References of "Bruls, Olivier"
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See detailSensitivity analysis for multibody systems formulated on a Lie group
Sonneville, Valentin ULg; Bruls, Olivier ULg

in Multibody System Dynamics (2014), 31

A direct differentiation method and an adjoint variable method are proposed for the efficient semi-analytical evaluation of the sensitivities of multibody systems formulated in a matrix Lie group ... [more ▼]

A direct differentiation method and an adjoint variable method are proposed for the efficient semi-analytical evaluation of the sensitivities of multibody systems formulated in a matrix Lie group framework. These methods rely on the linearization of the equations of motion and/or of the time integration procedure. The simpler structure of the equations of motion in the Lie group formalism appears as an advantage for that purpose. Lie bracket contributions and the non-linearity of the exponential map need to be taken into account in the sensitivity algorithms. Nevertheless, essential characteristics of formulations of the direct differentiation method and the adjoint variable method on linear spaces are recovered. Some implementation issues are discussed and two relevant examples illustrate the properties of these methods. [less ▲]

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See detailSensitivity analysis for multibody systems formulated on a Lie group
Sonneville, Valentin ULg; Bruls, Olivier ULg

in Multibody System Dynamics (2014), 31

A direct differentiation method and an adjoint variable method are proposed for the efficient semi-analytical evaluation of the sensitivities of multibody systems formulated in a matrix Lie group ... [more ▼]

A direct differentiation method and an adjoint variable method are proposed for the efficient semi-analytical evaluation of the sensitivities of multibody systems formulated in a matrix Lie group framework. These methods rely on the linearization of the equations of motion and/or of the time integration procedure. The simpler structure of the equations of motion in the Lie group formalism appears as an advantage for that purpose. Lie bracket contributions and the non-linearity of the exponential map need to be taken into account in the sensitivity algorithms. Nevertheless, essential characteristics of formulations of the direct differentiation method and the adjoint variable method on linear spaces are recovered. Some implementation issues are discussed and two relevant examples illustrate the properties of these methods. [less ▲]

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See detailGeometrically exact beam finite element formulated on the special Euclidean group SE(3)
Sonneville, Valentin ULg; Cardona, Alberto; Bruls, Olivier ULg

in Computer Methods in Applied Mechanics & Engineering (2014), 268

This paper describes a dynamic formulation of a straight beam finite element in the setting of the special Euclidean group SE(3). First, the static and dynamic equilibrium equations are derived in this ... [more ▼]

This paper describes a dynamic formulation of a straight beam finite element in the setting of the special Euclidean group SE(3). First, the static and dynamic equilibrium equations are derived in this framework from variational principles. Then, a non-linear interpolation formula using the exponential map is introduced. It is shown that this framework leads to a natural coupling in the interpolation of the position and rotation variables. Next, the discretized internal and inertia forces are developed. The semi-discrete equations of motion take the form of a second-order ordinary differential equation on a Lie group, which is solved using a Lie group time integration scheme. It is remarkable that no parameterization of the nodal variables needs to be introduced and that the proposed Lie group framework leads to a compact and easy-to-implement formulation. Some important numerical and theoretical aspects leading to a computationally efficient strategy are highlighted and discussed. For instance, the formulation leads to invariant tangent stiffness and mass matrices under rigid body motions and a locking free element. The proposed formulation is successfully tested in several numerical static and dynamic examples. [less ▲]

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See detailImportance of structural damping in the dynamic analysis of compliant deployable structures
Dewalque, Florence ULg; Rochus, Pierre ULg; Bruls, Olivier ULg

in Proceedings of the 65th International Astronautical Congress (IAC) (2014)

Compliant mechanisms such as tape springs are often used on satellites to deploy appendices, e.g. solar panels, antennas, telescopes and solar sails. Their main advantage comes from the fact that their ... [more ▼]

