References of "Sonneville, Valentin"
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See detailA formulation on the special Euclidean group for dynamic analysis of multibody systems
Sonneville, Valentin ULg; Bruls, Olivier ULg

in Journal of Computational and Nonlinear Dynamics (2014), 9(4), 041002

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See detailGeometric interpretation of a non-linear beam finite element on the Lie group SE(3)
Sonneville, Valentin ULg; Cardona, Alberto; Bruls, Olivier ULg

in Archive of Mechanical Engineering (2014), 61(2), 305-329

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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 ▲]

Detailed reference viewed: 62 (12 ULg)
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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 ▲]

Detailed reference viewed: 62 (12 ULg)
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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 ▲]

Detailed reference viewed: 62 (12 ULg)
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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 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 detailFormulation of Kinematic Joints and Rigidity Constraints in Multibody Dynamics using a Lie Group Approach
Sonneville, Valentin ULg; Bruls, Olivier ULg

in Proceedings of the 2nd Joint International Conference on Multibody System Dynamics (IMSD) (2012, May)

The matrix Lie group approach allows to formulate and solve the equations of motion of a multibody system in a parametrization-free framework. The kinematic joints and the rigidity constraints should also ... [more ▼]

The matrix Lie group approach allows to formulate and solve the equations of motion of a multibody system in a parametrization-free framework. The kinematic joints and the rigidity constraints should also be formulated as constraint equations on the Lie group. Working on the Special Euclidean group SE(3), we introduce a method to obtain appropriate vectorial constraint equations in terms of mixed coordinates. Moreover, we present an absolute coordinates formulation, based on an relative coordinates elimination method, so that the minimum number of constraint equations necessary to describe the joints is used. [less ▲]

Detailed reference viewed: 84 (14 ULg)