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 - Talebi, Hossein
A1 - Silani, Mohammad
A1 - Bordas, Stéphane Pierre Alain
A1 - Kerfriden, Pierre
A1 - Rabczuk, Timon
T1 - Molecular Dynamics/XFEM Coupling by a Three-Dimensional Extended Bridging Domain with Applications to Dynamic Brittle Fracture
JF - International Journal for Multiscale Computational Engineering
N2 - Molecular Dynamics/XFEM Coupling by a Three-Dimensional Extended Bridging Domain with Applications to Dynamic Brittle Fracture
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2013
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 - Talebi, Hossein
A1 - Silani, Mohammad
A1 - Bordas, Stéphane Pierre Alain
A1 - Kerfriden, Pierre
A1 - Rabczuk, Timon
T1 - A computational library for multiscale modeling of material failure
JF - Computational Mechanics
N2 - A computational library for multiscale modeling of material failure
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2014
ER -
TY - JOUR
A1 - Nguyen, V.P.
A1 - Kerfriden, Pierre
A1 - Bordas, Stéphane Pierre Alain
A1 - Rabczuk, Timon
T1 - Isogeometric analysis suitable trivariate NURBS representation of composite panels with a new offset algorithm
JF - Computer-Aided Design
N2 - Isogeometric analysis suitable trivariate NURBS representation of composite panels with a new offset algorithm
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2014
ER -
TY - JOUR
A1 - Kerfriden, Pierre
A1 - Goury, O.
A1 - Rabczuk, Timon
A1 - Bordas, Stéphane Pierre Alain
T1 - A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics
JF - Computer Methods in Applied Mechanics and Engineering
N2 - A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2013
SP - 169
EP - 188
ER -
TY - JOUR
A1 - Beex, L.A.A.
A1 - Kerfriden, Pierre
A1 - Rabczuk, Timon
A1 - Bordas, Stéphane Pierre Alain
T1 - Quasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation
JF - Computer Methods in Applied Mechanics and Engineering
N2 - Quasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2014
ER -
TY - JOUR
A1 - Kerfriden, Pierre
A1 - Schmidt, K.M.
A1 - Rabczuk, Timon
A1 - Bordas, Stéphane Pierre Alain
T1 - Statistical extraction of process zones and representative subspaces in fracture of random composites
JF - International Journal for Multiscale Computational Engineering
N2 - Statistical extraction of process zones and representative subspaces in fracture of random composites
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2013
ER -
TY - JOUR
A1 - Ghasemi, Hamid
A1 - Kerfriden, Pierre
A1 - Bordas, Stéphane Pierre Alain
A1 - Muthu, Jacob
A1 - Zi, Goangseup
A1 - Rabczuk, Timon
T1 - Interfacial shear stress optimization in sandwich beams with polymeric core using nonuniform distribution of reinforcing ingredients
JF - Composite Structures
N2 - Interfacial shear stress optimization in sandwich beams with polymeric core using nonuniform distribution of reinforcing ingredients
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 221
EP - 230
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 - 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 - Thai, Chien H.
A1 - Nguyen-Xuan, Hung
A1 - Bordas, Stéphane Pierre Alain
A1 - Nguyen-Thanh, Nhon
A1 - Rabczuk, Timon
T1 - Isogeometric analysis of laminated composite plates using the higher-order shear deformation theory
JF - Mechanics of Advanced Materials and Structures
N2 - Isogeometric analysis of laminated composite plates using the higher-order shear deformation theory
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 451
EP - 469
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 - 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 - Ilyani Akmar, A.B.
A1 - Lahmer, Tom
A1 - Bordas, Stéphane Pierre Alain
A1 - Beex, L.A.A.
