References of "Bordas, Stéphane 50000969"
     in
Bookmark and Share    
Full Text
See detailEnriched Element Free Galerkin Method for Gradient Elasticity
Natarajan, S; Kerfriden, P; Bordas, Stéphane UL et al

Scientific Conference (2011, June)

Detailed reference viewed: 105 (0 UL)
Full Text
See detailNatural frequencies of cracked isotropic & specially orthotropic plates using the extended finite element method
Natarajan, S; Baiz, P; Mahapatra, D Roy et al

Scientific Conference (2011, April)

In this paper, the linear free flexural vibration of cracked isotropic and specially orthotropic plates is studied using the extended finite element method. The mixed interpolation technique of the well ... [more ▼]

In this paper, the linear free flexural vibration of cracked isotropic and specially orthotropic plates is studied using the extended finite element method. The mixed interpolation technique of the well- established MITC4 [1] quadrilateral finite element with 12 standard degrees of freedom per element is used for this study. The natural frequencies of simply supported square plates are computed as a function of crack length and crack location. [less ▲]

Detailed reference viewed: 119 (1 UL)
Full Text
Peer Reviewed
See detailA robust preconditioning technique for the extended finite element method
Menk, A.; Bordas, Stéphane UL

in International Journal for Numerical Methods in Engineering (2011), 85(13), 1609-1632

The extended finite element method enhances the approximation properties of the finite element space by using additional enrichment functions. But the resulting stiffness matrices can become ill ... [more ▼]

The extended finite element method enhances the approximation properties of the finite element space by using additional enrichment functions. But the resulting stiffness matrices can become ill-conditioned. In that case iterative solvers need a large number of iterations to obtain an acceptable solution. In this paper a procedure is described to obtain stiffness matrices whose condition number is close to the one of the finite element matrices without any enrichments. A domain decomposition is employed and the algorithm is very well suited for parallel computations. The method was tested in numerical experiments to show its effectiveness. The experiments have been conducted for structures containing cracks and material interfaces. We show that the corresponding enrichments can result in arbitrarily ill-conditioned matrices. The method proposed here, however, provides well-conditioned matrices and can be applied to any sort of enrichment. The complexity of this approach and its relation to the domain decomposition is discussed. Computation times have been measured for a structure containing multiple cracks. For this structure the computation times could be decreased by a factor of 2. © 2010 John Wiley & Sons, Ltd. [less ▲]

Detailed reference viewed: 629 (0 UL)
Full Text
Peer Reviewed
See detailAccurate evaluation of K in XFEM using error estimation in quantities of interest based on equilibrated recovery
González-Estrada, O. A.; Ródenas, J. J.; Nadal, E. et al

in Bordas, Stéphane; Kerfriden, P (Eds.) 2nd International Conference on the Extended Finite Element Method (2011)

Detailed reference viewed: 94 (0 UL)
Full Text
Peer Reviewed
See detailOn the use of recovery techniques for accurate error estimation and error bounding in XFEM
Ródenas, J. J.; González-Estrada, O. A.; Fuenmayor, F. J. et al

in Bordas, Stéphane; Kerfriden, Pierre (Eds.) 2nd International Conference on the Extended Finite Element Method (2011)

Detailed reference viewed: 74 (1 UL)
Full Text
Peer Reviewed
See detailEstimación precisa del error en magnitudes de interés mediante técnicas de recovery con equilibrio local
Nadal, E.; Ródenas, J. J.; González-Estrada, O. A. et al

in Congress on Numerical Methods in Engineering (2011)

Detailed reference viewed: 96 (1 UL)
Full Text
Peer Reviewed
See detailEquilibrated patch recovery for accurate evaluation of upper error bounds in quantities of interest
González-Estrada, Octavio Andrés; Ródenas, J J; Nadal, Enrique et al

in Audry, D; Díez, P; Tie, B (Eds.) et al Adaptive Modeling and Simulation. Proceedings of V ADMOS 2011 (2011)

Detailed reference viewed: 88 (0 UL)
Full Text
Peer Reviewed
See detailAccurate evaluation of stress intensity factors using error estimation in quantities of interest based on equilibrated recovery
González-Estrada, O. A.; Ródenas, J. J.; Bordas, Stéphane UL et al

in Oliver, J; Jirasek, M; Allix, O (Eds.) et al Computational Modeling of Fracture and Failure of Materials and Structures. Proceedings of CFRAC 2011 (2011)

During the last years the use of error estimators which measure the error in a quantity of interest defined by the analyst, instead of the energy norm, have become increasingly popular as they provide an ... [more ▼]

