References of "Cardona, Alberto"
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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 detailSpurious oscillations in generalized-alpha time integration methods
Arnold, Martin; Bruls, Olivier ULg; Cardona, Alberto

Conference (2012, March)

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See detailLie group generalized-alpha time integration of constrained flexible multibody systems
Bruls, Olivier ULg; Cardona, Alberto; Arnold, Martin

in Mechanism & Machine Theory (2012), 48

This paper studies a Lie group extension of the generalized-alpha time integration method for the simulation of flexible multibody systems. The equations of motion are formulated as an index-3 ... [more ▼]

This paper studies a Lie group extension of the generalized-alpha time integration method for the simulation of flexible multibody systems. The equations of motion are formulated as an index-3 differential-algebraic equation (DAE) on a Lie group, with the advantage that rotation variables can be taken into account without the need of introducing any parameterization. The proposed integrator is designed to solve this equation directly on the Lie group without index reduction. The convergence of the method for DAEs is studied in detail and global second-order accuracy is proven for all solution components, i.e. for nodal translations, rotations and Lagrange multipliers. The convergence properties are confirmed by three benchmarks of rigid and flexible systems with large rotation amplitudes. The Lie group method is compared with a more classical updated Lagrangian method which is also formulated in a Lie group setting. The remarkable simplicity of the new algorithm opens interesting perspectives for real-time applications, model-based control and optimization of multibody systems. [less ▲]

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See detailModelling of frictional unilateral contact in automotive differentials
Virlez, Geoffrey ULg; Cardona, Alberto; Bruls, Olivier ULg et al

Conference (2011, November 14)

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See detailImproved stability and transient behaviour of generalized-alpha time integrators for constrained flexible systems
Arnold, Martin; Bruls, Olivier ULg; Cardona, Alberto

Conference (2011, November)

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See detailTwo Lie Group Formulations for Dynamic Multibody Systems with Large Rotations
Bruls, Olivier ULg; Arnold, Martin; Cardona, Alberto

in Proceedings of the ASME 2011 International Design Engineering Technical Conferences (2011, August)

This paper studies the formulation of the dynamics of multibody systems with large rotation variables and kinematic constraints as differential-algebraic equations on a matrix Lie group. Those equations ... [more ▼]

This paper studies the formulation of the dynamics of multibody systems with large rotation variables and kinematic constraints as differential-algebraic equations on a matrix Lie group. Those equations can then be solved using a Lie group time integration method proposed in a previous work. The general structure of the equations of motion are derived from Hamilton principle in a general and unifying framework. Then, in the case of rigid body dynamics, two particular formulations are developed and compared from the viewpoint of the structure of the equations of motion, of the accuracy of the numerical solution obtained by time integration, and of the computational cost of the iteration matrix involved in the Newton iterations at each time step. In the first formulation, the equations of motion are described on a Lie group defined as the Cartesian product of the group of translations R^3 (the Euclidean space) and the group of rotations SO(3) (the special group of 3 by 3 proper orthogonal transformations). In the second formulation, the equations of motion are described on the group of Euclidean transformations SE(3) (the group of 4 by 4 homogeneous transformations). Both formulations lead to a second-order accurate numerical solution. For an academic example, we show that the formulation on SE(3) offers the advantage of an almost constant iteration matrix. [less ▲]

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See detailConvergence analysis of generalized-alpha Lie group integrators for constrained systems
Arnold, Martin; Bruls, Olivier ULg; Cardona, Alberto

in Proceedings of Multibody Dynamics ECCOMAS Conference (2011, July)

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See detailConvergence analysis for a generalized-alpha Lie group time integrator
Arnold, Martin; Bruls, Olivier ULg; Cardona, Alberto

Conference (2011, January)

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See detailLie group integrators for the numerical solution of DAE’s in flexible multibody dynamics
Cardona, Alberto; Bruls, Olivier ULg; Arnold, Martin

Conference (2010, November)

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See detailNumerical solution of DAEs in flexible multibody dynamics using Lie group time integrators
Bruls, Olivier ULg; Cardona, Alberto; Arnold, Martin

in Proceedings of the First Joint International Conference on Multibody System Dynamics (2010, May)

This paper studies a family of Lie group time integrators for the simulation of flexible multibody systems. The method provides an elegant solution to the rotation parameterization problem and, as an ... [more ▼]

