Simultaneous enforcement of constraints at position and velocity levels in the nonsmooth generalized-alpha scheme Bruls, Olivier ; ; in Computer Methods in Applied Mechanics & Engineering (in press) This paper presents a formalism for the transient simulation of nonsmooth dynamic mechanical systems composed of rigid and flexible bodies, kinematic joints and frictionless contact conditions. The ... [more ▼] This paper presents a formalism for the transient simulation of nonsmooth dynamic mechanical systems composed of rigid and flexible bodies, kinematic joints and frictionless contact conditions. The proposed algorithm guarantees the exact satisfaction of the bilateral and unilateral constraints both at position and velocity levels. Thus, it significantly differs from penalty techniques since no penetration is allowed. The numerical scheme is obtained in two main steps. Firstly, a splitting method is used to isolate the contributions of impacts, which shall be integrated with only first-order accuracy, from smooth contributions which can be integrated using a higher order scheme. Secondly, following the idea of Gear, Gupta and Leimkuhler, the equations of motion are reformulated so that the bilateral and unilateral constraints appear both at position and velocity levels. After time discretization, the equations of motion involve two complementarity conditions and it can be solved at each time step using a monolithic semi-smooth Newton method. The numerical behaviour of the proposed method is studied and compared to other approaches for a number of numerical examples. It is shown that the formulation offers a unified and valid approach for the description of contact conditions between rigid bodies as well as between flexible bodies. [less ▲] Detailed reference viewed: 17 (0 ULg)Error analysis of generalized-alpha Lie group time integration methods for constrained mechanical systems ; Bruls, Olivier ; in Numerische Mathematik (in press) Generalized-alpha methods are very popular in structural dynamics. They are methods of Newmark type and combine favourable stability properties with second order convergence for unconstrained second order ... [more ▼] Generalized-alpha methods are very popular in structural dynamics. They are methods of Newmark type and combine favourable stability properties with second order convergence for unconstrained second order systems in linear spaces. Recently, they were extended to constrained systems in flexible multibody dynamics that have a configuration space with Lie group structure. In the present paper, the convergence of these Lie group methods is analysed by a coupled one-step error recursion for differential and algebraic solution components. It is shown that spurious oscillations in the transient phase result from order reduction that may be avoided by a perturbation of starting values or by index reduction. Numerical tests for a benchmark problem from the literature illustrate the results of the theoretical investigations. [less ▲] Detailed reference viewed: 1 (1 ULg)Geometric interpretation of a non-linear beam finite element on the Lie group SE(3) Sonneville, Valentin ; ; Bruls, Olivier in Archive of Mechanical Engineering (in press) Detailed reference viewed: 14 (2 ULg)A formulation on the special Euclidean group for dynamic analysis of multibody systems Sonneville, Valentin ; Bruls, Olivier in Journal of Computational and Nonlinear Dynamics (in press) Detailed reference viewed: 17 (2 ULg)A mortar method combined with an augmented Lagrangian approach for treatment of mechanical contact problems ; Bruls, Olivier ; in Terze, Zdravko (Ed.) Multibody Dynamics: Computational Methods and Applications (2015) This work presents a mixed penalty-duality formulation from an augmented Lagrangian approach for treating the contact inequality constraints. The augmented Lagrangian approach allows to regularize the non ... [more ▼] This work presents a mixed penalty-duality formulation from an augmented Lagrangian approach for treating the contact inequality constraints. The augmented Lagrangian approach allows to regularize the non differentiable contact terms and gives a C1 differentiable saddle-point functional. The relative displacement of two 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. To study the robustness and performance of the proposed algorithm, validation numerical examples with finite deformations and large slip motion are presented. [less ▲] Detailed reference viewed: 13 (2 ULg)Influence of players' level on racket speed and ball accuracy in the tennis serve Tubez, François ; Croisier, Jean-Louis ; Cordonnier, Caroline et al Conference (2014, July 06) INTRODUCTION Serve in modern tennis game is an important offensive weapon for players (1-2). In kinematic analysis, serve is the most studied stroke of this game. The aim of our study was to compare the ... [more ▼] INTRODUCTION Serve in modern tennis game is an important offensive weapon for players (1-2). In kinematic analysis, serve is the most studied stroke of this game. The aim of our study was to compare the performance of two specific populations: international players versus national players. In particular, racket speed at impact and accuracy of ball were assessed. METHODS A tennis court was reconstructed in a motion analysis laboratory. The position of the racket was evaluated in 3D at a frequency rate of 200 Hz. Tests were performed on 6 professional players (international level) and 9 non-professional players (national level). Each of them