During the last years the use of error estimators which measure the error in a quantity of interest defined by the analyst, instead of the energy norm, have become increasingly popular as they provide an error indicator for goal oriented adaptivity procedures. In this paper we propose an a posteriori recovery-based error estimation procedure which considers the stress intensity factor K typical of singular problems as the quantity of interest in finite element (FE) approximations. In general, error estimators in quantities of interest have been based on residual techniques and, although recovery techniques have been often preferred when considering the error in energy norm due to their robustness and simplicity, so far, there is no available procedure which considers an equilibrated recovery technique that can be used in standard FE frameworks. In [1] a standard SPR recovery technique is used to obtain an error measure of the J-integral, which is closely related to the value of the SIF. However, it does not consider any equilibrium constraints or the singularity near the crack tip, thus the obtained recovered stress field is not well suited for this kind of problems. The technique proposed herein relies on the enhanced superconvergent patch recovery technique presented in [2] to evaluate highly accurate recovered stress fields of the primal and dual problems, which are then used to obtain a sharp error estimate. The primal problem is simply the problem under analysis. To formulate the dual problem we consider the linear interaction integral representing K to obtain the applied loads of the dual FE approximation to solve. The high accuracy of the recovered stress fields for both the primal and dual solutions is obtained by decomposing the raw stress field obtained from the finite element approximations into singular and smooth parts, and enforcing the fulfilment of boundary and internal equilibrium equations. The results indicate an accurate estimation of the error in K for benchmark problems with exact solution. [less ▲]

Detailed reference viewed: 111 (1 UL)
Full Text
Peer Reviewed
See detailEnhanced recovery techniques for accurate evaluation of error estimates in FE aproximations
González-Estrada, O. A.; Ródenas, J. J.; Bordas, Stéphane UL et al

in Laghrouche, O; El Kacimi, A; Woodwaed, P (Eds.) et al 19th UK National Conference of the Association for Computational Mechanics in Engineering (2011)

When modelling critical structures, it is crucial to rationally assess the outcome of numerical simu- lations. Specifically, error estimation strategies are key tools in critical decision-based processes ... [more ▼]

When modelling critical structures, it is crucial to rationally assess the outcome of numerical simu- lations. Specifically, error estimation strategies are key tools in critical decision-based processes. The development of design tools that enhance performance of the final product and give reliability on the calculations is essential in todays industrial environment, which increasingly seeks to reduce develop- ment times for new products while improving the quality. During the last years there has been an increasing interest on the use of error estimates which help to measure and control the error committed in standard or enriched finite element approximations. The error can be defined in terms of energy norm or in quantities relevant for design purposes (such as the mean stress value in a particular area, displacements, the stress intensity factor for fracture problems). In this work, we discuss the use of different a posteriori recovery techniques to evaluate error estimates for different finite element (FE) approximations. These techniques are based on equilibrated supercon- vergent patch recovery or equilibrated moving least squares procedures and can be used in smooth or singular problems. Numerical results show the capabilities of the proposed techniques to provide good error estimates. [less ▲]

Detailed reference viewed: 91 (0 UL)
Full Text
Peer Reviewed
See detailNatural frequencies of cracked functionally graded material plates by the extended finite element method
Natarajan, S.; Baiz, P. M.; Bordas, Stéphane UL et al

in Composite Structures (2011), 93(11), 3082-3092

In this paper, the linear free flexural vibration of cracked functionally graded material plates is studied using the extended finite element method. A 4-noded quadrilateral plate bending element based on ... [more ▼]

In this paper, the linear free flexural vibration of cracked functionally graded material plates is studied using the extended finite element method. A 4-noded quadrilateral plate bending element based on field and edge consistency requirement with 20 degrees of freedom per element is used for this study. The natural frequencies and mode shapes of simply supported and clamped square and rectangular plates are computed as a function of gradient index, crack length, crack orientation and crack location. The effect of thickness and influence of multiple cracks is also studied. © 2011 Elsevier Ltd. [less ▲]

Detailed reference viewed: 153 (0 UL)
Full Text
Peer Reviewed
See detailLinear buckling analysis of cracked plates by SFEM and XFEM
Baiz, P. M.; Natarajan, S.; Bordas, Stéphane UL et al

in Journal of Mechanics of Material and Structures (2011), 6(9-10), 1213-1238

In this paper, the linear buckling problem for isotropic plates is studied using a quadrilateral element with smoothed curvatures and the extended finite element method. First, the curvature at each point ... [more ▼]