Compliant mechanisms such as tape springs are often used on satellites to deploy appendices, e.g. solar panels, antennas, telescopes and solar sails. Their main advantage comes from the fact that their motion results from the elastic deformation of structural components, unlike usual hinges or prismatic joints, the motion of which is dictated by contact surfaces. No actuators or external energy sources are required and the deployment is purely passive, which appears as a decisive feature for the design of low-cost missions with small satellites or cubesats. The mechanical behaviour of a tape spring is intrinsically complex and nonlinear involving buckling, hysteresis and self-locking phenomena. High-fidelity mechanical models are then needed to get a detailed understanding of the deployment process, improve the design and predict the actual behaviour in the space 0-g environment. In the majority of the previous works, dynamic simulations were performed without any physical representation of the structural damping. These simulations could be successfully achieved because of the presence of numerical damping in the transient solver. However, in this case, the dynamic response turns out to be quite sensitive to the amount of numerical dissipation, so that the predictive capabilities of the model are questionable. In this work based on numerical case studies, we show that the dynamic simulation of a tape spring can be made less sensitive to numerical parameters when the structural dissipation is taken into account. [less ▲]

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See detailExperimental Study of the Human Ability to Deliberately Excite a Flexible Floor
Schwartz, Cédric ULg; Berger, Alexis; Bruls, Olivier ULg et al

in Zingoni, Alphose (Ed.) Proceedings of the 5th International Conference on Structural Engineering, Mechanics and Computation (2014)

Human-structure interactions are not completely understood yet. This paper presents an experimental study focusing on the interaction between a human and a flexible support, with a major aim to better ... [more ▼]

Human-structure interactions are not completely understood yet. This paper presents an experimental study focusing on the interaction between a human and a flexible support, with a major aim to better understand how the behavior of a human subject, bouncing on a flexible structure, adapts to the support motion. Exploratory experiments are undertaken with a 7m-span timber footbridge tested in the Human Motion Analysis Laboratory of the University of Liege. The movements of the coupled system composed of the subject and the footbridge are recorded by Motion Capture technology; the subject\textquoteright{}s 3-D body motion is defined by three important angles: ankle, knee and hip. The interaction between the subject and the footbridge is also quantified by means of force platform measurements. The experiments indicate an influence of the support amplitude and natural frequency on the phase shift between the oscillatory floor motion and the three angles characterizing the motion. [less ▲]

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See detailDiscussion on the optimization problem formulation of flexible components in multibody systems
Tromme, Emmanuel ULg; Bruls, Olivier ULg; Emonds-Alt, Jonathan et al

in Structural and Multidisciplinary Optimization (2013), 48(6), 1189-1206

This paper is dedicated to the structural optimization of flexible components in mechanical systems modeled as multibody systems. While most of the structural optimization developments have been conducted ... [more ▼]

This paper is dedicated to the structural optimization of flexible components in mechanical systems modeled as multibody systems. While most of the structural optimization developments have been conducted under (quasi-)static loadings or vibration design criteria, the proposed approach aims at considering as precisely as possible the effects of dynamic loading under service conditions. Solving this problem is quite challenging and naive implementations may lead to inaccurate and unstable results. To elaborate a robust and reliable approach, the optimization problem formulation is investigated because it turns out that it is a critical point. Different optimization algorithms are also tested. To explain the efficiency of the various solution approaches, the complex nature of the design space is analyzed. Numerical applications considering the optimization of a two-arm robot subject to a trajectory tracking constraint and the optimization of a slider-crank mechanism with a cyclic dynamic loading are presented to illustrate the different concepts. [less ▲]

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See detailIntroduction to model order reduction methods for linear and nonlinear multiphysics systems
Bruls, Olivier ULg

Scientific conference (2013, November 08)

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See detail3D analysis of gait using accelerometer measurements
Boutaayamou, Mohamed ULg; Schwartz, Cédric ULg; Stamatakis, Julien et al

Scientific conference (2013, November 07)

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See detailA nonsmooth generalized-alpha scheme for flexible multibody systems with unilateral constraints
Chen, Qiong-zhong; Acary, Vincent; Virlez, Geoffrey ULg et al

in International Journal for Numerical Methods in Engineering (2013), 96(8), 487-511

Mechanical systems are usually subjected not only to bilateral constraints but also to unilateral constraints. Inspired by the generalized-alpha time integration method for smooth flexible multibody ... [more ▼]