This paper studies a family of Lie group time integrators for the simulation of flexible multibody systems. The method provides an elegant solution to the rotation parameterization problem and, as an extension of the classical generalized-alpha method for dynamic systems, it can deal with constrained equations of motion. Here, second-order accuracy of the Lie group method is demonstrated for constrained problems. The convergence analysis explicitly accounts for the nonlinear geometric structure of the Lie group. The performance is illustrated on two critical benchmarks of rigid and flexible systems with large rotation amplitudes. Second-order accuracy is evidenced in both of them. The remarkable simplicity of the new algorithms opens some interesting perspectives for real-time applications, model-based control and optimization of multibody systems. [less ▲]

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See detailTime integration of finite rotations in flexible multibody dynamics using Lie group integrators
Bruls, Olivier ULg; Cardona, Alberto

Conference (2010, May)

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See detailOn the use of Lie group time integrators in multibody dynamics
Bruls, Olivier ULg; Cardona, Alberto

in Journal of Computational and Nonlinear Dynamics (2010), 5(3), 031002

This paper proposes a family of Lie group time integrators for the simulation of flexible multibody systems. The method provides an elegant solution to the rotation parameterization problem. As an ... [more ▼]

This paper proposes a family of Lie group time integrators for the simulation of flexible multibody systems. The method provides an elegant solution to the rotation parameterization problem. As an extension of the classical generalized-alpha method for dynamic systems, it can deal with constrained equations of motion. Second-order accuracy is demonstrated in the unconstrained case. The performance is illustrated on several critical benchmarks of rigid body systems with high rotation speeds and second order accuracy is evidenced in all of them, even for constrained cases. The remarkable simplicity of the new algorithms opens some interesting perspectives for real-time applications, model-based control and optimization of multibody systems. [less ▲]

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See detailLie group vs. classical time integrators in multibody dynamics: Formulations and numerical benchmarks
Bruls, Olivier ULg; Cardona, Alberto

Conference (2009, September)

The dynamics of flexible multibody systems with large rotations is often described using large sets of index-3 differential-algebraic equations. In this context, the Lie group structure of the dynamic ... [more ▼]

The dynamics of flexible multibody systems with large rotations is often described using large sets of index-3 differential-algebraic equations. In this context, the Lie group structure of the dynamic system may be exploited in order to provide an elegant solution to the rotation parameterization problem. The talk discusses an original Lie-group extension of the classical generalized-alpha method, which can be used to solve index-3 differential-algebraic equations in multibody dynamics. Second-order accuracy is demonstrated at least in the unconstrained case and the performance is illustrated on several critical benchmarks with high rotational speeds. The remarkable simplicity of the new algorithms opens some interesting perspectives for real-time applications, model-based control and optimization of multibody systems. [less ▲]

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See detailModelling of the squeeze film air damping in MEMS
Barroso, Juan José Gómez; Bruls, Olivier ULg; Berli, Claudio et al

in Proceedings of the ENIEF Conference (2009)

We propose a formulation for modeling the squeeze film air damping in micro-plates typical of micro-electromechanical devices for micro switch applications. A special finite element is developed, in which ... [more ▼]

We propose a formulation for modeling the squeeze film air damping in micro-plates typical of micro-electromechanical devices for micro switch applications. A special finite element is developed, in which the nonlinear Reynolds equation for compressible film is used to analyze the air pressure field, whereas a standard linear elastic model is used for the displacement field. The formulation is based on a finite element discretization of both the pressure and displacement fields. The coupled equations of motion are established and, for harmonic oscillations, we show that the resulting damping matrix depends on the frequency. The typical dimensions and properties of the MEMS device are in the order of hundred micrometers length and some micrometers (3-8 micrometers) thick, with a separation from the substrate of also some micrometers (e.g. 3-5 micrometers). For these dimensions, the influence of damping owing to the surrounding air cannot be neglected, having an important contribution to the quality factor of the device. The influence of plate holes, which are necessary because of the fabrication process, determines also the dynamic behavior of the plate. Examples are presented, with comparisons to results of the bibliography. [less ▲]

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See detailModelling, simulation and control of flexible multibody systems
Bruls, Olivier ULg; Cardona, Alberto; Géradin, Michel ULg

in Arnold, Martin; Schiehlen, Werner (Eds.) Simulation Techniques in Applied Dynamics (2008)

This chapter concerns the dynamic analysis of flexible multibody systems. After a brief review of the inertial frame, the corotational frame and the floating frame approaches, a general simulation ... [more ▼]

This chapter concerns the dynamic analysis of flexible multibody systems. After a brief review of the inertial frame, the corotational frame and the floating frame approaches, a general simulation framework is presented in detail. Based on the finite element concept, the proposed approach allows the coupled analysis of dynamic systems composed of rigid and flexible bodies, kinematic joints and control elements. The text is illustrated with some didactic examples and industrial applications. [less ▲]

Detailed reference viewed: 56 (3 ULg)