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The smoothed extended finite element method for strong discontinuities ; Bordas, Stéphane ; Scientific Conference (2009, June) Detailed reference viewed: 106 (0 UL)The smoothed extended finite element method ; Bordas, Stéphane ; et al in Proceedings of the 6th International Conference on Engineering Computational Technology (2008) This paper shows how the strain smoothing technique recently proposed by G.R.Liu [1] coined as smoothed finite element method (SFEM) can be coupled to partition of unity methods, namely extended finite ... [more ▼] This paper shows how the strain smoothing technique recently proposed by G.R.Liu [1] coined as smoothed finite element method (SFEM) can be coupled to partition of unity methods, namely extended finite element method (XFEM) [2] to give birth to the smoothed extended finite element method (SmXFEM), which shares properties both with the SFEM and the XFEM. The proposed method suppresses the need to compute and integrate the derivatives of shape functions (which are singular at the tip in linear elastic fracture mechanics). Additionally, integration is performed along the boundary of the finite elements or smoothing cells and no isoparametric mapping is required, which allows elements of arbitrary shape. We present numerical results for cracks in linear elastic fracture mechanics problems. The method is verified on several examples and comparisons are made to the conventional XFEM. © 2008 Civil-Comp Press. [less ▲] Detailed reference viewed: 199 (2 UL)A smoothed finite element method for plate analysis ; ; Bordas, Stéphane et al in Computer Methods in Applied Mechanics and Engineering (2008), 197(13-16), 1184-1203 A quadrilateral element with smoothed curvatures for Mindlin-Reissner plates is proposed. The curvature at each point is obtained by a non-local approximation via a smoothing function. The bending ... [more ▼] A quadrilateral element with smoothed curvatures for Mindlin-Reissner plates is proposed. The curvature at each point is obtained by a non-local approximation via a smoothing function. The bending stiffness matrix is calculated by a boundary integral along the boundaries of the smoothing elements (smoothing cells). Numerical results show that the proposed element is robust, computational inexpensive and simultaneously very accurate and free of locking, even for very thin plates. The most promising feature of our elements is their insensitivity to mesh distortion. [less ▲] Detailed reference viewed: 103 (2 UL)A smoothed finite element method for shell analysis ; ; et al in Computer Methods in Applied Mechanics and Engineering (2008), 198(2), 165-177 A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on ... [more ▼] A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples. [less ▲] Detailed reference viewed: 131 (2 UL)Socially assistive robots for teaching emotional abilities to children with autism spectrum disorder Pinto Costa, Andreia ; Steffgen, Georges ; Rodriguez Lera, Francisco Javier et al Scientific Conference (2017, March) Socially assistive robots, when used in a way that takes into consideration children’s needs and developmental characteristics, can be useful tools to enable children’s development. More specifically, due ... [more ▼] Socially assistive robots, when used in a way that takes into consideration children’s needs and developmental characteristics, can be useful tools to enable children’s development. More specifically, due to their characteristics (predictability, simplicity, and repetition) robots can be especially helpful to teach emotional abilities to children with autism spectrum disorder (ASD). Previous research has provided preliminary evidence that robots can help children improve in some domains such as joint attention and imitation. However, no studies have examined how robots can be integrated in intervention protocols targeting the acquisition of emotional abilities in children with ASD. This paper presents a work in progress on an emotional ability training developed for children with ASD using the QT socially assistive robot. This training aims to test whether children with ASD can benefit from a robot-mediated training to improve emotional ability. [less ▲] Detailed reference viewed: 492 (15 UL)A solution for Multi-Alignment by Transformation Synchronisation Bernard, Florian ; Thunberg, Johan ; et al in The proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2015) The alignment of a set of objects by means of transformations plays an important role in computer vision. Whilst the case for only two objects can be solved globally, when multiple objects are considered ... [more ▼] The alignment of a set of objects by means of transformations plays an important role in computer vision. Whilst the case for only two objects can be solved globally, when multiple objects are considered usually iterative methods are used. In practice the iterative methods perform well if the relative transformations between any pair of objects are free of noise. However, if only noisy relative transformations are available (e.g. due