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See detailAn adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order
Nguyen-Xuan, H.; Liu, G. R.; Bordas, Stéphane UL et al

in Computer Methods in Applied Mechanics & Engineering (2013), 253

This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded ... [more ▼]

This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient enrichment with desired terms for the displacement field near the singular-point with the satisfaction of partition-of-unity property. The stiffness matrix of the discretized system is then obtained using the assumed displacement values (not the derivatives) over smoothing domains associated with the edges of elements. An adaptive procedure for the sES-FEM is proposed to enhance the quality of the solution with minimized number of nodes. Several numerical examples are provided to validate the reliability of the present sES-FEM method. © 2012 Elsevier B.V. [less ▲]

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See detailIsogeometric boundary element analysis using unstructured T-splines
Scott, M. A.; Simpson, R. N.; Evans, J. A. et al

in Computer Methods in Applied Mechanics & Engineering (2013), 254

We couple collocated isogeometric boundary element methods and unstructured analysis-suitable T-spline surfaces for linear elastostatic problems. We extend the definition of analysis-suitable T-splines to ... [more ▼]

We couple collocated isogeometric boundary element methods and unstructured analysis-suitable T-spline surfaces for linear elastostatic problems. We extend the definition of analysis-suitable T-splines to encompass unstructured control grids (unstructured meshes) and develop basis functions which are smooth (rational) polynomials defined in terms of the Bézier extraction framework and which pass standard patch tests. We then develop a collocation procedure which correctly accounts for sharp edges and corners, extraordinary points, and T-junctions. This approach is applied to several three-dimensional problems, including a real-world T-spline model of a propeller. We believe this work clearly illustrates the power of combining new analysis-suitable computer aided design technologies with established analysis methodologies, in this case, the boundary element method. © 2012 Elsevier B.V. [less ▲]

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See detailAn adaptive eXtended Bridging Scale Method for crack propagation
Pattabhi Ramaiah, Budarapu; Robert, Gracie; Bordas, Stéphane UL et al

in An adaptive eXtended Bridging Scale Method for crack propagation (2012, September)

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See detailThe Simple Shear and Simple Tension Problems in Linear and Nonlinear Elasticity
Lee, Chang-Kye; Bordas, Stéphane UL

Report (2012)

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See detailAddressing lack of scale separation in fracture simulations
Kerfriden, Pierre; Akbari R., Ahmad; Goury, Olivier et al

Scientific Conference (2012, July)

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See detailSensitivity analysis and shape optimisation with the isogeometric boundary element methods
Lian, Haojie; Simpson, Robert; Bordas, Stéphane UL

Scientific Conference (2012, March 27)

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See detailALGEBRAIC COARSE-GRAINING METHODS IN FRACTURE MECHANICS: TACKLING LOCAL LACK OF CORRELATION USING DOMAIN DECOMPOSITION
Goury, Olivier; Kerfriden, Pierre; Rabczuk, Timon et al

Scientific Conference (2012, March)

In this paper, we propose to couple model order reduction techniques with domain decomposition meth- ods for the solution to parametric problems of fracture. The nonlinear nature of the problems requires ... [more ▼]

In this paper, we propose to couple model order reduction techniques with domain decomposition meth- ods for the solution to parametric problems of fracture. The nonlinear nature of the problems requires the use of a system approximation method to speed-up the assembly of the non-linear opreators. We show that the method efficiently computes a solution faster than a full order model for a given accuracy. The speed-up increases with the problem size. [less ▲]

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See detailRecent developments in CAD/analysis integration
Lian, Haojie; Bordas, Stéphane UL; Sevilla, Rubén

in Computational Technology Reviews (2012), 6

For linear elastic problems, it is well-known that mesh generation dominates the total analysis time. Different types of methods have been proposed to directly or indirectly alleviate this burden ... [more ▼]

For linear elastic problems, it is well-known that mesh generation dominates the total analysis time. Different types of methods have been proposed to directly or indirectly alleviate this burden associated with mesh generation. We review in this paper a subset of such methods centred on tighter coupling between computer aided design (CAD) and analysis (finite element or boundary element methods). We focus specifically on frameworks which rely on constructing a discretisation directly from the functions used to describe the geometry of the object in CAD. Examples include B-spline subdivision surfaces, isogeometric analysis, NURBS-enhanced FEM and parametric-based implicit boundary definitions. We review recent advances in these methods and compare them to other paradigms which also aim at alleviating the burden of mesh generation in computational mechanics. [less ▲]

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See detailEnriched residual free bubbles for semiconductor device simulation
Simpson, R. N.; Bordas, Stéphane UL; Asenov, A. et al

in Computational Mechanics (2012), 50(1), 119-133

This article outlines a method for stabilising the current continuity equations which are used for semiconductor device simulation. Residual-free bubble functions (RfBF) are incorporated into a finite ... [more ▼]

