TY - CHAP
A1 - Nguyen-Thanh, Nhon
A1 - Nguyen-Xuan, Hung
A1 - Bordas, Stéphane Pierre Alain
A1 - Rabczuk, Timon
T1 - Isogeometric finite element analysis using polynomial splines over hierarchical T-meshes
N2 - Isogeometric finite element analysis has become a powerful alternative to standard finite elements due to their flexibility in handling complex geometries. One major drawback of NURBS based isogeometric finite elements is their less effectiveness of local refinement. In this study, we present an alternative to NURBS based isogeometric finite elements that allow for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. We will demonstrate the efficiency of the proposed method by two numerical examples.
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2010
U6 - http://dx.doi.org/10.1088/1757-899X/10/1/012238
ER -
TY - JOUR
A1 - Nguyen-Thanh, Nhon
A1 - Rabczuk, Timon
A1 - Nguyen-Xuan, Hung
A1 - Bordas, Stéphane Pierre Alain
T1 - An alternative alpha finite element method (A?FEM) free and forced vibration analysis of solids using triangular meshes
JF - Journal of Computational and Applied Mathematics
N2 - An alternative alpha finite element method (A?FEM) free and forced vibration analysis of solids using triangular meshes
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2009
SP - 2112
EP - 2135
ER -
TY - JOUR
A1 - Nguyen-Xuan, Hung
A1 - Rabczuk, Timon
A1 - Nguyen-Thanh, Nhon
A1 - Nguyen-Thoi, T.
A1 - Bordas, Stéphane Pierre Alain
T1 - A node-based smoothed finite element method (NS-FEM) for analysis of Reissner-Mindlin plates
JF - Computational Mechanics
N2 - A node-based smoothed finite element method (NS-FEM) for analysis of Reissner-Mindlin plates
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2010
SP - 679
EP - 701
ER -
TY - JOUR
A1 - Nguyen-Thanh, Nhon
A1 - Rabczuk, Timon
A1 - Nguyen-Xuan, Hung
A1 - Bordas, Stéphane Pierre Alain
T1 - An alternative alpha finite element method with stabilized discrete shear gap technique for analysis of Mindlin-Reissner plates
JF - Finite Elements in Analysis & Design
N2 - An alternative alpha finite element method with stabilized discrete shear gap technique for analysis of Mindlin-Reissner plates
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2011
SP - 519
EP - 535
ER -
TY - JOUR
A1 - Nguyen-Thanh, Nhon
A1 - Nguyen-Xuan, Hung
A1 - Bordas, Stéphane Pierre Alain
A1 - Rabczuk, Timon
T1 - Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids
JF - Computer Methods in Applied Mechanics and Engineering
N2 - Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2011
SP - 1892
EP - 1908
ER -
TY - JOUR
A1 - Simpson, R.
A1 - Bordas, Stéphane Pierre Alain
A1 - Trevelyan, J.
A1 - Kerfriden, Pierre
A1 - Rabczuk, Timon
T1 - An Isogeometric Boundary Element Method for elastostatic analysis
JF - Computer Methods in Applied Mechanics and Engineering
N2 - The concept of isogeometric analysis, where functions that are used to describe geometry in CAD software are used to approximate the unknown fields in numerical simulations, has received great attention in recent years. The method has the potential to have profound impact on engineering design, since the task of meshing, which in some cases can add significant overhead, has been circumvented. Much of the research effort has been focused on finite element implementations of the isogeometric concept, but at present, little has been seen on the application to the Boundary Element Method. The current paper proposes an Isogeometric Boundary Element Method (BEM), which we term IGABEM, applied to two-dimensional elastostatic problems using Non-Uniform Rational B-Splines (NURBS). We find it is a natural fit with the isogeometric concept since both the NURBS approximation and BEM deal with quantities entirely on the boundary. The method is verified against analytical solutions where it is seen that superior accuracies are achieved over a conventional quadratic isoparametric BEM implementation.
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2012
U6 - http://dx.doi.org/10.1016/j.cma.2011.08.008
ER -
TY - JOUR
A1 - Chen, Lei
A1 - Rabczuk, Timon
A1 - Liu, G.R.
A1 - Zeng, K.Y.
A1 - Kerfriden, Pierre
A1 - Bordas, Stéphane Pierre Alain
T1 - Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth
JF - Computer Methods in Applied Mechanics and Engineering
N2 - This paper presents a strain smoothing procedure for the extended finite element method (XFEM). The resulting “edge-based” smoothed extended finite element method (ESm-XFEM) is tailored to linear elastic fracture mechanics and, in this context, to outperform the standard XFEM. In the XFEM, the displacement-based approximation is enriched by the Heaviside and asymptotic crack tip functions using the framework of partition of unity. This eliminates the need for the mesh alignment with the crack and re-meshing, as the crack evolves. Edge-based smoothing (ES) relies on a generalized smoothing operation over smoothing domains associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, “super-convergence” and “ultra-accurate” solutions. The present method takes advantage of both the ES-FEM and the XFEM. Thanks to the use of strain smoothing, the subdivision of elements intersected by discontinuities and of integrating the (singular) derivatives of the approximation functions is suppressed via transforming interior integration into boundary integration. Numerical examples show that the proposed method improves significantly the accuracy of stress intensity factors and achieves a near optimal convergence rate in the energy norm even without geometrical enrichment or blending correction.
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2012
U6 - http://dx.doi.org/10.1016/j.cma.2011.08.013
ER -
TY - JOUR
A1 - Nguyen-Vinh, H.
A1 - Bakar, I.
A1 - Msekh, Mohammed Abdulrazzak
A1 - Song, Jeong-Hoon
A1 - Muthu, Jacob
A1 - Zi, Goangseup
A1 - Le, P.
A1 - Bordas, Stéphane Pierre Alain
A1 - Simpson, R.
A1 - Natarajan, S.
A1 - Lahmer, Tom
A1 - Rabczuk, Timon
T1 - Extended Finite Element Method for Dynamic Fracture of Piezo-Electric Materials
JF - Engineering Fracture Mechanics
N2 - We present an extended finite element formulation for dynamic fracture of piezo-electric materials. The method is developed in the context of linear elastic fracture mechanics. It is applied to mode I and mixed mode-fracture for quasi-steady cracks. An implicit time integration scheme is exploited. The results are compared to results obtained with the boundary element method and show excellent agreement.
KW - Angewandte Mathematik
KW - Stochastik
KW - Strukturmechanik
Y1 - 2012
U6 - http://dx.doi.org/10.1016/j.engfracmech.2012.04.025
SP - 19
EP - 31
ER -
TY - JOUR
A1 - Natarajan, S.
A1 - Chakraborty, S.
A1 - Thangavel, M.
A1 - Bordas, Stéphane Pierre Alain
A1 - Rabczuk, Timon
T1 - Size dependent free flexural vibration behavior of functionally graded nanoplates
JF - Computational Materials Science
N2 - Size dependent free flexural vibration behavior of functionally graded nanoplates
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2012
SP - 74
EP - 80
ER -
TY - JOUR
A1 - Nguyen-Xuan, Hung
A1 - Liu, G.R.
A1 - Bordas, Stéphane Pierre Alain
A1 - Natarajan, S.
A1 - Rabczuk, Timon
T1 - An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order
JF - Computer Methods in Applied Mechanics and Engineering
N2 - An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2013
SP - 252
EP - 273
ER -