to missing data or wrong correspondences) the iterative methods may fail. Based on the observation that the underlying noise-free transformations lie in the null space of a matrix that can directly be obtained from pairwise alignments, this paper presents a novel method for the synchronisation of pairwise transformations such that they are globally consistent. Simulations demonstrate that for a high amount of noise, a large proportion of missing data and even for wrong correspondence assignments the method delivers encouraging results. [less ▲] Detailed reference viewed: 215 (38 UL)Solving extremely ill-posed structures Beex, Lars ; ; Scientific Conference (2016, April) Detailed reference viewed: 79 (4 UL)Space-time goal-oriented reduced basis approximation for linear wave equation ; ; Bordas, Stéphane Report (2013) In this paper, we study numerically the linear damped second-order hyperbolic partial differen-tial equation (PDE) with affine parameter dependence using a goal-oriented approach by finite element (FE ... [more ▼] In this paper, we study numerically the linear damped second-order hyperbolic partial differen-tial equation (PDE) with affine parameter dependence using a goal-oriented approach by finite element (FE) and reduced basis (RB) methods. The main contribution of this paper is the “goal-oriented” proper orthogonal decomposition (POD)–Greedy sampling procedure within the RB approximation context. First, we introduce the RB recipe: Galerkin projection onto a space YN spanned by solutions of the governing PDE at N selected points in parameter space. This set of N parameter points is constructed by the standard POD–Greedy sampling procedure already developed. Second, based on the affine parameter dependence, we make use of the offline-online computational procedures: in the offline stage, we generate the RB space; in the online stage, given a new parameter value, we calculate rapidly and accurately the space-time RB output of interest and its associated asymptotic error. The proposed goal-oriented POD–Greedy sampling procedure can now be implemented and will look for the parameter points such that it minimizes this (asymptotic) output error rather than the solution error (or, error indicator which is the dual norm of residual) as in the standard POD–Greedy procedure. Numerical results show that the new goal-oriented POD–Greedy sampling procedure improves significantly the accuracy of the space-time output computation in comparison with the standard POD–Greedy one. The method is thus ideally suited for repeated, rapid and reliable evaluation of input-output relationships within the space-time setting. [less ▲] Detailed reference viewed: 138 (3 UL)Space-time reduced basis approximation and goal-oriented a posteriori error estimation for wave equation ; ; Bordas, Stéphane in Theory and Application of Model Order Reduction (2013, December) We study numerically the linear second order wave equation with an output quantity of interest which is a linear functional of the field variable using reduced basis approximation methods in the space ... [more ▼] We study numerically the linear second order wave equation with an output quantity of interest which is a linear functional of the field variable using reduced basis approximation methods in the space-time domain. The essential new ingredient is the a posteriori error estimation of the output quantity of interest. The technique, which is based on the well-known dual-weighted residual (DWR) method is deployed within a reduced basis approximation context. First, we introduce the reduced basis recipe - Galerkin projection onto a space spanned by the reduced basis functions which are constructed from the solutions of the governing PDE at several selected points in the parameter space. Second, in order to construct these basis functions we propose a new “goal-oriented” Proper Orthogonal Decomposition (POD)-Greedy sampling procedure, which is based on these new a posteriori error estimations. Finally, this a posteriori error estimation is also used to evaluate approximately the quality of many output computations in the online stage within the reduced basis procedure. [less ▲] Detailed reference viewed: 310 (3 UL)Space-Time Shear-Slip Mesh Update Method for Fluid-Structure Interaction Problems ; Zilian, Andreas Presentation (2013) Many practical problems in engineering consist of a structure surrounded by a fluid. These are all from the theoretical point of view fluid-structure interaction problems, in which the movement of the ... [more ▼] Many practical problems in engineering consist of a structure surrounded by a fluid. These are all from the theoretical point of view fluid-structure interaction problems, in which the movement of the structure influences the flow field of the fluid and vice versa. In this contribution the structure is described in a total Lagrangian representation based on velocities and the 2nd Piola-Kirchhoff stress state as primal variables in a hybrid-mixed formulation, while the fluid is modelled via the incompressible Navier-Stokes equations with velocities and pressure as