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See detailA geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures
Rabczuk, Timon; Zi, Goangseup; Bordas, Stéphane UL et al

in Engineering Fracture Mechanics (2008), 75(16), 4740-4758

A three-dimensional meshfree method for modeling arbitrary crack initiation and crack growth in reinforced concrete structure is presented. This meshfree method is based on a partition of unity concept ... [more ▼]

A three-dimensional meshfree method for modeling arbitrary crack initiation and crack growth in reinforced concrete structure is presented. This meshfree method is based on a partition of unity concept and formulated for geometrically non-linear problems. The crack kinematics are obtained by enriching the solution space in order to capture the correct crack kinematics. A cohesive zone model is used after crack initiation. The reinforcement modeled by truss or beam elements is connected by a bond model to the concrete. We applied the method to model the fracture of several reinforced concrete structures and compared the results to experimental data. [less ▲]

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See detailGEOMETRY-INDEPENDENT FIELD APPROXIMATION FOR SPLINE-BASED FINITE ELEMENT METHODS
Xu, Gang; Atroshchenko, Elena; Bordas, Stéphane UL

in Proceedings of the 11th World Congress in Computational Mechanics (2014, July)

We propose a discretization scheme where the spline spaces used for the geometry and the field variables can be chosen independently in spline-based FEM. he method is thus applicable to arbitrary domains ... [more ▼]

We propose a discretization scheme where the spline spaces used for the geometry and the field variables can be chosen independently in spline-based FEM. he method is thus applicable to arbitrary domains with spline representation. (2) It is possible to flexibly choose between different spline spaces with different properties to better represent the solution of the PDE, e.g. the continuity of the solution field. (3) Refinement operations by knot insertion and degree elevation are performed directly on the spline space of the solution field, independently of the spline space of the geometry of the domain, i.e. the parameterization of the given geometry is not altered during the refinement process. Hence, the initial design can be optimized in the subsequent shape optimization stage without constraining the geometry discretization space to conform to the field approximation space. [less ▲]

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See detailGeometry-Independent Field approximaTion: CAD-Analysis Integration, geometrical exactness and adaptivity
Xu, Gang; Atroshchenko, Elena; Ma, Weiyin et al

in Computer Methods in Applied Mechanics & Engineering (2014)

In isogeometric analysis (IGA), the same spline representation is employed for both the geometry of the domain and approximation of the unknown fields over this domain. This identity of the geometry and ... [more ▼]

In isogeometric analysis (IGA), the same spline representation is employed for both the geometry of the domain and approximation of the unknown fields over this domain. This identity of the geometry and field approximation spaces was put forward in the now classic 2005 paper [20] as a key advantage on the way to the integration of Computer Aided Design (CAD) and subsequent analysis in Computer Aided Engineering (CAE). [20] claims indeed that any change to the geometry of the domain is automatically inherited by the approximation of the field variables, without requiring the regeneration of the mesh at each change of the domain geometry. Yet, in Finite Element versions of IGA, a parameterization of the interior of the domain must still be constructed, since CAD only provides information about the boundary. The identity of the boundary and field representation decreases the flexibility in which this parameterization can be generated and somewhat constrains the modeling and simulation process, because an approximation able to represent the domain geometry accurately need not be adequate to also approximate the field variables accurately, in particular when the solution is not smooth. We propose here a new paradigm called Geometry-Independent Field approximaTion (GIFT) where the spline spaces used for the geometry and the field variables can be chosen and adapted independently while preserving geometric exactness and tight CAD integration. GIFT has the following features: (1) It is possible to flexibly choose between different spline spaces with different properties to better represent the solution of the problem, e.g. the continuity of the solution field, boundary layers, singularities, whilst retaining geometrical exactness of the domain boundary. (2) For multi-patch analysis, where the domain is composed of several spline patches, the continuity condition between neighboring patches on the solution field can be automatically guaranteed without additional constraints in the variational form. (3) Refinement operations by knot insertion and degree elevation are performed directly on the spline space of the solution field, independently of the spline space of the geometry of the domain, which makes the method versatile. GIFT with PHT-spline solution spaces and NURBS geometries is used to show the effectiveness of the proposed approach. Keywords : Super-parametric methods, Isogeometric analysis (IGA), Geometry-independent Spline Space, PHT-splines, local refinement, adaptivity [less ▲]

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See detailGestural Interfaces for Elderly Users - Help or Hindrance?
Stossel, Christian UL

Doctoral thesis (2012)

