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See detailError estimation of recovered solutions in FE analysis. Higher order h-adaptive refinement strategies
Ródenas, J. J.; Nadal, E.; González-Estrada, O. A. et al

in Pimienta, P M (Ed.) 10th World Congress on Computational Mechanics (WCCM 2012) (2012)

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See detailError estimation in quantities of interest for XFEM using recovery techniques
González-Estrada, O. A.; Nadal, E.; Ródenas, J. J. et al

in Yang, Z J (Ed.) 20th UK National Conference of the Association for Computational Mechanics in Engineering (ACME) (2012)

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See detailPractical error bounds in energy norm based on a recovered displacement field
Nadal, E.; González-Estrada, O. A.; Ródenas, J. J. et al

in Pimienta, P M (Ed.) 10th World Congress on Computational Mechanics (WCCM 2012) (2012)

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See detailAccurate error estimate in energy norm using a nearly-equilibrated kinematically-admissible displacement recovery technique
Nadal, E.; González-Estrada, O. A.; Ródenas, J. J. et al

in Pimienta, P M (Ed.) 10th World Congress on Computational Mechanics (WCCM 2012) (2012)

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See detailError estimation and bounding in energy norm based on a displacement recovery technique
Nadal, E.; González-Estrada, O. A.; Ródenas, J. J. et al

in Eberhardsteiner, Josef; Böhm, Helmut; Rammerstorfer, F G (Eds.) 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) (2012)

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See detailExtended finite element method for dynamic fracture of piezo-electric materials
Nguyen-Vinh, H.; Bakar, I.; Msekh, M. A. et al

in Engineering Fracture Mechanics (2012), 92

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 ... [more ▼]

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. [less ▲]

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See detailRationalised computational time in fracture simulation: adaptive model reduction and domain decomposition
Goury, Olivier; Kerfriden, Pierre; Margetts, Lee et al

Scientific Conference (2011, June)

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See detailEnriched Element Free Galerkin Method for Gradient Elasticity
Natarajan, S; Kerfriden, P; Bordas, Stéphane UL et al

Scientific Conference (2011, June)

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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 ▲]

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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 ▲]

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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 ▲]

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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 ▲]

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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 & 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 ▲]

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See detailLifetime prediction for solder joints with the extended finite element method
Menk, Alexander; Pearce, Chris J.; Lanier, Olivier et al

in Proceedings of 12th Int. Conf. on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2011 (2011)

Predicting the lifetime of solder joints undergoing thermal cycling is crucial for the electronics industry in order to guarantee a certain performance of their products in the field. Semi-empirical ... [more ▼]

Predicting the lifetime of solder joints undergoing thermal cycling is crucial for the electronics industry in order to guarantee a certain performance of their products in the field. Semi-empirical methods are often used to predict the average lifetime of the critical joints. However, to get a reliable failure probability the standard deviation must also be addressed. The deviation of the lifetime from the mean value is a consequence of the variation in microstructure found in actual joints. We therefore propose a new methodology that calculates crack growth based on microstructural features of the joint. A series of random microstructures is generated. Crack growth calculations are performed for each of these structures. The structural problem is solved numerically with the extended finite element method which allows a complete automation of the process. The mean crack length and standard deviation are calculated from the crack growth simulations and the result is compared to experimental data. [less ▲]

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See detailLinear free flexural vibration of cracked functionally graded plates in thermal environment
Natarajan, S.; Baiz, P. M.; Ganapathi, M. et al

in Computers & Structures (2011), 89(15-16), 1535-1546

In this paper, the linear free flexural vibrations of functionally graded material plates with a through center crack is studied using an 8-noded shear flexible element. The material properties are ... [more ▼]

In this paper, the linear free flexural vibrations of functionally graded material plates with a through center crack is studied using an 8-noded shear flexible element. The material properties are assumed to be temperature dependent and graded in the thickness direction. The effective material properties are estimated using the Mori-Tanaka homogenization scheme. The formulation is developed based on first-order shear deformation theory. The shear correction factors are evaluated employing the energy equivalence principle. The variation of the plates natural frequency is studied considering various parameters such as the crack length, plate aspect ratio, skew angle, temperature, thickness and boundary conditions. The results obtained here reveal that the natural frequency of the plate decreases with increase in temperature gradient, crack length and gradient index. © 2011 Elsevier Ltd. All rights reserved. [less ▲]

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See detailIsogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids
Nguyen-Thanh, N.; Nguyen-Xuan, H.; Bordas, Stéphane UL et al

in Computer Methods in Applied Mechanics & Engineering (2011), 200(21-22), 1892-1908

Isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries. One of the major drawbacks of NURBS-based isogeometric finite ... [more ▼]

Isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries. One of the major drawbacks of NURBS-based isogeometric finite elements is the inefficiency of local refinement. In this study, we present an alternative to NURBS-based isogeometric analysis that allows 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. Several numerical examples are used to demonstrate the reliability of the present method. [less ▲]

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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 ▲]

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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 ▲]

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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 ▲]

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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 ▲]

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