unknowns. The governing equations of fluid and structural dynamics are uniformly discretised using space-time finite elements [1]. The discretised model equations of the fluid are stabilised using a SUPG/PSPG approach. Shape and test functions are continuous within the space-time slabs, while across the space- time slabs the shape and test functions are continuous only in space, but discontinuous in time yielding a time-discontinuous Galerkin approach. The space-time discretisation of the coupled system with velocities and pressure as remaining unknowns lays the basis for a mathematically profound analysis due to its methodical uniformity. During the mesh generation of the fluid-structure problem a fitting mesh at the conjoint interface of fluid and structure is generated ensuring natively the geometric continuity. In the discretised flow domain, which model equations are formulated in the Eulerian framework, a mesh-moving scheme needs to be applied to avoid severe mesh distortions. In case of large but regular structural displacements a discontinuous mesh-moving scheme like the Shear-Slip Mesh Update Method (SSMUM) is applicable [2]. In order to increase robustness and conservation behaviour of the classical SSMUM a modification based on the space-time discretisation of the problem described above is investigated. In the Space- Time SSMUM (ST-SSMUM) the alteration of the spatial connectivity takes place continuously in the space-time domain. By avoiding sudden changes in the spatial connectivity between two adjacent space-time slabs any difficulty in evaluating the jump term is circumvented. The properties of the introduced ST-SSMUM is shown by a computation of the flow field of a rotating impeller, which can be interpreted as a simplified water turbine or blood pump. [less ▲] Detailed reference viewed: 120 (2 UL)Spare parts planning and control for maintenance operations Arts, Joachim in Civil-Comp Proceedings (2014), 104 Detailed reference viewed: 89 (0 UL)A Sparse Bayesian Approach to the Identification of Nonlinear State-Space Systems Pan, Wei ; ; Goncalves, Jorge et al in IEEE Transaction on Automatic Control (2016), 61(1), 182-187 This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated ... [more ▼] This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear functional forms and their associated parameters from a limited number of time-series data points. For this, we cast this identification problem as a sparse linear regression problem and take a Bayesian viewpoint to solve it. As such, this approach typically leads to nonconvex optimisations. We propose a convexification procedure relying on an efficient iterative re-weighted ℓ1-minimisation algorithm that uses general sparsity inducing priors on the parameters of the system and marginal likelihood maximisation. Using this approach, we also show how convex constraints on the parameters can be easily added to our proposed iterative re-weighted ℓ1-minimisation algorithm. In the supplementary material \cite{appendix}, we illustrate the effectiveness of the proposed identification method on two classical systems in biology and physics, namely, a genetic repressilator network and a large scale network of interconnected Kuramoto oscillators. [less ▲] Detailed reference viewed: 279 (18 UL)Spatial play effects in a tangible game with an f-formation of multiple players Jungmann, Manuela ; ; in Proceedings of the Fifteenth Australasian User Interface Conference (2014, January), 150 Drawing on Kendon's F-formation framework of social interaction, we analysed the game-space activity of collocated players engaged in a tangible multiplayer game. Game input from groups of 3 players ... [more ▼] Drawing on Kendon's F-formation framework of social interaction, we analysed the game-space activity of collocated players engaged in a tangible multiplayer game. Game input from groups of 3 players interacting competitively in a natural spatial arrangement via balance-boards requiring whole-body movements was logged and analysed quantitatively. The spatial analysis of a range of players' activities in game-space revealed synergistic effects combining perceptual-motor factors with game-strategy behaviour which were reflected in preferred game-board playing regions. The findings illustrate the importance for HCI designers of considering interactions between human spatial behaviour, physical space and virtual game-space as games become increasingly embodied and social. [less ▲] Detailed reference viewed: 35 (3 UL)Stable 3D extended finite elements with higher order enrichment for accurate non planar fracture Agathos, Konstantinos ; ; Bordas, Stéphane in Computer Methods in Applied Mechanics and Engineering (2016), 306 An extended finite element method (XFEM) for three dimensional (3D) non-planar linear elastic fracture is introduced, which provides optimal convergence through the use of enrichment in a fixed area ... [more ▼] An extended finite element method (XFEM) for three dimensional (3D) non-planar linear elastic fracture is introduced, which provides optimal convergence through the use of enrichment in a fixed