In this paper, the linear buckling problem for isotropic plates is studied using a quadrilateral element with smoothed curvatures and the extended finite element method. First, the curvature at each point is obtained by a nonlocal approximation via a smoothing function. This element is later coupled with partition of unity enrichment to simplify the simulation of cracks. The proposed formulation suppresses locking and yields elements which behave very well, even in the thin plate limit. The buckling coefficient and mode shapes of square and rectangular plates are computed as functions of crack length, crack location, and plate thickness. The effects of different boundary conditions are also studied. © 2011 by Mathematical Sciences Publishers. [less ▲]

Detailed reference viewed: 189 (0 UL)
Full Text
Peer Reviewed
See detailOn the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)
Bordas, Stéphane UL; Natarajan, S.; Kerfriden, P. et al

in International Journal for Numerical Methods in Engineering (2011), 86(4-5), 637-666

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 ... [more ▼]

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). © 2011 John Wiley & Sons, Ltd. [less ▲]

Detailed reference viewed: 202 (1 UL)
Full Text
Peer Reviewed
See detailA node-based smoothed extended finite element method (NS-XFEM) for fracture analysis
Vu-Bac, N.; Nguyen-Xuan, H.; Chen, L. et al

in Computer Modeling in Engineering and Sciences (2011), 73(4), 331-355

This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into the extended finite element method (XFEM) to form a novel numerical method (NS-XFEM) for analyzing fracture ... [more ▼]

This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into the extended finite element method (XFEM) to form a novel numerical method (NS-XFEM) for analyzing fracture problems of 2D elasticity. NS-FEM uses the strain smoothing technique over the smoothing domains associated with nodes to compute the system stiffness matrix, which leads to the line integrations using directly the shape function values along the boundaries of the smoothing domains. As a result, we avoid integration of the stress singularity at the crack tip. It is not necessary to divide elements cut by cracks when we replace interior integration by boundary integration, simplifying integration of the discontinuous approximation. The key advantage of the NS-XFEM is that it provides more accurate solutions compared to the XFEM-T3 element. We will show for two numerical examples that the NS-XFEM significantly improves the results in the energy norm and the stress intensity factors. For the examples studied, we obtain super-convergent results. [less ▲]

Detailed reference viewed: 51 (2 UL)
Full Text
Peer Reviewed
See detailCrack growth calculations in solder joints based on microstructural phenomena with X-FEM
Menk, Alexander; Bordas, Stéphane UL

in Computational Materials Science (2011), 50(3), 1145-1156

Determining the lifetime of solder joints subjected to thermomechanical loads is crucial to guarantee the quality of electronic devices. The fatigue process is heavily dependent on the microstructure of ... [more ▼]

Determining the lifetime of solder joints subjected to thermomechanical loads is crucial to guarantee the quality of electronic devices. The fatigue process is heavily dependent on the microstructure of the joints. We present a new methodology to determine the lifetime of the joints based on microstructural phenomena. Random microstructures are generated to capture the statistical variety of possible microstructures and crack growth calculations are performed. The extended finite element method is used to solve the structural problem numerically which allows a complete automation of the process. Numerical examples are given and compared to experimental data. [less ▲]

Detailed reference viewed: 97 (0 UL)
Full Text
Peer Reviewed
See detailAn alternative alpha finite element method with discrete shear gap technique for analysis of isotropic Mindlin-Reissner plates
Nguyen-Thanh, N.; Rabczuk, Timon; Nguyen-Xuan, H. et al

in Finite Elements in Analysis and Design (2011), 47(5), 519-535

An alternative alpha finite element method (AαFEM) coupled with a discrete shear gap technique for triangular elements is presented to significantly improve the accuracy of the standard triangular finite ... [more ▼]

An alternative alpha finite element method (AαFEM) coupled with a discrete shear gap technique for triangular elements is presented to significantly improve the accuracy of the standard triangular finite elements for static, free vibration and buckling analyses of MindlinReissner plates. In the AαFEM, the piecewise constant strain field of linear triangular elements is enhanced by additional strain terms with an adjustable parameter α which results in an effectively softer stiffness formulation compared to the linear triangular element. To avoid the transverse shear locking, the discrete shear gap technique (DSG) is utilized and a novel triangular element, the Aα-DSG3 is obtained. Several numerical examples show that the Aα-DSG3 achieves high reliability compared to other existing elements in the literature. Through selection of α, under or over estimation of the strain energy can be achieved. [less ▲]

Detailed reference viewed: 93 (2 UL)
Full Text
Peer Reviewed
See detailBridging proper orthogonal decomposition methods and augmented Newton-Krylov algorithms: An adaptive model order reduction for highly nonlinear mechanical problems
Kerfriden, P.; Gosselet, P.; Adhikari, S. et al

in Computer Methods in Applied Mechanics and Engineering (2011), 200(5-8), 850-866

This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, " on-the-fly ... [more ▼]