Mechanical systems are usually subjected not only to bilateral constraints but also to unilateral constraints. Inspired by the generalized-alpha time integration method for smooth flexible multibody dynamics, this paper presents a nonsmooth generalized-alpha method, which allows a consistent treatment of the nonsmooth phenomena induced by unilateral constraints and an accurate description of the structural vibrations during free motions. Both the algorithm and the implementation are illustrated in detail. Numerical example tests are given in the scope of both rigid and flexible body models, taking account for both linear and nonlinear systems, and comprising both unilateral and bilateral constraints. The extended nonsmooth generalized-alpha method is verified through comparison to the traditional Moreau-Jean method and the fully implicit Newmark method. Results show that the nonsmooth generalized-alpha method benefits from the accuracy and stability property of the classical generalized-alpha method with controllable numerical damping. In particular, when it comes to the analysis of flexible systems, the nonsmooth generalized-alpha method shows much better accuracy property than the other two methods. [less ▲]

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See detailLie group formalisms in flexible multibody dynamics
Bruls, Olivier ULg

Conference (2013, September)

This course presents a recently-developed Lie group approach for the analysis of flexible multibody systems with large rotations and kinematic constraints in a parameterization-free setting. More ... [more ▼]

This course presents a recently-developed Lie group approach for the analysis of flexible multibody systems with large rotations and kinematic constraints in a parameterization-free setting. More precisely, the equations of motion are formulated as differential-algebraic equations (DAE) on a matrix Lie group and are then solved using a Lie group time integration method. Based on a nonlinear finite element approach, the lecture shows how the kinematics of a flexible multibody system, including the description of nodal frames, velocity fields, constraints, and flexible bodies, are described in the Lie group framework. The general structure of the equations of motion are derived from the Hamilton principle in a general and unifying approach. A Lie group generalized-alpha time integration scheme is proposed for DAEs on a Lie group and practical implementation issues are discussed. Finally, semi-analytical algorithms for sensitivity analysis on a Lie group are proposed for optimization purpose. The theoretical concepts and the numerical properties of the algorithms are illustrated with a number of examples. [less ▲]

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See detailReference populations for shoulder studies should be selected carefully
Schwartz, Cédric ULg; Denoël, Vincent ULg; Bruls, Olivier ULg et al

Conference (2013, August 06)

To assess various shoulder pathologies / treatments, non pathological populations are often used as references. However, some factors may influence significantly the scapular kinematics within a healthy ... [more ▼]

To assess various shoulder pathologies / treatments, non pathological populations are often used as references. However, some factors may influence significantly the scapular kinematics within a healthy population and consequently alter the final kinematic evaluation. Results of 3D shoulder assessment found in this study show that small (≈5°) but significant differences exist between gender and between the dominant and non-dominant arms. Therefore the populations used for referential data should be selected carefully. [less ▲]

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See detailA FEW GOOD REASONS TO CONSIDER A BEAM FINITE ELEMENT FORMULATION ON THE LIE GROUP SE(3)
Sonneville, Valentin ULg; Bruls, Olivier ULg

in Proceedings of the ASME 2013 International Design Engineering Technical Conference & Computers and Information in Engineering Conference IDETC/CIE 2013 (2013, August)

Based on an original interpolation method we develop a beam finite element formulation on the Lie group SE(3) which relies on a mathematically rigorous framework and provides compact and generic notations ... [more ▼]

Based on an original interpolation method we develop a beam finite element formulation on the Lie group SE(3) which relies on a mathematically rigorous framework and provides compact and generic notations. We work out the beam kinematics in the SE(3) context, the beam deformation measure and obtain the expression of the internal forces using the virtual work principle. The proposed formulation exhibits important features from both the theoretical and numerical points of view. The approach leads to a natural coupling of position and rotation variables and thus differs from classical Timoshenko/Cosserat formulations. We highlight several important properties such as a constant deformation measure over the element, an invariant tangent stiffness matrix under of rigid motions or the absence of shear locking. [less ▲]

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See detailContact model between superelements in dynamic multibody systems
Virlez, Geoffrey ULg; Bruls, Olivier ULg; Sonneville, Valentin ULg et al

in Proceedings of ASME2013 International Design Engineering Technical Conference & Computers and Information in Engineering Conference IDETC/CIE 2013 (2013, August)

