Begell House
International Journal for Multiscale Computational Engineering
International Journal for Multiscale Computational Engineering
1543-1649
1
2-3
2003
Foreword to Special Issue on Multibody Computational Dynamics—Modeling Involving Scales from Atoms to the Motion of the Planets
Kurt S.
Anderson
Rensselaer Polytechnic Institute, USA
2
Assessment of the Significance of Nonlinear Terms in the Simulation of Flexible Multibody Systems
The work is concerned with the dynamics of multibody systems with flexible parts undergoing large rigid body motions and small elastic deformations. An attempt to evaluate the influence of nonlinear terms with respect to elastic parameters occurring in the global motion of the system is performed. These nonlinear terms come from centrifugal and Coriolis forces related to the rigid rotation of the bodies. Several studies have been made in the past about this problem, and some approximations or simplifications are sometimes suggested. In order to quantify the relative size of these nonlinear terms, a non dimensional analysis is performed, with some assumptions about the order of magnitude of the different parameters occurring in the dynamical system obtained by Kane’s method. A flexible slider crank mechanism is used as a test example.
Y. C. Mbono
Samba
Universite de Yaoude I, Departement de Mathematiques, Yaounde, Cameroun
M.
Pascal
Laboratoire CEMIF Systemes Complexes, Universite d’Evry Val d’Essonne, Evry, France
12
A Procedure for Modeling Multibody Systems Using Subsystem Models
With the increasing use of microprocessors to control multibody systems, the inclusion of both analogue and digital electronic components in multibody formulations has become one of the challenges facing the multibody community. Models of mechanical systems that incorporate these types of components are referred to as "mechatronic" systems, while multibody systems incorporating only analogue components are dubbed "electromechanical" systems. Traditional approaches to modeling such systems can be very time-intensive and result in extremely complex equations. The following article proposes a method for efficiently generating the governing symbolic equations for an electromechanical multibody system. The key to the proposed approach lies in exploiting the topology of a given system by applying subsystems derived using a newly developed extension to linear graph theory. Exploiting the topology in this manner accommodates parallel formulation strategies and helps to clarify and organize the system level models, thereby increasing the efficiency of the modeling process and subsequent numerical simulations. In addition, because the subsystem models are developed using a linear graph formulation, it is shown that they naturally combine with graph models of electrical subsystems to model electromechanical systems.
Chad
Schmitke
Systems Design Engineering, University of Waterloo, Ontario, Canada
John
McPhee
Systems Design Engineering, University of Waterloo, Ontario, Canada
22
Formulation of Modal-Based Elements in Nonlinear, Flexible Multibody Dynamics
This article is concerned with modeling elastic components in nonlinear, flexible multibody systems. The behavior of the elastic components will be represented by a modal expansion, thereby greatly reducing the computational cost of the simulation. In this work, a floating frame approach is used. The total motion of the elastic body consists of the superposition of the rigid body motions of the floating frame and of elastic motions that are assumed to remain small. The proposed formulation makes use of a component mode synthesis technique that leaves the analyst free to choose any type of modal basis and simplifies the connection of the elastic components to other components of the system. The proposed formulation is independent of the finite element analysis package used to compute the modes of the elastic components. It is also shown that in the absence of elastic deformations, the formulation recovers the exact equations of motion for a rigid body.
Jesus
Rodriguez
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA
Olivier A.
Bauchau
Georgia Inst. of Technology
20
A Generalized Recursive Coordinate Reduction Method for Multibody System Dynamics
The method of recursive coordinate reduction (RCR) offers solutions to the forward problem of multibody dynamics at a cost in which the number of operations is linear in both the number of generalized coordinates, n, and the number of independent algebraic constraints, m (e.g., O(n + m)). However, the RCR is presently restricted in applicability (albeit broad) and susceptible to formulation singularities. This article develops two methods for avoiding formulation singularities as well as a recursive general coupled loop solution that extends the RCR to the complete set of multibody systems. Application of these techniques are further illustrated with a special five-bar linkage. The existing RCR coupled with these developments constitute a generalized recursive coordinate reduction method that should be used in place of the traditional "O(n)" constraint technique (truly O(n + nm2 + m3)) for superior O(n + m) computational performance.
J. H.
Critchley
Department of Mechanical, Aeronautical, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York, USA
Kurt S.
Anderson
Rensselaer Polytechnic Institute, USA
20
Body Reference Frames in Deformable Multibody Systems
One interesting topic in multibody dynamics is how a reference frame is attached to a moving deformable body. Two known forms of reference axes are the nodal-fixed and the mean axes frames; the former is commonly used in structural finite element modeling, and the latter is known as a floating frame. In this article we introduce a new reference frame based on the principal axes that is also a form of floating frame. The equations of motion for a deformable body are derived first, and then the conditions for different types of reference axes are implemented. Next, the equations of motion for a rigid-deformable multibody system are constructed, where the deformation variables are kept in the nodal space. Through several simulation examples, some phenomena associated with each type of reference frame are discussed.
Parviz E.