This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, " on-the-fly" , the reduced order modelling of highly nonlinear problems undergoing strong topological changes. Damage initiation problems tackled via a corrected hyperreduction method are used as an example. It is shown that the relevancy of reduced order model can be significantly improved with reasonable additional costs when using this algorithm, even when strong topological changes are involved. © 2010. [less ▲]

Detailed reference viewed: 255 (10 UL)
Full Text
Peer Reviewed
See detailFinite element analysis on implicitly defined domains: An accurate representation based on arbitrary parametric surfaces
Moumnassi, M.; Belouettar, S.; Béchet, T. et al

in Computer Methods in Applied Mechanics and Engineering (2011), 200(5-8), 774-796

In this paper, we present some novel results and ideas for robust and accurate implicit representation of geometric surfaces in finite element analysis. The novel contributions of this paper are threefold ... [more ▼]

In this paper, we present some novel results and ideas for robust and accurate implicit representation of geometric surfaces in finite element analysis. The novel contributions of this paper are threefold: (1) describe and validate a method to represent arbitrary parametric surfaces implicitly; (2) represent arbitrary solids implicitly, including sharp features using level sets and boolean operations; (3) impose arbitrary Dirichlet and Neumann boundary conditions on the resulting implicitly defined boundaries. The methods proposed do not require local refinement of the finite element mesh in regions of high curvature, ensure the independence of the domain's volume on the mesh, do not rely on boundary regularization, and are well suited to methods based on fixed grids such as the extended finite element method (XFEM). Numerical examples are presented to demonstrate the robustness and effectiveness of the proposed approach and show that it is possible to achieve optimal convergence rates using a fully implicit representation of object boundaries. This approach is one step in the desired direction of tying numerical simulations to computer aided design (CAD), similarly to the isogeometric analysis paradigm. © 2010 Elsevier B.V. [less ▲]

Detailed reference viewed: 478 (9 UL)
Full Text
Peer Reviewed
See detailA cell - based smoothed finite element method for free vibration and buckling analysis of shells
Thai-Hoang, Chien; Nguyen-Thanh, Nhon; Nguyen-Xuan, Hung et al

in KSCE Journal of Civil Engineering (2011), 15(2), 347-361

This paper further extends a cell-based smoothed finite element method for free vibration and buckling analysis of shells. A four-node quadrilateral Mindlin-Reissner shell element with a gradient ... [more ▼]

This paper further extends a cell-based smoothed finite element method for free vibration and buckling analysis of shells. A four-node quadrilateral Mindlin-Reissner shell element with a gradient smoothing operator is adopted. The membrane-bending and geometrical stiffness matrices are computed along the boundaries of the smoothing cells while the shear stiffness matrix is calculated by an independent interpolation in the natural coordinates as in the MITC4 (the Mixed Interpolation of Tensorial Components) element. Various numerical results are compared with existing exact and numerical solutions and they are in good agreement. The advantage of the present formulation is that it retains higher accurate than the MITC4 element even for heavily distorted meshes without increasing the computational cost. © 2011 Korean Society of Civil Engineers and Springer-Verlag Berlin Heidelberg. [less ▲]

Detailed reference viewed: 94 (1 UL)
Full Text
Peer Reviewed
See detailAccurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling
Zhuang, Xiaoying; Augarde, Charles; Bordas, Stéphane UL

in International Journal for Numerical Methods in Engineering (2011), 86(2), 249-268

Fracture modelling using numerical methods is well-advanced in 2D using techniques such as the extended finite element method (XFEM). The use of meshless methods for these problems lags somewhat behind ... [more ▼]

Fracture modelling using numerical methods is well-advanced in 2D using techniques such as the extended finite element method (XFEM). The use of meshless methods for these problems lags somewhat behind, but the potential benefits of no meshing (particularly in 3D) prompt continued research into their development. In methods where the crack face is not explicitly modelled (as the edge of an element for instance), two procedures are instead used to associate the displacement jump with the crack surface: the visibility criterion and the diffraction method. The visibility criterion is simple to implement and efficient to compute, especially with the help of level set coordinates. However, spurious discontinuities have been reported around crack tips using the visibility criterion, whereas implementing the diffraction method in 3D is much more complicated than the visibility criterion. In this paper, a tying procedure is proposed to remove the difficulty with the visibility criterion so that crack tip closure can be ensured while the advantages of the visibility criterion can be preserved. The formulation is based on the use of level set coordinates and the element-free Galerkin method, and is generally applicable for single or multiple crack problems in 2D or 3D. The paper explains the formulation and provides verification of the method against a number of 2D crack problems. [less ▲]

Detailed reference viewed: 101 (3 UL)