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See detailGlobal analysis of piecewise linear systems using impact maps and quadratic surface Lyapunov functions
Goncalves, Jorge UL; Megretski, A.; Dahleh, M. A.

in Proceedings of the European Control Conference (ECC) 2001 (2001)

In this paper we develop an entirely new constructive global analysis methodology for a class of hybrid systems known as Piecewise Linear Systems (PLS). This methodology consists in inferring global ... [more ▼]

In this paper we develop an entirely new constructive global analysis methodology for a class of hybrid systems known as Piecewise Linear Systems (PLS). This methodology consists in inferring global properties of PLS solely by studying their behavior at switching surfaces associated with PLS. The main idea is to analyze impact maps, i.e., maps from one switching surface to the next switching surface, by constructing quadratic Lyapunov functions on switching surfaces. We found that an impact map induced by an LTI flow between two switching surfaces can be represented as a linear transformation analytically parameterized by a scalar function of the state. This representation of impact maps allows the search for quadratic surface Lyapunov functions to be done by simply solving a set of LMIs. Global asymptotic stability, robustness, and performance of limit cycles and equilibrium points of PLS can this way be efficiently checked. These new results were successfully applied to certain classes of PLS. Although this analysis methodology yields only sufficient criteria of stability, it has shown to be very successful in globally analyzing a large number of examples with a locally stable limit cycle or equilibrium point. In fact, it is still an open problem whether there exists an example with a globally stable limit cycle or equilibrium point that cannot be successfully analyzed with this new methodology. Examples analyzed include systems of relative degree larger than one and of high dimension, for which no other analysis methodology could be applied. [less ▲]

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See detailGlobal analysis of piecewise linear systems using impact maps and quadratic surface Lyapunov functions
Goncalves, Jorge UL; Megretski, A.; Dahleh, M.

in IEEE Transactions on Automatic Control (2003), 48(12), 2089-2106

This paper presents an entirely new constructive global analysis methodology for a class of hybrid systems known as piecewise linear systems (PLS). This methodology infers global properties of PLS solely ... [more ▼]

This paper presents an entirely new constructive global analysis methodology for a class of hybrid systems known as piecewise linear systems (PLS). This methodology infers global properties of PLS solely by studying the behavior at switching surfaces associated with PLS. The main idea is to analyze impact maps, i.e., maps from one switching surface to the next switching surface. Such maps are known to be “unfriendly” maps in the sense that they are highly nonlinear, multivalued, and not continuous. We found, however, that an impact map induced by an linear time-invariant flow between two switching surfaces can be represented as a linear transformation analytically parametrized by a scalar function of the state. This representation of impact maps allows the search for surface Lyapunov functions (SuLF) to be done by simply solving a semidefinite program, allowing global asymptotic stability, robustness, and performance of limit cycles and equilibrium points of PLS to be efficiently checked. This new analysis methodology has been applied to relay feedback, on/off and saturation systems, where it has shown to be very successful in globally analyzing a large number of examples. In fact, it is still an open problem whether there exists an example with a globally stable limit cycle or equilibrium point that cannot be successfully analyzed with this new methodology. Examples analyzed include systems of relative degree larger than one and of high dimension, for which no other analysis methodology could be applied. This success in globally analyzing certain classes of PLS has shown the power of this new methodology, and suggests its potential toward the analysis of larger and more complex PLS. [less ▲]

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See detailGlobal Asymptotic Stability of Oscillations with Sliding Modes
Goncalves, Jorge UL

in Proceedings of the 15th IFAC World Congress (2003)

This paper explores a new methodology based on quadratic surface Lyapunov functions to globally analyze oscillations with sliding modes in relay feedback systems (RFS). The method consists in efficiently ... [more ▼]

This paper explores a new methodology based on quadratic surface Lyapunov functions to globally analyze oscillations with sliding modes in relay feedback systems (RFS). The method consists in efficiently construct quadratic Lyapunov functions on switching surfaces that can be used to show that impact maps, i.e., maps from one switch to the next, are contracting. This, in turn, shows that the system is globally stable. Several classes of piecewise linear systems (PLS) were previously successfully analyzed with this methodology. In this paper, we consider PLS whose trajectories switch between subsystems of different dimensions. We present and discuss distinct relaxations leading to sufficient conditions of different conservatism and computationally complexity. The results in this paper open the door to the analysis of other, more complex classes of PLS. [less ▲]

