Finite-element based recursive formulation for real time dynamic simulation of flexible multibody systems

1991 ◽  
Vol 40 (4) ◽  
pp. 939-945 ◽  
Author(s):  
S.K. Ider
1999 ◽  
Vol 122 (4) ◽  
pp. 498-507 ◽  
Author(s):  
Marcello Campanelli ◽  
Marcello Berzeri ◽  
Ahmed A. Shabana

Many flexible multibody applications are characterized by high inertia forces and motion discontinuities. Because of these characteristics, problems can be encountered when large displacement finite element formulations are used in the simulation of flexible multibody systems. In this investigation, the performance of two different large displacement finite element formulations in the analysis of flexible multibody systems is investigated. These are the incremental corotational procedure proposed in an earlier article (Rankin, C. C., and Brogan, F. A., 1986, ASME J. Pressure Vessel Technol., 108, pp. 165–174) and the non-incremental absolute nodal coordinate formulation recently proposed (Shabana, A. A., 1998, Dynamics of Multibody Systems, 2nd ed., Cambridge University Press, Cambridge). It is demonstrated in this investigation that the limitation resulting from the use of the infinitesmal nodal rotations in the incremental corotational procedure can lead to simulation problems even when simple flexible multibody applications are considered. The absolute nodal coordinate formulation, on the other hand, does not employ infinitesimal or finite rotation coordinates and leads to a constant mass matrix. Despite the fact that the absolute nodal coordinate formulation leads to a non-linear expression for the elastic forces, the results presented in this study, surprisingly, demonstrate that such a formulation is efficient in static problems as compared to the incremental corotational procedure. The excellent performance of the absolute nodal coordinate formulation in static and dynamic problems can be attributed to the fact that such a formulation does not employ rotations and leads to exact representation of the rigid body motion of the finite element. [S1050-0472(00)00604-8]


2015 ◽  
Vol 10 (2) ◽  
Author(s):  
Wenhao Guo ◽  
Tianshu Wang

By means of a recursive formulation method, a generalized impulse–momentum-balance method, and a constraint violation elimination (CVE) method, we propose a new global simulation method for flexible multibody systems with kinematic structure changes. The constraint equations of a pair of adjacent bodies, considering body flexibility in Cartesian space, are derived for a recursive formulation. Constraint equations in configuration space, which are obtained from the constraints presented in this paper via recursive formulation, are very useful for modeling different kinematic structures and impacting governing equations. The novelty is that the impact governing equations, which calculate the jumps of generalized velocities, are modified by taking velocity-level CVE into consideration. Numerical examples are given to validate the presented method. Simulation results show that the new method can effectively suppress constraint drifts at the velocity level and stabilize constraint violations at the position level.


Author(s):  
Marcello Berzeri ◽  
Marcello Campanelli ◽  
A. A. Shabana

Abstract In this investigation, the performance of two different large displacement finite element formulations in the analysis of flexible multibody systems is investigated. These are the incremental corotational procedure proposed by Rankin and Brogan [8] and the non-incremental absolute nodal coordinate formulation recently proposed [9]. It is demonstrated in this investigation that the limitation resulting from the use of the nodal rotations in the incremental corotational procedure can lead to simulation problems even when very simple flexible multibody applications are considered.


Author(s):  
Frank Naets ◽  
Gert H. K. Heirman ◽  
Wim Desmet

This paper introduces a novel model reduction technique, namely Sub-System Global Modal Parameterization (SS-GMP), for real-time simulation of flexible multibody systems. In the past, other system-level model reduction techniques have been proposed for this purpose, but these were limited in applicability due to the large storage requirements for systems with many rigid degrees-of-freedom (DOFs). However, in the SS-GMP approach, the motion of a mechanism is split up into a global motion and a relative motion of the (sub-)system. The relative motion is then reduced according to the Global Modal Parameterization, which is a model reduction procedure suitable for closed chain flexible multibody systems. In combination with suitable explicit solvers, the SS-GMP approach enables (hard) real-time simulations due to the strong reduction in the number of DOFs and the conversion of a system of differential-algebraic equations into a system of ordinary differential equations. The proposed approach is validated numerically with a quarter-car model. This fully flexible mechanism is simulated faster than real-time on a regular PC with the SS-GMP approach while providing accurate results.


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