served 25 trials in direction of the “T” area of deuce diagonal. Two squares of 1m² and 2 m² respectively were delimited on the corner of the serve square. The instruction for both groups was to serve in the “T” area with the highest ball speed and minimal ball rotation (flat serve). RESULTS Although the forward speed of the racket at impact was identical between the two groups of players (International 36.35 ± 2.37 m/s and national 36.37 ± 2.90 m/s, p-value 0,991), the accuracy and consistency of serves on the target area is better for international players group (1m² area: International 33% ± 7% and national 14% ± 12%, p-value 0.0053; 2m² area (including 1m² area): International 71% ± 8% and national 54% ± 12%, p-value 0.0096; Out of zone: International 29% ± 8% and national 46% ± 12%, p-value 0.014). DISCUSSION High-velocity ball seems to be a key factor for serve performance (3). It is known that there is a relationship between racket speed and ball velocity (4). Both groups have high racket speed. However, international players serve with better accuracy and consistency than national players. We hypothesize that these differences are due to capacity of international players to adapt to a particular environment. Moreover, international players could give priority to consistency over velocity. We conclude that high-velocity serve is not a sufficient criterion to perform at international level; consistency and accuracy are two important factors to reach this level. [less ▲] Detailed reference viewed: 27 (16 ULg)Comparison between first and second landing for different vertical drop jump tasks. Implication in injury risk prevention Cordonnier, Caroline ; Croisier, Jean-Louis ; Forthomme, Bénédicte et al Conference (2014, July 04) Detailed reference viewed: 16 (5 ULg)Dynamic simulation of flexible gear pairs using a contact modelling between superelements Virlez, Geoffrey ; Bruls, Olivier ; Tromme, Emmanuel et al Conference (2014, July 02) Detailed reference viewed: 14 (4 ULg)Advanced Aeroservoelastic Modeling for Horizontal axis Wind Turbines Prasad, Chandra Shekhar ; ; Dimitriadis, Grigorios et al in Cunha, A.; Caetano, E.; Riberio, P. (Eds.) et al Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 (2014, July) This paper describes the development of a complete methodology for the unsteady aeroelastic and aeroservoelastic modeling of horizontal axis wind turbines at the design stage. The methodology is based on ... [more ▼] This paper describes the development of a complete methodology for the unsteady aeroelastic and aeroservoelastic modeling of horizontal axis wind turbines at the design stage. The methodology is based on the implementation of unsteady aerodynamic modeling, advanced control strategies and nonlinear finite element calculations in the S4WT wind turbine design package. The aerodynamic modeling is carried out by means of the unsteady Vortex Lattice Method, including a free wake model. The complete model also includes a description of a doubly fed induction generator and its control system for variable speed operation and enhanced power output. The S4WT software features a non-linear finite element solver with multi-body dynamics capability. The complete methodology is used to perform complete aeroservoelastic simulations of a 2MW wind turbine prototype model. The interaction between the three components of the approach is carefully analyzed and presented here. [less ▲] Detailed reference viewed: 12 (2 ULg)FORMULATION OF A NON-LINEAR SHELL FINITE ELEMENT ON THE LIE GROUP SE(3) Sonneville, Valentin ; Bruls, Olivier Conference (2014, July) Detailed reference viewed: 7 (1 ULg)Model reduction of geometrically exact structures formulated on the Lie group SE(3) Sonneville, Valentin ; Bruls, Olivier Conference (2014, July) Detailed reference viewed: 9 (0 ULg)Order reduction in time integration caused by velocity projection ; ; Bruls, Olivier in Proceedings of the 3rd Joint International Conference on Multibody System Dynamics and the 7th Asian Conference on Multibody Dynamics (2014, July) Holonomic constraints restrict the configuration of a multibody system to a subset of the configuration space. They imply so called hidden constraints at the level of velocity coordinates that may ... [more ▼] Holonomic constraints restrict the configuration of a multibody system to a subset of the configuration space. They imply so called hidden constraints at the level of velocity coordinates that may formally be obtained from time derivatives of the original holonomic constraints. A numerical solution that satisfies hidden constraints as well as the original constraint equations may be obtained considering both types of constraints simultaneously in each time step (stabilized index-2 formulation) or using projection techniques. Both approaches are well established in the time integration of differential-algebraic equations. Recently, we have introduced a generalized- alpha Lie group time integration method for the stabilized index-2 formulation that achieves second order convergence for all solution components. In the present paper, we show that a separate velocity projection would be less favourable since it may result in an order reduction and in large transient errors after each projection step. This undesired numerical behaviour is analysed by a one-step error recursion that considers the coupled error propagation in differential and algebraic solution components. This one-step error recursion has been used before to prove second order convergence