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See detailGlobal asymptotic stability of the limit cycle in piecewise linear versions of the Goodwin oscillator
Salinas Varela, A. A.; Stan, G. B. V.; Goncalves, Jorge UL

in Proceedings of the 17th IFAC World Congress (2008)

Conditions in the form of linear matrix inequalities (LMIs) are used in this paper to guarantee the global asymptotic stability of a limit cycle oscillation for a class of piecewise linear (PWL) systems ... [more ▼]

Conditions in the form of linear matrix inequalities (LMIs) are used in this paper to guarantee the global asymptotic stability of a limit cycle oscillation for a class of piecewise linear (PWL) systems defined as the feedback interconnection of a saturation controller with a single input, single output (SISO) linear time-invariant (LTI) system. The proposed methodology extends previous results on impact maps and surface Lyapunov functions to the case when the sets of expected switching times are arbitrarily large. The results are illustrated on a PWL version of the Goodwin oscillator. [less ▲]

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See detailGlobal energy minimization for multi-crack growth in linear elastic fracture using the extended finite element method
Bordas, Stéphane UL

Scientific Conference (2014, April 02)

We investigate multiple fracture evolution under quasi-static conditions in an isotropic linear elastic solid based on the principle of minimum potential elastic energy in the framework of the extended ... [more ▼]

We investigate multiple fracture evolution under quasi-static conditions in an isotropic linear elastic solid based on the principle of minimum potential elastic energy in the framework of the extended finite element method. The technique enables a minimization of the potential energy with respect to all crack increment directions. Results show that the maximum hoop stress criterion and the energy minimization approach converge to the same fracture path. It is found that the converged solution lies in between the fracture paths obtained by each criterion for coarser meshes. This presents an opportunity to estimate an upper and lower bound of the true fracture path as well as an error on the crack path [less ▲]

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See detailGlobal energy minimization for multiple fracture growth
Sutula, Danas; Bordas, Stéphane UL

Report (2013)

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See detailA global optimization heuristic for the decomposed static anticipatory network traffic control problem anticipatory network traffic control problem
Rinaldi, Marco UL; Tampére, Chris; Viti, Francesco UL

in Transportation Research Procedia (2017)

Developing traffic control strategies taking explicitly into account the route choice behavior of users has been widely recognized irregularities in the solution space shape, such as non-convexity and non ... [more ▼]

Developing traffic control strategies taking explicitly into account the route choice behavior of users has been widely recognized irregularities in the solution space shape, such as non-convexity and non-smoothness. In this work, we propose an extended as a very challenging problem. Furthermore, the inclusion of user behavior in optimization based control schemes introduces strong decomposition scheme for the anticipatory traffic control problem, based upon our previous contributions, which aims at i) reducing irregularities in the solution space shape, such as non-convexity and non-smoothness. In this work, we propose an extended the computational complexity of the problem by approaching it in a controller-by-controller fashion, and ii) internalizing specific decomposition scheme for the anticipatory traffic control problem, based upon our previous contributions, which aims at i) reducing constraints in the objective function, guiding the optimization process away from non-significant minima, such as flat regions. the computational complexity of the problem by approaching it in a controller-by-controller fashion, and ii) internalizing specific Through two small scale test networks and different, randomly chosen initial points, we compare how the proposed extension constraints in the objective function, guiding the optimization process away from non-significant minima, such as flat regions. influences optimization results with respect to our previously developed decomposed approach, as well as centralized schemes. Through two small scale test networks and different, randomly chosen initial points, we compare how the proposed extension influences optimization results with respect to our previously developed decomposed approach, as well as centralized schemes. [less ▲]

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See detailGlobal stability analysis of on/off systems
Goncalves, Jorge UL

in Proceedings of the 39th IEEE Conference on Decision and Control (2000)

This paper considers quadratic surface Lyapunov functions in the study of global stability analysis of on/off systems (OFS), including those OFS with unstable nonlinearity sectors. In previous work ... [more ▼]

This paper considers quadratic surface Lyapunov functions in the study of global stability analysis of on/off systems (OFS), including those OFS with unstable nonlinearity sectors. In previous work, quadratic surface Lyapunov functions were successfully applied to prove global asymptotic stability of limit cycles of relay feedback systems. In this work, we show that these ideas can be used to prove global asymptotic stability of equilibrium points of piecewise linear systems (PLS). We present conditions in the form of LMI that, when satisfied, guarantee global asymptotic stability of an equilibrium point. A large number of examples was successfully proven globally stable. These include systems with an unstable affine linear subsystem, systems of relative degree larger than one and of high dimension, and systems with unstable nonlinearity sectors, for which all classical fail to analyze. In fact, existence of an example with a globally stable equilibrium point that could not be successfully analyzed with this new methodology is still an open problem. This work opens the door to the possibility that more general PLS can be systematically globally analyzed using quadratic surface Lyapunov functions. [less ▲]

