Variational Integrators and Energy-Momentum Schemes for Flexible Multibody Dynamics

2010 ◽  
Vol 5 (3) ◽  
Author(s):  
Peter Betsch ◽  
Christian Hesch ◽  
Nicolas Sänger ◽  
Stefan Uhlar
Keyword(s):  
Multibody Dynamics ◽  
Flexible Multibody Dynamics ◽  
Discrete Systems ◽  
Differential Algebraic Equations ◽  
Nonlinear Finite Element ◽  
Variational Integrators ◽  
Algebraic Equations ◽  
Variational Integrator ◽  
Nonlinear Finite Element Methods ◽  
Flexible Multibody

This work contains a comparison between variational integrators and energy-momentum schemes for flexible multibody dynamics. In this connection, a specific “rotationless” formulation of flexible multibody dynamics is employed. Flexible components such as continuum bodies and geometrically exact beams and shells are discretized in space by using nonlinear finite element methods. The motion of the resulting discrete systems are governed by a uniform set of differential-algebraic equations (DAEs). This makes possible the application and comparison of previously developed structure-preserving methods for the numerical integration of the DAEs. In particular, we apply a specific variational integrator and an energy-momentum scheme. The performance of both integrators is assessed in the context of three representative numerical examples.

Discontinuous Galerkin Method and Dual-SLERP for Time Integration of Flexible Multibody Dynamics

2020 ◽  
Vol 15 (9) ◽  
Author(s):  
Shilei Han ◽  
Olivier A. Bauchau
Keyword(s):  
Discontinuous Galerkin ◽  
Multibody Dynamics ◽  
Time Integration ◽  
Flexible Multibody Dynamics ◽  
Differential Algebraic Equations ◽  
Body Motion ◽  
Motion Field ◽  
Algebraic Equations ◽  
Time Step ◽  
Flexible Multibody

Abstract A novel time-discontinuous Galerkin (DG) method is introduced for the time integration of the differential-algebraic equations governing the dynamic response of flexible multibody systems. In contrast to traditional Galerkin methods, the rigid-body motion field is interpolated using the dual spherical linear scheme. Furthermore, the jumps inherent to time-DG methods are expressed in terms of a parameterization of the relative motion from one time-step to the next. The proposed scheme is third-order accurate for initial value problems of both rigid and flexible multibody dynamics.

Numerical Solution and Experiment Researches on Flexible Multibody Dynamics

1994 ◽  
Author(s):  
Liu Hongzhao ◽  
Cao Weiqing
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Multibody Dynamics ◽  
Lagrange Multipliers ◽  
Flexible Multibody Dynamics ◽  
Differential Algebraic Equations ◽  
Measuring System ◽  
Linkage Test ◽  
Test Bed ◽  
Flexible Multibody

Abstract In this paper, a numerical solution method and an experiment research on flexible multibody dynamics are presented. The augment method is employed to transfer the differential-algebraic equations into differential equations, both generalized coordinates and lagrange multipliers are treated as unknowns, and the second-order self-correcting algorithm is introduced to guarantee convergence. The lagrange multipliers are eliminated analytically, and the half implicit Runge-Kutta formula is taken for solving the differential equations. The whole procedure is developed into a FORTRAN program. An elastic linkage test bed and a measuring system are made for verification. The computing results are in agreement with the measuring data.

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

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