for the application of generalized-alpha methods to constrained systems. As a technical detail, we discuss the extension of these results from symmetric, positive definite mass matrices to the rank deficient case. [less ▲] Detailed reference viewed: 9 (2 ULg)A semi-analytical sensitivity analysis for multibody systems described using Level Sets Tromme, Emmanuel ; Bruls, Olivier ; Duysinx, Pierre et al Conference (2014, June) Detailed reference viewed: 8 (2 ULg)Recent progresses in the nonsmooth contact dynamics method for flexible multibody systems Bruls, Olivier Scientific conference (2014, January 10) This talk will start with a brief overview of the current research activities undertaken at the Multibody & Mechatronic Systems Laboratory with a number of applications in the fields of wind turbines ... [more ▼] This talk will start with a brief overview of the current research activities undertaken at the Multibody & Mechatronic Systems Laboratory with a number of applications in the fields of wind turbines, deployable space structures, robotics and human motion analysis. Then, the presentation will focus on some recent results related with the modelling of dynamic contact conditions in multibody systems. Typical applications include the modelling of non-ideal joints with backlash and friction, the analysis of mechanical transmission systems and gearboxes, the modelling of grasping tasks or the description of the foot-ground contact in gait analysis. The proposed formalism relies on the nonsmooth contact dynamics method. Accordingly, the condition of impenetrability of the bodies in contact is expressed as a unilateral constraint, with the consequence that impacts and/or instantaneous changes in the velocities may arise in the dynamic response. Also, the resulting set of equations is solved in the time domain using a time-stepping strategy, which is known its robustness and its ability to deal with a large number of events in an efficient way. After a review of the time-stepping method originally proposed by Moreau and Jean, a number of improvements are addressed during the talk. Firstly, a splitting method is introduced to isolate the contributions of impacts, which can only be integrated with first-order accuracy, from smooth contributions, which can be integrated using a higher order scheme. Secondly, following the idea of Gear, Gupta and Leimkuhler, the equation of motion is reformulated so that the bilateral and unilateral constraints appear both at position and velocity levels. This strategy leads to an algorithm which exactly satisfies the constraints at both levels, i.e., no penetration is allowed in the numerical response. After time discretization, the equation of motion involves two complementarity conditions and it can be solved at each time step using a monolithic semi-smooth Newton method. The numerical behaviour of the proposed scheme is studied and compared to other approaches for a number of numerical examples. It is shown that the formulation offers a unified and valid approach for the description of contact conditions between rigid bodies as well as between flexible bodies. [less ▲] Detailed reference viewed: 12 (1 ULg)A stable inversion method for feedforward control of constrained flexible multibody systems Bruls, Olivier ; ; in Journal of Computational and Nonlinear Dynamics (2014), 9(1), 011014 The inverse dynamics of flexible multibody systems is formulated as a two-point boundary value problem for an index-3 differential-algebraic equation (DAE). This DAE represents the equation of motion with ... [more ▼] The inverse dynamics of flexible multibody systems is formulated as a two-point boundary value problem for an index-3 differential-algebraic equation (DAE). This DAE represents the equation of motion with kinematic and trajectory constraints. For so-called nonminimum phase systems, the remaining dynamics of the inverse model is unstable. Therefore, boundary conditions are imposed not only at the initial time but also at the final time in order to obtain a bounded solution of the inverse model. The numerical solution strategy is based on a reformulation of the DAE in index-2 form and a multiple shooting algorithm, which is known for its robustness and its ability to solve unstable problems. The paper also describes the time integration and sensitivity analysis methods that are used in each shooting phase. The proposed approach does not require a reformulation of the problem in input-output normal form known from nonlinear control theory. It can deal with serial and parallel kinematic topology, minimum phase and nonminimum phase systems, and rigid and flexible mechanisms. [less ▲] Detailed reference viewed: 3 (0 ULg)Sensitivity analysis for multibody systems formulated on a Lie group Sonneville, Valentin ; Bruls, Olivier 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: 61 (12 ULg)Sensitivity analysis for multibody systems formulated on a Lie group Sonneville, Valentin ; Bruls, Olivier 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: 61 (12 ULg)Sensitivity analysis for multibody systems formulated on a Lie group Sonneville, Valentin ; Bruls, Olivier 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: 61 (12 ULg)Sonneville, Valentin ; Bruls, Olivier in Multibody System Dynamics (2014), 31 Geometrically exact beam finite element formulated on the special Euclidean group SE(3) Sonneville, Valentin ; ; Bruls, Olivier 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 ▲] Detailed reference viewed: 38 (12 ULg) |
||