This article outlines a method for stabilising the current continuity equations which are used for semiconductor device simulation. Residual-free bubble functions (RfBF) are incorporated into a finite element (FE) implementation that are able to prevent oscillations which are seen when using the conventional Bubnov-Galerkin FE implementation. In addition, it is shown that the RfBF are able to provide stabilisation with very distorted meshes and curved interface boundaries. Comparison with the commonly used SUPG scheme is made throughout, showing that in the case of 2D problems the RfBF allow faster convergence of the coupled semiconductor device equations, especially in the case of distorted meshes. [less ▲]

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See detailLocal/global model order reduction strategy for the simulation of quasi-brittle fracture
Kerfriden, P.; Passieux, J. C.; Bordas, Stéphane UL

in International Journal for Numerical Methods in Engineering (2012), 89(2), 154-179

This paper proposes a novel technique to reduce the computational burden associated with the simulation of localized failure. The proposed methodology affords the simulation of damage initiation and ... [more ▼]

This paper proposes a novel technique to reduce the computational burden associated with the simulation of localized failure. The proposed methodology affords the simulation of damage initiation and propagation while concentrating the computational effort where it is most needed, that is, in the localization zones. To do so, a local/global technique is devised where the global (slave) problem (far from the zones undergoing severe damage and cracking) is solved for in a reduced space computed by the classical proper orthogonal decomposition while the local (master) degrees of freedom (associated with the part of the structure where most of the damage is taking place) are fully resolved. Both domains are coupled through a local/global technique. This method circumvents the difficulties associated with model order reduction for the simulation of highly nonlinear mechanical failure and offers an alternative or complementary approach to the development of multiscale fracture simulators. © 2011 John Wiley & Sons, Ltd. [less ▲]

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See detailSize-dependent free flexural vibration behavior of functionally graded nanoplates
Natarajan, S.; Chakraborty, S.; Thangavel, M. et al

in Computational Materials Science (2012), 65

In this paper, size dependent linear free flexural vibration behavior of functionally graded (FG) nanoplates are investigated using the iso-geometric based finite element method. The field variables are ... [more ▼]

In this paper, size dependent linear free flexural vibration behavior of functionally graded (FG) nanoplates are investigated using the iso-geometric based finite element method. The field variables are approximated by non-uniform rational B-splines. The nonlocal constitutive relation is based on Eringen's differential form of nonlocal elasticity theory. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG plate are computed using Mori-Tanaka homogenization scheme. The accuracy of the present formulation is demonstrated considering the problems for which solutions are available. A detailed numerical study is carried out to examine the effect of material gradient index, the characteristic internal length, the plate thickness, the plate aspect ratio and the boundary conditions on the global response of the FG nanoplate. From the detailed numerical study it is seen that the fundamental frequency decreases with increasing gradient index and characteristic internal length. © 2012 Elsevier B.V. All rights reserved. [less ▲]

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See detailA cell-based smoothed finite element method for three dimensional solid structures
Nguyen-Xuan, Hung; Nguyen, Ha Manh UL; Bordas, Stéphane UL et al

in KSCE Journal of Civil Engineering (2012), 16(7), 1230-1242

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 ... [more ▼]

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. [less ▲]

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See detailA two-dimensional Isogeometric Boundary Element Method for elastostatic analysis
Simpson, R. N.; Bordas, Stéphane UL; Trevelyan, J. et al

in Computer Methods in Applied Mechanics & Engineering (2012), 209-212

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 ... [more ▼]

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. © 2011 Elsevier B.V. [less ▲]

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See detailAn adaptive multiscale method for fracture based on concurrent-hierarchical hybrid modelling
Akbari R, Ahmad; Kerfriden, Pierre; Rabczuk, Timon et al

Scientific Conference (2012)

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See detailA force-based large increment method for 2D continuum solids and the mesh convergence study
Long, D.; Guo, Z.; Liu, X. et al

in AIP Conference Proceedings (2012), 1504

In this paper, a triangular plane stress element is implemented based on the large increment method (LIM) to solve 2D continuum mechanics problems. In the LIM, after the governing equations are ... [more ▼]

In this paper, a triangular plane stress element is implemented based on the large increment method (LIM) to solve 2D continuum mechanics problems. In the LIM, after the governing equations are established using the generalized elemental force variables as primary unknowns, an iteration procedure is employed to obtain an optimised approximate solution of the problem. Two numerical examples are investigated to study the mesh convergence of the proposed triangular LIM element. Structured meshes as well as unstructured meshes with different element densities are generated to illustrate the convergence of the total strain energy in both examples. The numerical results obtained from the LIM (including the total strain energy, the displacement and the stress) are compared with the analytical solutions as well as the results from the commercial FEM software ABAQUS. All the results show that the performance of the LIM is as good as the FEM in linear elastic problems. A simple elastoplastic example suggests that the LIM may obtain better result than the FEM. © 2012 American Institute of Physics. [less ▲]