A1 - Rabczuk, Timon
T1 - Uncertainty quantification of dry woven fabrics: A sensitivity analysis on material properties
JF - Composite Structures
N2 - Uncertainty quantification of dry woven fabrics: A sensitivity analysis on material properties
KW - Angewandte Mathematik
KW - Stochastik
KW - Strukturmechanik
Y1 - 2014
U6 - http://dx.doi.org/10.1016/j.compstruct.2014.04.014
SP - 1
EP - 17
ER -
TY - JOUR
A1 - Nguyen-Xuan, Hung
A1 - Nguyen, Hiep Vinh
A1 - Bordas, Stéphane Pierre Alain
A1 - Rabczuk, Timon
A1 - Duflot, Marc
T1 - A cell-based smoothed finite element method for three dimensional solid structures
JF - KSCE Journal of Civil Engineering
N2 - This paper extends further the strain smoothing technique in finite elements to 8-noded hexahedral elements (CS-FEM-H8). The idea behind the present method is similar to the cell-based smoothed 4-noded quadrilateral finite elements (CS-FEM-Q4). In CSFEM, the smoothing domains are created based on elements, and each element can be further subdivided into 1 or several smoothing cells. It is observed that: 1) The CS-FEM using a single smoothing cell can produce higher stress accuracy, but insufficient rank and poor displacement accuracy; 2) The CS-FEM using several smoothing cells has proper rank, good displacement accuracy, but lower stress accuracy, especially for nearly incompressible and bending dominant problems. We therefore propose 1) an extension of strain smoothing to 8-noded hexahedral elements and 2) an alternative CS-FEM form, which associates the single smoothing cell issue with multi-smoothing cell one via a stabilization technique. Several numerical examples are provided to show the reliability and accuracy of the present formulation.
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2014
U6 - http://dx.doi.org/10.1007/s12205-012-1515-7
SP - 1230
EP - 1242
ER -
TY - JOUR
A1 - Valizadeh, N.
A1 - Natarajan, S.
A1 - Gonzalez-Estrada, O.A.
A1 - Rabczuk, Timon
A1 - Tinh Quoc, Bui
A1 - Bordas, Stéphane Pierre Alain
T1 - NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter
JF - Composite Structures
N2 - NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2013
SP - 309
EP - 326
ER -
TY - JOUR
A1 - Budarapu, Pattabhi Ramaiah
A1 - Gracie, Robert
A1 - Bordas, Stéphane Pierre Alain
A1 - Rabczuk, Timon
T1 - An adaptive multiscale method for quasi-static crack growth
JF - Computational Mechanics
N2 - This paper proposes an adaptive atomistic- continuum numerical method for quasi-static crack growth. The phantom node method is used to model the crack in the continuum region and a molecular statics model is used near the crack tip. To ensure self-consistency in the bulk, a virtual atom cluster is used to model the material of the coarse scale. The coupling between the coarse scale and fine scale is realized through ghost atoms. The ghost atom positions are interpolated from the coarse scale solution and enforced as boundary conditions on the fine scale. The fine scale region is adaptively enlarged as the crack propagates and the region behind the crack tip is adaptively coarsened. An energy criterion is used to detect the crack tip location. The triangular lattice in the fine scale region corresponds to the lattice structure of the (111) plane of an FCC crystal. The Lennard-Jones potential is used to model the atom–atom interactions. The method is implemented in two dimensions. The results are compared to pure atomistic simulations; they show excellent agreement.
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2014
U6 - http://dx.doi.org/10.1007/s00466-013-0952-6
SP - 1129
EP - 1148
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 -
TY - JOUR
A1 - Bakar, I.
A1 - Kramer, O.
A1 - Bordas, Stéphane Pierre Alain
A1 - Rabczuk, Timon
T1 - Optimization of Elastic Properties and Weaving Patterns of Woven Composites
JF - Composite Structures
N2 - Optimization of Elastic Properties and Weaving Patterns of Woven Composites
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2013
SP - 575
EP - 591
ER -
TY - JOUR
A1 - Chen, Lei
A1 - Nguyen-Thanh, Nhon
A1 - Nguyen-Xuan, Hung
A1 - Rabczuk, Timon
A1 - Bordas, Stéphane Pierre Alain
A1 - Limbert, Georges
T1 - Explicit finite deformation analysis of isogeometric membranes
JF - Computer Methods in Applied Mechanics and Engineering
N2 - Explicit finite deformation analysis of isogeometric membranes
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2014
SP - 104
EP - 130
ER -
TY - JOUR
A1 - Thai, Chien H.
A1 - Ferreira, A.J.M.
A1 - Bordas, Stéphane Pierre Alain
A1 - Rabczuk, Timon
A1 - Nguyen-Xuan, Hung
T1 - Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory
JF - European Journal of Mechanics
N2 - Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2014
SP - 89
EP - 108
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 - 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 - Yang, Shih-Wei
A1 - Budarapu, Pattabhi Ramaiah
A1 - Mahapatra, D.R.
A1 - Bordas, Stéphane Pierre Alain
A1 - Zi, Goangseup
A1 - Rabczuk, Timon
T1 - A Meshless Adaptive Multiscale Method for Fracture
JF - Computational Materials Science
N2 - A Meshless Adaptive Multiscale Method for Fracture
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 382
EP - 395
ER -