2011 John Wiley & Sons, Ltd.read more
Citations
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Journal ArticleDOI
An extended isogeometric thin shell analysis based on Kirchhoff-Love theory
Nhon Nguyen-Thanh,N. Valizadeh,Minh Nguyen,Hung Nguyen-Xuan,Xiaoying Zhuang,Pedro M. A. Areias,Goangseup Zi,Yuri Bazilevs,L. De Lorenzis,Timon Rabczuk,Timon Rabczuk +10 more
TL;DR: An extended isogeometric element formulation (XIGA) for analysis of through-the-thickness cracks in thin shell structures is developed in this article, where the discretization is based on Non-Uniform Rational B-Splines (NURBS).
Journal ArticleDOI
Element-wise fracture algorithm based on rotation of edges
TL;DR: In this article, the authors proposed an alternative, simpler algorithm for FEM-based computational fracture in brittle, quasi-brittle and ductile materials based on edge rotations.
Journal ArticleDOI
Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth
TL;DR: In this article, a strain smoothing procedure for the extended finite element method (XFEM) is presented, which is tailored to linear elastic fracture mechanics and, in this context, to outperform the standard XFEM.
Journal ArticleDOI
Efficient coarse graining in multiscale modeling of fracture
Pattabhi R. Budarapu,Robert Gracie,Shih Wei Yang,Shih Wei Yang,Xiaoying Zhuang,Timon Rabczuk,Timon Rabczuk +6 more
TL;DR: In this paper, a coarse-graining technique is proposed to reduce a given atomistic model into an equivalent coarse grained continuum model, tailored for problems involving complex crack patterns in 2D and 3D including crack branching and coalescence.
Journal ArticleDOI
Smoothed Finite Element Methods (S-FEM): An Overview and Recent Developments
Wei Zeng,Gui-Rong Liu +1 more
TL;DR: The smoothed finite element methods (S-FEM) as discussed by the authors are a family of methods formulated through carefully designed combinations of the standard FEM and some of the techniques from the mesh free methods.
References
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Journal ArticleDOI
Elastic crack growth in finite elements with minimal remeshing
Ted Belytschko,T. Black +1 more
TL;DR: In this article, a minimal remeshing finite element method for crack growth is presented, where Discontinuous enrichment functions are added to the finite element approximation to account for the presence of the crack.
Journal ArticleDOI
The Partition of Unity Method
Ivo Babuška,Jens Markus Melenk +1 more
TL;DR: In this article, a new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved, which can therefore be more efficient than the usual finite element methods.
Journal ArticleDOI
A stabilized conforming nodal integration for Galerkin mesh-free methods
TL;DR: In this paper, a strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integrations, where an integration constraint is introduced as a necessary condition for a linear exactness in the mesh-free Galerkin approximation.
Journal ArticleDOI
Modeling holes and inclusions by level sets in the extended finite-element method
TL;DR: In this paper, a methodology to model arbitrary holes and material interfaces (inclusions) without meshing the internal boundaries is proposed, which couples the level set method with the extended finite element method (X-FEM).
Journal ArticleDOI
Arbitrary discontinuities in finite elements
TL;DR: In this article, a technique for modeling arbitrary discontinuities in finite elements is presented, in which both the signed distance function and its derivatives are considered, and a standard displacement Galerkin method is used for developing the discrete equations.