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See detailExtended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth
Chen, L.; Rabczuk, T.; Bordas, Stéphane UL et al

in Computer Methods in Applied Mechanics & Engineering (2012), 209-212

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 ... [more ▼]

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. [less ▲]

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

in ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers (2012)

Traditionally, recovery based error estimators in linear elasticity have considered the evaluation of an enhanced stress field obtained from the raw Finite Element (FE) stress solution. Instead of that ... [more ▼]

Traditionally, recovery based error estimators in linear elasticity have considered the evaluation of an enhanced stress field obtained from the raw Finite Element (FE) stress solution. Instead of that, one can also obtain a recovered displacement field from the FE displacements. Herein, we describe a superconvergent patch recovery of the displacement field which considers the local fulfilment of boundary and internal equilibrium equations, Dirichlet constraints and, for singular problems, the splitting of the displacement and stress fields into singular and smooth parts. Numerical tests using problems with known analytical solution have been carried out to validate the proposed technique for error estimation and error bounding in energy norm and quantities of interest. [less ▲]

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See detailOn the role of enrichment and statistical admissibility of recovered fields in a posteriori error estimation for enriched finite element methods
González-Estrada, O. A.; Ródenas, J. J.; Bordas, Stéphane UL et al

in Engineering Computations (2012), 29(8), 814-841

Purpose - The purpose of this paper is to assess the effect of the statistical admissibility of the recovered solution and the ability of the recovered solution to represent the singular solution; also ... [more ▼]

Purpose - The purpose of this paper is to assess the effect of the statistical admissibility of the recovered solution and the ability of the recovered solution to represent the singular solution; also the accuracy, local and global effectivity of recovery-based error estimators for enriched finite element methods (e.g. the extended finite element method, XFEM). Design/methodology/approach - The authors study the performance of two recovery techniques. The first is a recently developed superconvergent patch recovery procedure with equilibration and enrichment (SPR-CX). The second is known as the extended moving least squares recovery (XMLS), which enriches the recovered solutions but does not enforce equilibrium constraints. Both are extended recovery techniques as the polynomial basis used in the recovery process is enriched with singular terms for a better description of the singular nature of the solution. Findings - Numerical results comparing the convergence and the effectivity index of both techniques with those obtained without the enrichment enhancement clearly show the need for the use of extended recovery techniques in Zienkiewicz-Zhu type error estimators for this class of problems. The results also reveal significant improvements in the effectivities yielded by statistically admissible recovered solutions. Originality/value - The paper shows that both extended recovery procedures and statistical admissibility are key to an accurate assessment of the quality of enriched finite element approximations. © Emerald Group Publishing Limited. [less ▲]

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See detailError estimation and error bounding in quantities of interest based on equilibrated recovered displacement fields
Nadal, E.; González-Estrada, O. A.; Ródenas, J. J. et al

in ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers (2012)

Over the last ten years there has been an increase on the use of goal-oriented error estimates aimed to quantify the local error on a (non)linear quantity of interest (QoI) that might result relevant for ... [more ▼]

Over the last ten years there has been an increase on the use of goal-oriented error estimates aimed to quantify the local error on a (non)linear quantity of interest (QoI) that might result relevant for design purposes. Residual-based error estimators have been used recursively to obtain upper and lower bounds of the error in quantities of interest for finite element approximations. In this paper, we present a recovery technique for 2D linear elasticity problems, based on the superconvergent patch recovery (SPR), which provides recovered displacement and stress fields that are then utilised to evaluate practical upper and lower error bounds in QoI. [less ▲]

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See detailEquilibrated patch recovery for accurate evaluation of upper error bounds in quantities of interest
González-Estrada, O. A.; Ródenas, J. J.; Nadal, E. et al

in ECCOMAS Thematic Conference - ADMOS 2011: International Conference on Adaptive Modeling and Simulation, An IACM Special Interest Conference (2012)

There is an increasing interest on the use of goal-oriented error estimates which help to measure and control the local error on a linear or non-linear quantity of interest (QoI) that might result ... [more ▼]

There is an increasing interest on the use of goal-oriented error estimates which help to measure and control the local error on a linear or non-linear quantity of interest (QoI) that might result relevant for design purposes (e.g. the mean stress value in a particular area, displacements, the stress intensity factor for fracture problems,⋯). In general, residual-based error estimators have been used to obtain upper and lower bounds of the error in quantities of interest for finite element approximations. In this work, we propose a novel a posteriori recovery technique to obtain an upper error bound of the QoI. We use a recovery procedure based on the superconvergent patch recovery (SPR) technique to obtain nearly statically admissible recovered stress fields for the primal and dual problems. This recovery technique was previously used to obtain upper bounds of the error in energy norm and has been used in this paper to obtain a computable version of the upper bound for the quantity of interest. [less ▲]

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