area around the crack front, while also improving the conditioning of the resulting system matrices. This is achieved by fusing a novel form of enrichment with existing blending techniques. Further, the adoption of higher order terms of theWilliams expansion is also considered and the effects in the accuracy and conditioning of the method are studied. Moreover, some problems regarding the evaluation of stress intensity factors (SIFs) and element partitioning are dealt with. The accuracy and convergence properties of the method as well as the conditioning of the resulting stiffness matrices are investigated through the use of appropriate benchmark problems. It is shown that the proposed approach provides increased accuracy while requiring, for all cases considered, a reduced number of iterations for the solution of the resulting systems of equations. The positive impact of geometrical enrichment is further demonstrated in the accuracy of the computed SIFs where, for the examined cases, an improvement of up to 40% is achieved. [less ▲] Detailed reference viewed: 104 (3 UL)Stable 3D extended finite elements with higher order enrichment for accurate non planar fracture ; ; Bordas, Stéphane in Computer Methods in Applied Mechanics and Engineering (2015) We present an extended finite element method (XFEM) for 3D nonplanar linear elastic fracture. The new approach not only provides optimal convergence using geometrical enrichment but also enables to ... [more ▼] We present an extended finite element method (XFEM) for 3D nonplanar linear elastic fracture. The new approach not only provides optimal convergence using geometrical enrichment but also enables to contain the increase in conditioning number characteristic of enriched finite element formulations: the number of iterations to convergence of the conjugate gradient solver scales similarly to and converges faster than the topologically-enriched version of the standard XFEM. This has two advantages: (1) the residual can be driven to zero to machine precision for at least 50% fewer iterations than the standard version of XFEM; (2) additional enrichment functions can be added without significant deterioration of the conditioning. Numerical examples also show that our new approach is up to 40% more accurate in terms of stress intensity factors, than the standard XFEM. [less ▲] Detailed reference viewed: 230 (10 UL)Stable 3D XFEM/vector-level sets for non-planar 3D crack propagation and comparison of enrichment schemes Agathos, Konstantinos ; ; et al in International Journal for Numerical Methods in Engineering (2017) We present a three-dimensional (3D) vector level set method coupled to a recently developed stable extended finite element method (XFEM). We further investigate a new enrichment approach for XFEM adopting ... [more ▼] We present a three-dimensional (3D) vector level set method coupled to a recently developed stable extended finite element method (XFEM). We further investigate a new enrichment approach for XFEM adopting discontinuous linear enrichment functions in place of the asymptotic near-tip functions. Through the vector level set method, level set values for propagating cracks are obtained via simple geometrical operations, eliminating the need for solution of differential evolution equations. The first XFEM variant ensures optimal convergence rates by means of geometrical enrichment, i.e., the use of enriched elements in a fixed volume around the crack front, without giving rise to conditioning problems. The linear enrichment approach significantly simplifies implementation and reduces the computational cost associated with numerical integration. The two dicretization schemes are tested for different benchmark problems, and their combination to the vector level set method is verified for non-planar crack propagation problems. [less ▲] Detailed reference viewed: 348 (28 UL)Stable extended finite element method: Convergence, Accuracy, Properties and Diffpack implementation ; ; Bordas, Stéphane et al in International Conference on Extended Finite Element Methods - XFEM 2013, September 11 – 13, 2013, Lyon, France (2013) Problems involving singularities and moving boundaries, especially when they involve discontinuities, create difficulties for the finite element method. On another, albeit related, front, two diametrally ... [more ▼] Problems involving singularities and moving boundaries, especially when they involve discontinuities, create difficulties for the finite element method. On another, albeit related, front, two diametrally opposed approaches are attempting to simplify the CAD to Analysis pipeline: isogeometric methods on the one hand [1] aim at coupling the geometry and field approximations, whilst implicit boundary definition-based methods attempt to decouple them [3,4,5]. We examine in this paper one instance of the latter approach, and rely on partition of unity enrichment of the field variable to capture discontinuities along material interface or domain boundaries. We study in particular the stable generalized finite element method of Babuˇka and Banerjee [6] for higher order approximations