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See detailGlobal stability of relay feedback systems
Goncalves, Jorge UL; Megretski, A.; Dahleh, M. A.

in IEEE Transactions on Automatic Control (2001), 46(4), 550--562

For a large class of relay feedback systems (RFS) there will be limit cycle oscillations. Conditions to check existence and local stability of limit cycles for these systems are well known. Global ... [more ▼]

For a large class of relay feedback systems (RFS) there will be limit cycle oscillations. Conditions to check existence and local stability of limit cycles for these systems are well known. Global stability conditions, however, are practically nonexistent. This paper presents conditions in the form of linear matrix inequalities (LMIs) that, when satisfied, guarantee global asymptotic stability of limit cycles induced by relays with hysteresis in feedback with linear time-invariant (LTI) stable systems. The analysis consists in finding quadratic surface Lyapunov functions for Poincaré maps associated with RFS. These results are based on the discovery that a typical Poincaré map induced by an LTI flow between two hyperplanes can be represented as a linear transformation analytically parametrized by a scalar function of the state. Moreover, level sets of this function are convex subsets of linear manifolds. The search for quadratic Lyapunov functions on switching surfaces is done by solving a set of LMIs. Although this analysis methodology yields only a sufficient criterion of stability, it has proved very successful in globally analyzing a large number of examples with a unique locally stable symmetric unimodal limit cycle. In fact, it is still an open problem whether there exists an example with a globally stable symmetric unimodal limit cycle that could not be successfully analyzed with this new methodology. Examples analyzed include minimum-phase systems, systems of relative degree larger than one, and of high dimension. Such results lead us to believe that globally stable limit cycles of RFS frequently have quadratic surface Lyapunov functions. [less ▲]

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See detailGlobal stability of relay feedback systems
Goncalves, Jorge UL; Megretski, A.; Dahleh, M. A.

in Proceedings of the IEEE American Control Conference (2000 ACC) (2000)

For a large class of relay feedback systems (RFS) there will be limit cycle oscillations. Conditions to check existence and local stability of limit cycles for these systems are well known. Global ... [more ▼]

For a large class of relay feedback systems (RFS) there will be limit cycle oscillations. Conditions to check existence and local stability of limit cycles for these systems are well known. Global stability conditions, however, are practically non-existent. The paper presents conditions in the form of linear matrix inequalities (LMIs) that guarantee global asymptotic stability of a limit cycle induced by a relay with hysteresis in feedback with an LTI stable system. The analysis is based on finding global quadratic Lyapunov functions for a Poincare map associated with the RFS. We found that a typical Poincare map induced by an LTI flow between two hyperplanes can be represented as a linear transformation analytically parametrized by a scalar function of the state. Moreover, level sets of this function are convex. The search for globally quadratic Lyapunov functions is then done by solving a set of LMIs. Most examples of RFS analyzed by the authors were proven globally stable. Systems analyzed include minimum-phase systems, systems of relative degree larger than one, and of high dimension. This leads us to believe that quadratic stability of associated Poincare maps is common in RFS. [less ▲]

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See detailGlobal State Synchronization in Networks of Cyclic Feedback Systems
Hamadeh, Abdullah; Stan, Guy-Bart; Sepulchre, Rodolphe et al

in IEEE Transactions on Automatic Control (2012), 57(2), 478-483

This technical note studies global asymptotic state synchronization in networks of identical systems. Conditions on the coupling strength required for the synchronization of nodes having a cyclic feedback ... [more ▼]

This technical note studies global asymptotic state synchronization in networks of identical systems. Conditions on the coupling strength required for the synchronization of nodes having a cyclic feedback structure are deduced using incremental dissipativity theory. The method takes advantage of the incremental passivity properties of the constituent subsystems of the network nodes to reformulate the synchronization problem as one of achieving incremental passivity by coupling. The method can be used in the framework of contraction theory to constructively build a contracting metric for the incremental system. The result is illustrated for a network of biochemical oscillators. [less ▲]

