Multibody system dynamic simulation

W. Schiehlen (ed.) Advanced Multibody System Dynamics. Simulation and Software Tools. 

ABSTRACT We describe a method based on mass-orthogonal projections that can be used to eliminate the algebraic variables in the DAEs of index 2 of multibody system dynamics, reducing them to ODEs. A choice among the infinitely many ODE systems that describe the dynamics correctly is proposed. A reduction of the computational cost of linear algebra operations is described. We present DYNAMITE, a tool-kit based software for the simulation of multibody systems that implements the methods discussed, and illustrate its application to a low-voltage circuit breaker. 

This approach makes the database independent of the multibody system dynamics formalisms. As an example, we have written interfaces both to a traditional mechanical engineer simulator, ADAMS [11], which is commercially available, and to a new code, Sophia2 [12,13], developed by M. Lesser at the Royal Institute of Technology in Sweden. 

The notation Z)/ in the first term indicates a summation over all atoms in the system and Vi(r/) represents the potential in an external force field. The second term, usually called the pair potential, is probably the most important energy term in a molecular dynamics simulation. The pair potential sums over all distinct atom pairs i and j without counting any pair twice. The function V2(r/, Vj) depends only on the separation between atoms i and j and hence can also be expressed as V2(r,y). Three-body and other multibody potentials are normally avoided in molecular dynamics simulations since they are not easy to implement and can be extremely time consuming. The multi-body effects are usually taken into account by modifying the pair potential, i.e., using an effective pair potential, which is not the exact interaction potential between the two... 

The primary objective of this bode is the concise derivation and clear presentation of efficient algorithms for the dynamic simulation of robotic systems. In particular, robots and other multibody systems with closed-loop kinematic configurations are considered. It is assumed that each robot cr muldbody system is comprised of rigid bodies which are connected by ideal Joints and powered by ideal actuator. 

In general, the inertia matrix of a manipulator defines the relationship between certain forces exerted on the system and some corresponding acceleration vector. This relationship is of great importance both in real-time control and in the simulation of multibody systems. In the control realm, for example, the inertia matrix has been used to decouple robot dynamics so that control schemes may be more effectively tq>plied [19]. This may be accomplished either in joint space O operational space, since the inertia matrix may be defined in eith domain. The inertia matrix has also been used in the analysis of collision effects [43]. In addition to its use in control applications, the inertia matrix is an explicit and integral part of certain Direct Dynamics algorithms which are used to solve the simulation problem for manipulators and other multibody systems [2, 8, 31, 33,42]. 

In this section we introduce the concept of implicit Runge-Kutta methods of collocation type without aiming for completeness. The use of implicit Runge-Kutta methods is quite recent in multibody dynamics. There are higher order A-stable methods in this class for simulating highly oscillatory problems as well as methods specially designed for constrained multibody systems, see Sec. 5.4.2. 

Arn95] Arnold M. (1995) A perturbation analysis for the dynamical simulation of mechanical multibody systems. Applied Numerical Mathematics 18 37-56. 

ABSTRACT. This paper presents an efficient algorithm based on velocity transformations for real-time dynamic simulation of multibody systems. Closed-loop systems are turned into open-loop systems by cutting joints. The closure conditions of the cut joints are imposed by explicit constraint equations. An algorithm for real-time simulation is presented that is well suited for parallel processing. The most computationally demanding tasks are matrix and vector products that may computed in parallel for each body. Four examples are presented that illustrate the performance of the method. 

Anderson, K. S., Recursive Derivation of Explicit Equations of Motion for Efficient Dynamics/Control Simulation of Large Multibody Systems, Ph.D. Dissertation, Stanford University, July, 1990. 

Wallrapp, O. and Schwertassek, R., Geometric Stiffening in Multibody Systems Simulation, Proceedings of Int. Forum on Aeroelasticity and Structural Dynamics 1991 Aachen, DGLR, D-5300 Bonn. 

The second approach to vehicle dynamics simulation involves mathematical models which incorporate representations of the vehicle kinematics, tyre characteristics and suspension geometry effects. This approach to vehicle dynamics simulation can result in mathematical models which are highly complex. Consequently, automated model generation facilities based on multibody systems (MBS) modelling techniques are widely employed. 

Classical molecular dynamics (MD) simulations rely on model potentials describing the interactions between the particles in the system, rather than a first-principles calculation of the system energy at each time step. Obviously, the quality of the outcome depends on the quality of the model potential. Model potentials are normally either fit to experimental results, or based on first-principles calculation. Since the majority of the model potentials is based on two-body interactions only, such potentials generally ignore the multibody character of real interactions. The time evolution of the system is computed by solving numerically Newton s laws of motion. Molecular dynamics or molecular simulation is a vast field with many fields of applications. For detailed discussions, see Refs. [9, 10]. 

As an application of the theory discussed earlier, the crash responses of aircraft occupant/stnicture will be presented. To improve aircraft crash safety, conditions critical to occupants survival during a crash must be known. In view of the importance of this problem, studies of post-crash dynamic behavior of victims are necessary in order to reduce severe injuries. In this study, crash dynamics program SOM-LA/TA (Seat Occupant Model - Light Aircraft / Transport Aircraft) was used (13,14]. Modifications were performed in the program for reconstruction of an occupant s head impact with the interior walls or bulkhead. A viscoelastic-type contact force model of exponential form was used to represent the compliance characteristics of the bulkhead. Correlated studies of analytical simulations with impact sled test results were accomplished. A parametric study of the coefficients in the contact force model was then performed in order to obtain the correlations between the coefficients and the Head Injury Criteria. A measure of optimal values for the bulkhead compliance and displacement requirements was thus achieved in order to keep the possibility of a head injury as little as possible. This information could in turn be usm in the selection of suitable materials for the bulkhead, instrument panel, or interior walls of an aircraft. Before introducing the contact force model representing the occupant head impacting the interior walls, descriptions of impact sled test facilities, multibody dynamics and finite element models of the occupant/seat/restraint system, duplication of experiments, and measure of head injury are provided. 

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