in two and three dimensions and propose a generic implementation within the C++ library Diffpack from inuTech GmbH [7]. In a companion paper, the implementation of enrichment within Diffpack is presented in more detail. We will present results obtained with our 3D implementation of partition of unity enrichment within Diffpack. This implementation represents the interfaces through level-sets and palliates blending problems using various approaches. We study here the stabilisation approach proposed in [6] in more detail and pay particular attention to the global convergence rate of the approach and to the stability and the local flux converence close to the interfaces. [less ▲] Detailed reference viewed: 358 (1 UL)The stable GFEM. Convergence, accuracy and Diffpack implementation ; ; Bordas, Stéphane et al Presentation (2015, May 12) Detailed reference viewed: 89 (1 UL)A staggered cell-centered finite element method for compressible and nearly-incompressible linear elasticity on general meshes ; ; Bordas, Stéphane et al in SIAM Journal on Numerical Analysis (2015), 53(4), 2051-2073 We propose a new numerical method, namely, the staggered cell-centered finite element method for compressible and nearly incompressible linear elasticity problems. By building a dual mesh and its ... [more ▼] We propose a new numerical method, namely, the staggered cell-centered finite element method for compressible and nearly incompressible linear elasticity problems. By building a dual mesh and its triangular submesh, the scheme can be constructed from a general mesh in which the displacement is approximated by piecewise linear (P1) functions on the dual submesh and, in the case of nearly incompressible problems, the pressure is approximated by piecewise constant (P0) functions on the dual mesh. The scheme is cell centered in the sense that the solution can be computed by cell unknowns of the primal mesh (for the displacement) and of the dual mesh (for the pressure). The method is presented within a rigorous theoretical framework to show stability and convergence. In particular, for the nearly incompressible case, stability is proved by using the macroelement technique. Numerical results show that the method, compared with other methods, is effective in terms of accuracy and computational cost. [less ▲] Detailed reference viewed: 131 (2 UL)Static and fatigue strength of a novel anatomically contoured implant compared to five current open-wedge high tibial osteotomy plates Diffo Kaze, Arnaud ; Maas, Stefan ; et al in Journal of Experimental Orthopaedics (2017), 4(39), Abstract Background The purpose of the present study was to compare the mechanical static and fatigue strength of the size 2 osteotomy plate “Activmotion” with the following five other common implants for ... [more ▼] Abstract Background The purpose of the present study was to compare the mechanical static and fatigue strength of the size 2 osteotomy plate “Activmotion” with the following five other common implants for the treatment of medial knee joint osteoarthritis: the TomoFix small stature, the TomoFix standard, the Contour Lock, the iBalance and the second generation PEEKPower. Methods Six fourth-generation tibial bone composites underwent a medial open-wedge high tibial osteotomy (HTO), according to standard techniques, using size 2 Activmotion osteotomy plates. All bone-implant constructs were subjected to static compression load to failure and load-controlled cyclic fatigue failure testing, according to a previously defined testing protocol. The mechanical stability was investigated by considering different criteria and parameters: maximum forces, the maximum number of loading cycles, stiffness, the permanent plastic deformation of the specimens during the cyclic fatigue tests, and the maximum displacement range in the hysteresis loops of the cyclic loading responses. Results In each test, all bone-implant constructs with the size 2 Activmotion plate failed with a fracture of the lateral cortex, like with the other five previously tested implants. For the static compression tests the failure occurred in each tested implant above the physiological loading of slow walking (> 2400 N). The load at failure for the Activmotion group was the highest (8200 N). In terms of maximum load and number of cycles performed prior to failure, the size 2 Activmotion plate showed higher results than all the other tested implants except the ContourLock plate. The iBalance implant offered the highest stiffness (3.1 kN/mm) for static loading on the lateral side, while the size 2 Activmotion showed the highest stiffness (4.8 kN/mm) in cyclic loading. Conclusions Overall, regarding all of the analysed strength parameters, the size 2 Activmotion plate provided equivalent or higher mechanical stability compared to the previously tested implant. Implants with a metaphyseal slope adapted to the tibia anatomy, and positioned more anteriorly on the proximal medial side of the tibia, should provide good mechanical stability. [less ▲] Detailed reference viewed: 174 (20 UL) |
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