A direct violation correction method in numerical simulation of constrained multibody systems

2000 ◽  
Vol 26 (1) ◽  
pp. 52-57 ◽  
Author(s):  
Q. Yu ◽  
I.-M. Chen
Keyword(s):  
Numerical Simulation ◽  
Multibody Systems ◽  
Correction Method ◽  
Constrained Multibody Systems

On the Use of the Canonical Equations of Motion for the Dynamic Analysis of Constrained Multibody Systems

1992 ◽  
Author(s):  
E. Bayo ◽  
J. M. Jimenez
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Numerical Algorithms ◽  
Constrained Multibody Systems ◽  
Constrained Mechanical Systems ◽  
First Order ◽  
Canonical Variables ◽  
Lagrange’S Multipliers

Abstract We investigate in this paper the different approaches that can be derived from the use of the Hamiltonian or canonical equations of motion for constrained mechanical systems with the intention of responding to the question of whether the use of these equations leads to more efficient and stable numerical algorithms than those coming from acceleration based formalisms. In this process, we propose a new penalty based canonical description of the equations of motion of constrained mechanical systems. This technique leads to a reduced set of first order ordinary differential equations in terms of the canonical variables with no Lagrange’s multipliers involved in the equations. This method shows a clear advantage over the previously proposed acceleration based formulation, in terms of numerical efficiency. In addition, we examine the use of the canonical equations based on independent coordinates, and conclude that in this second case the use of the acceleration based formulation is more advantageous than the canonical counterpart.

Numerical Simulation of Multibody Systems With Time Dependant Structure

1993 ◽  
Author(s):  
Pierre Joli ◽  
Madeleine Pascal ◽  
René Gibert
Keyword(s):  
Numerical Simulation ◽  
Multibody Systems ◽  
Computational Algorithm ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Integration Step ◽  
General Systems ◽  
Articulated Systems ◽  
Jump Velocity ◽  
Assembly Tasks

Abstract Current dynamic simulation programs are able to calculate the continuous motions of articulated systems or more general systems of rigid bodies in the absence of contact between members of the system or between the system and its environment. Some are able to simulate the effects of isolated contacts and impacts but none are able to simulate the motion with unrestricted multiple concurrent contacts. However, in special robotic programs such as robots performing assembly tasks or walking, it would be very interesting to simulate appropriate commands before implementing them on the robots. This paper develops intrinsic problems of collision to produce an efficient computational algorithm. This algorithm handles the detection of collision in three dimensions, the reduction of the integration step in order to avoid interpenetration between the bodies before impact, the jump velocity caused by a new collision and indicator magnitudes which determine the addition or deletion of constraints.

Utilizing the Effort/Motion Approach in the Simulation of Interconnected Rigid Body Systems

1997 ◽  
Author(s):  
N. Duke Perreira
Keyword(s):  
Numerical Simulation ◽  
Rigid Body ◽  
Multibody Systems ◽  
Invariant Form ◽  
Second Law ◽  
Orthogonal Projections ◽  
Gauge Invariant ◽  
Motion Equations ◽  
Newton's Second Law ◽  
Constraint Surface

Abstract The effort/motion approach has been developed for use in designing, simulating and controlling multibody systems. Some aspects of each of these topics are discussed here. In the effort/motion formulation two sets of equations based on the orthogonal projections of a dimensional gauge invariant form of Newton’s Second Law occur. The projections are onto the normal and tangent directions of a dimensional gauge invariant constraint surface. The paper shows how these equations are obtained for a particular linkage with redundant effort and motion actuation. Two alternative Runga-Kutta based approaches for numerical simulation of the effort/motion equations are developed and applied in simulating the motion and determining the effort generated in the example linkage under various conditions. Oscillation about equilibrium positions, solutions with constant motion and with constant effort are given as examples of the approach.

Dynamics of Flexible Beams and Plates in Large Overall Motions

1992 ◽  
Vol 59 (4) ◽  
pp. 991-999 ◽  
Author(s):  
Z. E. Boutaghou ◽  
Arthur G. Erdman ◽  
Henryk K. Stolarski
Keyword(s):  
Dynamic Response ◽  
Nonlinear Interaction ◽  
Multibody Systems ◽  
Present Theory ◽  
Rigid Body Dynamics ◽  
Flexible Beams ◽  
Constrained Multibody Systems ◽  
Dynamic Stiffening ◽  
Body Dynamics ◽  
Arbitrary Representation

The dynamic response of flexible beams, plates, and solids undergoing arbitrary spatial motions are systematically derived via a proposed approach. This formulation is capable of incorporating arbitrary representation of the kinematics of deformation, phenomenon of dynamic stiffening, and complete nonlinear interaction between elastic and rigid-body dynamics encountered in constrained multibody systems. It is shown that the present theory captures the phenomenon of dynamic stiffening due to the transfer of the axial and membrane forces to the bending equations of beams and plates, respectively. Examples are presented to illustrate the proposed formulations.

Numerical Simulation of Flash Floods Routing Based on Improved Leap-Frog Method

2013 ◽  
Vol 347-350 ◽  
pp. 2173-2177
Author(s):  
Jia Hua Zhang ◽  
Chi Zhang
Keyword(s):  
Numerical Simulation ◽  
Moving Boundary ◽  
Simulation Analysis ◽  
Flash Flood ◽  
Mass Conservation ◽  
Correction Method ◽  
Gansu Province ◽  
Simulation Accuracy ◽  
Whole Process ◽  
Steep Terrain

in the 2-d numerical simulation of flash flood disaster, due to flood often occurred in the steep terrain and water flow rapidly changed, lead to that the calculated value is unstable and even the calculation diverge in the simulation. This paper presents a grid outflow correction method, which is based on the leap-frog finite difference format, through modifying the outflow rate of the grid circularly, to ensure the mass conservation in the whole process of computing. In the local dam bursting model, the simulated result comparison of the grid outflow correction method and the algorithm of implicit alternating direction on the mass conservation shows that, the new method can ensure the simulation accuracy and the numerical stability under the condition of steep terrain and moving boundary. According to the proposed method, the simulation analysis in the process of extreme flash flood disasters which happened in 2010 Zhouqu county in Gansu province was carried out. The comparison of simulation results and remote sensing estimation results shows that the deviation of the flood evolution time, speed and impact height are within 5%, and the consistency of evolution path is good, which verifies the validity of the algorithm.

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