In this paper, a new contact formulation defined between flexible bodies modeled as superelements is investigated. Unlike rigid contact models, this approach enables to study the deformation and vibration ... [more ▼]

In this paper, a new contact formulation defined between flexible bodies modeled as superelements is investigated. Unlike rigid contact models, this approach enables to study the deformation and vibration phenomena induced by hard contacts. Compared with full-scale finite element models of flexible bodies, the proposed method is computationally more efficient, especially in case of a large number of bodies and contact conditions. The compliance of each body is described using a reduced-order elastic model which is defined in a corotational frame that follows the gross motion of the body. The basis used to reduce the initial finite element model relies on the Craig-Bampton method which uses both static boundary modes and internal vibration modes. The formulation of the contact condition couples all degrees of freedom of the reduced model in a nonlinear way. The relevance of the approach is demonstrated by simulation results first on a simple example, and then on a gear pair model. [less ▲]

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See detailFormulation of a geometrically exact beam finite element on the Lie group SE(3)
Sonneville, Valentin ULg; Cardona, Alberto; Bruls, Olivier ULg

Conference (2013, July)

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See detailAn augmented Lagrangian and reduced index formulation for the analysis of multibody systems with impacts
Bruls, Olivier ULg; Acary, Vincent; Cavalieri, Federico J. et al

Conference (2013, July)

This paper presents a formalism for the simulation of nonsmooth dynamic systems with unilateral constraints, which integrates the contributions of impacts with first order accuracy in a fully implicit way ... [more ▼]

This paper presents a formalism for the simulation of nonsmooth dynamic systems with unilateral constraints, which integrates the contributions of impacts with first order accuracy in a fully implicit way, while the other contributions are integrated with second-order accuracy. Here, the smooth contribution of the reaction forces associated with bilateral and unilateral constraints is also integrated with second-order accuracy. Therefore, in free flight phases, the algorithm is strictly equivalent to a classical second-order scheme. Moreover, following the idea of Gear, Gupta and Leimkuhler, bilateral and unilateral constraints are imposed both at position and velocity levels. This means that the constraints are enforced exactly and no penetration is allowed. In the absence of unilateral constraints, the method leads to a formulation of the equation of motion as an index-2 differential-algebraic equation. Finally, the method is based on a reformulation of the LCP as an augmented Lagrangian equation with a suitable activation / deactivation criterion for the unilateral constraints. The resulting system of nonsmooth equations is solved using a monolithic semi-smooth Newton algorithm. [less ▲]

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See detailA mortar algorithm combined with an Augmented Lagrangian approach for treatment of frictional contact problems
Cavalieri, Federico J.; Bruls, Olivier ULg; Cardona, Alberto

Conference (2013, July)

Contact mechanics is present in a wide range of mechanical engineering applications, and numerous works have been dedicated to the numerical solution of contact problems. Mathematically, the frictional ... [more ▼]

Contact mechanics is present in a wide range of mechanical engineering applications, and numerous works have been dedicated to the numerical solution of contact problems. Mathematically, the frictional contact problem can be seen as defined by a variational inequality. The solution corresponds to the minimum of the total energy of the system, subjected to inequalities constraints associated to the normal and tangential components of the traction and distance vectors, respectively. Nonlinear contact mechanics can be related to nonlinear optimization problems formulated by using the method of Lagrange multipliers, resulting in a saddle point system to be solved at each iteration. The method of Lagrange multipliers is very popular in contact mechanics because it overcomes the ill-conditioning inconvenience of the penalty methods. However, the size of the global matrix increases due to the additional unknowns (the Lagrange multipliers) and zero entries appear on the main diagonal of the stiffness matrix. These drawbacks can be avoided by using an augmented Lagrangian method, which consists in a combination of both the penalty and the Lagrange multipliers techniques. In this work, a mixed penalty-duality formulation based on an augmented Lagrangian approach for treating the contact and the friction inequality constraints is presented. The augmented Lagrangian approach allows to regularize the non differentiable contact terms, giving a C1 differentiable saddle-point function. The relative displacement of the contacting bodies is described in the framework of the Finite Element Method (FEM) using the mortar method, which gives a smooth representation of the contact forces across the bodies interface. [less ▲]