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See detailA goal-oriented reduced basis method for the wave equation in inverse analysis
Hoang, Khac Chi; Kerfriden, Pierre; Bordas, Stéphane UL

in International Conference on Computational Mechanics CM13 Proceedings (2013, March)

In this paper, we extend the reduced-basis methods developed earlier for wave equations to goal-oriented wave equations with a ne parameter dependence. The essential new ingredient is the dual (or adjoint ... [more ▼]

In this paper, we extend the reduced-basis methods developed earlier for wave equations to goal-oriented wave equations with a ne parameter dependence. The essential new ingredient is the dual (or adjoint) problem and the use of its solution in a sampling procedure to pick up “goal-orientedly” parameter samples. First, we introduce the reduced-basis recipe — Galerkin projection onto a space YN spanned by the reduced basis functions which are constructed from the solutions of the governing partial di erential equation at several selected points in parameter space. Second, we propose a new “goal-oriented” Proper Orthogonal Decomposition (POD)–Greedy sampling procedure to construct these associated ba-sis functions. Third, based on the assumption of a ne parameter dependence, we use the o ine-online computational procedures developed earlier to split the computational procedure into o ine and online stages. We verify the proposed computational procedure by applying it to a three-dimensional simulation dental implant problem. The good numeri-cal results show that our proposed procedure performs better than the standard POD–Greedy procedure in terms of the accuracy of output functionals. [less ▲]

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See detailA gradient weighted extended finite element method (GW-XFEM) for fracture mechanics
Feng, S. Z.; Bordas, Stéphane UL; Han, X. et al

in Acta Mechanica (2019), 230

In this study, a gradient weighted extended finite element method (GW-XFEM) is presented for the analysis of fracture problems. For this method, the domain discretization is the same as the standard XFEM ... [more ▼]

In this study, a gradient weighted extended finite element method (GW-XFEM) is presented for the analysis of fracture problems. For this method, the domain discretization is the same as the standard XFEM. However, the gradient field is constructed by considering the influences of the element itself and its adjacent elements. Based on the Shepard interpolation, the weighted strain filed can be obtained, which will be utilized to construct the discretized system equations. The validity of the presented method is fully investigated through several numerical examples. From these results, it is shown that compared with standard XFEM, the presented method can achieve much better accuracy, efficiency and higher convergence, when dealing with fracture analysis. [less ▲]

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See detailGraft materials provide greater static strength to medial opening wedge high tibial osteotomy than when no graft is included
Belsey, James; Diffo Kaze, Arnaud UL; Jobson, Simon et al

in Journal of Experimental Orthopaedics (2019), 6(13),

Background The purpose of this study was to compare the stability of medial opening-wedge high tibial osteotomy (MOWHTO) with and without different graft materials. Good clinical and radiological outcomes ... [more ▼]

Background The purpose of this study was to compare the stability of medial opening-wedge high tibial osteotomy (MOWHTO) with and without different graft materials. Good clinical and radiological outcomes have been demonstrated when either using or not using graft materials during MOWHTO. Variations in the biomechanical properties of different graft types, regarding the stability they provide a MOWHTO, have not been previously investigated. Methods A 10 mm biplanar MOWHTO was performed on 15 artificial sawbone tibiae, which were fixed using the Activmotion 2 plate. Five bones had OSferion60 wedges (synthetic group), five had allograft bone wedges (allograft group), and five had no wedges (control group) inserted into the osteotomy gap. Static compression was applied axially to each specimen until failure of the osteotomy. Ultimate load, horizontal and vertical displacements were measured and used to calculate construct stiffness and valgus malrotation of the tibial head. Results The synthetic group failed at 6.3 kN, followed by the allograft group (6 kN), and the control group (4.5 kN). The most valgus malrotation of the tibial head was observed in the allograft group (2.6°). The synthetic group showed the highest stiffness at the medial side of the tibial head (9.54 kN·mm− 1), but the lowest stiffness at the lateral side (1.59 kN·mm-1). The allograft group showed high stiffness on the medial side of the tibial head (7.54 kN·mm− 1) as well as the highest stiffness on the lateral side (2.18 kN·mm− 1). Conclusions The use of graft materials in MOWHTO results in superior material properties compared to the use of no graft. The static strength of MOWHTO is highest when synthetic grafts are inserted into the osteotomy gap. Allograft wedges provide higher mechanical strength to a MOWHTO than when no graft used. In comparison to the synthetic grafts, allograft wedges result in the stiffness of the osteotomy being more similar at the medial and lateral cortices. [less ▲]

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