Nikravesh
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, Arizona, USA
Yi-shih
Lin
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, Arizona, USA
18
Multibody Mass Matrix Sensitivity Analysis Using Spatial Operators
This article discusses an approach for sensitivity analysis of multibody dynamics using spatial operators. The spatial operators are rooted in the function space approach to estimation theory developed in the decades following the introduction of the Kalman filter and used extensively to develop a range of results in multibody dynamics. The operators provide a mathematical framework for studying a wide range of analytical and computational problems associated with multibody system dynamics. This article focuses on the computation of the sensitivity of the system mass matrix for tree-topology multibody systems and develops an analytical expression for the same using spatial operators. As an application example, mass matrix sensitivity is used to derive analytical expressions based on composite body inertias for the Christoffel symbols associated with the equations of motion.
Guillermo
Rodriguez
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109
Abhinandan
Jain
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109
16
Treatment of Constraints in Complex Multibody Systems. Part I: Methods of Constrained Dynamics
The objective of this investigation is to discuss the use of several nonlinear dynamic formulations for modeling constraints in large-scale multibody systems in general, and tracked vehicles in particular. Among the formulations discussed in this article are the augmented method, the nonpartitioning augmented method, the recursive method, and the penalty method. In the augmented formulation, the vehicle kinematic constraints that describe mechanical joints and specified motion trajectories are augmented to the system dynamic equations using the technique of Lagrange multipliers. A Newton–Raphson algorithm and a coordinate partitioning scheme are used to ensure that the kinematic constraint equations are satisfied at the position level. In the nonpartitioning augmented formulation, no check is made to satisfy the kinematic constraint equations and, as a consequence, no coordinate partitioning is required. In the recursive formulation, the system kinematic equations are expressed in terms of the joint degrees of freedom. This formulation allows for modeling spherical, revolute, prismatic, and cylindrical joints. Using this formulation, closed loop chains are modeled using the recursive joint formulation, and cuts are made at selected secondary joints in order to avoid the singular configurations. In the penalty formulation, mechanical joints are modeled using elastic force elements that have assumed stiffness and damping coefficients. These above-mentioned four formulations are discussed in this article. Results of the computer simulations of a large-scale bulldozer model are presented in Part II of this two-part article.
Taira
Ozaki
Construction Equipment Technical Center 1, Development Division, Komatsu Ltd., Osaka, Japan
Ahmed A.
Shabana
Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, Illinois, USA
18
Treatment of Constraints in Complex Multibody Systems. Part II: Application to Tracked Vehicles
In Part I of this two-part article, different methods for modeling the joints in constrained multibody dynamics were presented. These methods led to different forms of the dynamic equations and required the use of different solution procedures. It was demonstrated that the solutions obtained using these methods were in a good agreement when simple systems were considered. In Part II, the performance of different formulations discussed in Part I is evaluated using a heavily constrained mechanical system that is subjected to impulsive forces. To this end, the tracked vehicle model described in Part I is used. Crucial to the success of modeling such vehicles is the development of accurate models for joint constraints and the impulsive contact forces that result from the interaction between the track chains and the vehicle components as well as the interaction between these chains and the ground. The nonlinear contact force models used in the numerical study presented in this investigation are developed, and the formulations of the generalized forces associated with the generalized coordinates used in each of the formulations presented in Part I are discussed. The numerical algorithms and implementation of these algorithms as well as evaluation of the performance of different methods in the analysis of detailed tracked vehicle models are discussed.
Taira
Ozaki
Construction Equipment Technical Center 1, Development Division, Komatsu Ltd., Osaka, Japan
Ahmed A.
Shabana
Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, Illinois, USA
24
Efficient Computation of Fluid Drag Forces on Micromachined Devices Using a Boundary Integral Equation-Based Approach
In this article, we report several techniques for improving the efficiency and accuracy of a precorrected fast Fourier transform (FFT)-accelerated solver for the computation of fluid drag forces on micromachined devices using a boundary element discretization of the integral form of the incompressible Stokes flow equations. The boundary element formulation necessitates the discretization of the surface of the device using a large number of "panels," whose interactions are coupled by multidimensional Stokes kernels. The resulting "n-body" problem generates dense matrices that can be solved in O(n log n) complexity using a precorrected FFT approach, where n is the number of panels used in discretizing the surface of the device.
Suvranu
De
Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, New York, USA
12
A Robust Simulation Algorithm for Conservative Linear Mechanical Systems
Proposed in this article is an inherently conservative simulation scheme, based on the zero-order hold and a closed-form time response of the system at hand. It is shown that the simulation algorithm can be cast in a form in which the state-transition matrix, mapping a state at instant tk into a state at instant tk+1, is proper orthogonal. Hence, for an n-degree-of-freedom (dof) system, this matrix represents a rotation in the 2n-dimensional space of state variables. As a result, the numerical damping required in the simulation of undamped systems is obviated. The performance of the algorithm is illustrated with two examples drawn from engineering systems.
Khalid
Al-Widyan
Department of Mechanical Engineering and Centre for Intelligent Machines, McGill University, Montreal, Canada
Jorge
Angeles
Department of Mechanical Engineering and Centre for Intelligent Machines, McGill University, Montreal, Canada
Svetlana
Ostrovskaya
Department of Mechanical Engineering and Centre for Intelligent Machines, McGill University, Montreal, Canada
22
Unilateral Multibody Dynamics
For many years existing multibody theories could only deal with bilateral constraints. Recent developments allow for an inclusion of unilateral constraints, which always accompany contact processes such as contact/detachment, stick/slip, or impacts with and without friction. This article gives a survey.
Friedrich
Pfeiffer
Lehrstuhl fur Angewandte Mechanik, TU-Munchen, Boltzmannstra.e 15, D-85748 Garching
16