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See detailValidation of an accelerometer-based approach to quantify gait events
Boutaayamou, Mohamed ULg; Schwartz, Cédric ULg; Stamatakis, Julien et al

Poster (2013, June)

Researchers rarely provide solid performance and validation information about their acceleometer-based approaches to human gait analysis. We present here a novel signal processing and analysis algorithm ... [more ▼]

Researchers rarely provide solid performance and validation information about their acceleometer-based approaches to human gait analysis. We present here a novel signal processing and analysis algorithm that automatically extracts four consecutive fundamental events of walking: heel strike (HS), toe strike (TS), heel off (HO), and toe off (TO). In addition, we validate this accelerometer-based technique by comparing these extracted gait events with those obtained by a kinematic 3D analysis system and a force plate, used as gold standards. [less ▲]

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See detailStructural optimization of flexible components under dynamic loading within a multibody system approach: a comparative evaluation of optimization methods based on a 2-dof robot application.
Tromme, Emmanuel ULg; Bruls, Olivier ULg; Virlez, Geoffrey ULg et al

in Proceedings of the 10th World Congress on Structural and Multidisciplinary Optimization: Orlanda (USA), 19-24 mai 2013 (2013, May)

This paper is dedicated to a comparative evaluation between two methods of optimization to realize the structural optimization of flexible components in mechanical systems modeled as multibody systems. A ... [more ▼]

This paper is dedicated to a comparative evaluation between two methods of optimization to realize the structural optimization of flexible components in mechanical systems modeled as multibody systems. A nonlinear finite element method based formalism is considered for the dynamic simulation of the flexible multibody system. The first method is the Equivalent Static Load method which enables to transform a dynamic response optimization problem into a set of static response optimization problems. The second method treats directly the dynamic optimization problem in an integrated manner where the optimization process is carried out directly based on the time response coming from the multibody system approach. However, the first method proposed by Kang, Park and Arora was developed under the assumption that the multibody system is described using a floating frame of reference. Therefore, in order to carry on the comparison using a unique multibody system approach, a method is first proposed to derive the equivalent static loads when using a nonlinear finite element method based formalism. The comparative evaluation is then carried out on the simple academic example of the mass minimization of a two-arm robot subject to tracking deviation constraints. Conclusions are finally drawn for future work and stringent comparison. [less ▲]

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See detailInverse dynamics of serial and parallel underactuated multibody systems using a DAE optimal control approach
Guimaraes Bastos Junior, Guaraci ULg; Seifried, Robert; Bruls, Olivier ULg

in Multibody System Dynamics (2013)

The inverse dynamics analysis of underactuated multibody systems aims at determining the control inputs in order to track a prescribed trajectory. This paper studies the inverse dynamics of non-minimum ... [more ▼]

The inverse dynamics analysis of underactuated multibody systems aims at determining the control inputs in order to track a prescribed trajectory. This paper studies the inverse dynamics of non-minimum phase underactuated multibody systems with serial and parallel planar topology, e.g. for end-effector control of flexible manipulators or manipulators with passive joints. Unlike for minimum phase systems, the inverse dynamics of non-minimum phase systems cannot be solved by adding trajectory constraints (servoconstraints) to the equations of motion and applying a forward time integration. Indeed, the inverse dynamics of a non-minimum phase system is known to be non-causal, which means that the control forces and torques should start before the beginning of the trajectory (preactuation phase) and continue after the end-point is reached (post-actuation phase). The existing stable inversion method roposed for general nonlinear non-minimum phase systems requires to derive explicitly the equations of the internal dynamics and to solve a boundary value problem. This paper proposes an alternative solution strategy which is based on an optimal control approach using a direct transcription method. The method is illustrated for the inverse dynamics of an underactuated serial manipulator with rigid links and four degrees-of-freedom and an underactuated parallel machine. An important advantage of the proposed approach is that it can be applied directly to the standard equations of motion of multibody systems either in ODE or in DAE form. Therefore, it is easier to implement this method in a general purpose simulation software. [less ▲]

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