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  • 1
    Electronic Resource
    Electronic Resource
    Flexible Multibody Simulation and Choice of Shape Functions (1999)
    Springer
    Nonlinear dynamics 20 (1999), S. 361-380 
    Details
    ISSN: 1573-269X
    Keywords: multibody simulation ; flexible body modelling ; interaction of multibody- and finite-element-codes ; shape functions and quasi-comparison functions ; nodal and modal coordinates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The approach most widely used for the modelling of flexible bodies in multibody systems has been called the floating frame of reference formulation. In this methodology the flexible body motion is subdivided into a reference motion and deformation. The displacement field due to deformation is approximated by the Ritz method as a product of known shape functions and unknown coordinates depending on time only. The shape functions may be obtained using finite-element-models of flexible bodies in multibody systems, resulting in a detailed system representation and a high number of system equations. The number of system equations of such a nodal approach can be reduced considerably using a modal representation of deformation. This modal approach, however, leads to the fundamental problem of selecting the shape functions. The floating frame of reference formulation is reviewed here using a generic flexible body model, from which the various body models used in multibody simulations may be derived by formulation of specific constraint equations. Special attention is given in this investigation to the following subjects: • The separation of flexible body motion into a reference motion and deformation requires the definition of a body reference frame, which in turn affects the choice of shape functions. Some alternatives will be outlined together with their advantages and disadvantages. • Assuming the body deformation to be small, the system equations can be linearized. This may require considering geometric stiffening terms. The problem of how to compute these terms has been solved in literature on the instability of structures under critical loads. For finite element models the geometric stiffening terms are obtained from the tangential stiffness matrix. • The generality of the flexible body model allows the definition of an object oriented data base to describe the system bodies. Such a data base includes a general interface between multibody- and finite-element-codes. • By combining eigenfunctions and static deformation modes to represent body deformation one obtains a set of so-called quasi-comparison functions. When selected properly these functions can be shown to improve the representation of stresses significantly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008314826838
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  • 2
    Electronic Resource
    Electronic Resource
    Flexible Multibody Dynamics: Review of Past and Recent Developments (1997)
    Springer
    Multibody system dynamics 1 (1997), S. 189-222 
    Details
    ISSN: 1573-272X
    Keywords: flexible multibody dynamics ; finite element formulations ; incremental methods ; large rotations ; finite segment method ; linear theory of elastodynamics ; elastic body inertia ; rigid body inertia ; impact in flexible body dynamics ; control-structure interaction ; computer graphics ; large deformation problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In this paper, a review of past and recent developments in the dynamics of flexible multibody systems is presented. The objective is to review some of the basic approaches used in the computer aided kinematic and dynamic analysis of flexible mechanical systems, and to identify future directions in this research area. Among the formulations reviewed in this paper are the floating frame of reference formulation, the finite element incremental methods, large rotation vector formulations, the finite segment method, and the linear theory of elastodynamics. Linearization of the flexible multibody equations that results from the use of the incremental finite element formulations is discussed. Because of space limitations, it is impossible to list all the contributions made in this important area. The reader, however, can find more references by consulting the list of articles and books cited at the end of the paper. Furthermore, the numerical procedures used for solving the differential and algebraic equations of flexible multibody systems are not discussed in this paper since these procedures are similar to the techniques used in rigid body dynamics. More details about these numerical procedures as well as the roots and perspectives of multibody system dynamics are discussed in a companion review by Schiehlen [79]. Future research areas in flexible multibody dynamics are identified as establishing the relationship between different formulations, contact and impact dynamics, control-structure interaction, use of modal identification and experimental methods in flexible multibody simulations, application of flexible multibody techniques to computer graphics, numerical issues, and large deformation problem. Establishing the relationship between different flexible multibody formulations is an important issue since there is a need to clearly define the assumptions and approximations underlying each formulation. This will allow us to establish guidelines and criteria that define the limitations of each approach used in flexible multibody dynamics. This task can now be accomplished by using the “absolute nodal coordinate formulation” which was recently introduced for the large deformation analysis of flexible multibody systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009773505418
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  • 3
    Electronic Resource
    Electronic Resource
    Computer Implementation of the Absolute Nodal Coordinate Formulation for Flexible Multibody Dynamics (1998)
    Springer
    Nonlinear dynamics 16 (1998), S. 293-306 
    Details
    ISSN: 1573-269X
    Keywords: Multibody dynamics ; finite elementmethod ; QR decomposition ; Cholesky decomposition ; absolute nodal coordinate formulation ; floating frameof reference formulation ; incremental methods ; large deformation ; large rotation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Deformable components in multibody systems are subject to kinematic constraints that represent mechanical joints and specified motion trajectories. These constraints can, in general, be described using a set of nonlinear algebraic equations that depend on the system generalized coordinates and time. When the kinematic constraints are augmented to the differential equations of motion of the system, it is desirable to have a formulation that leads to a minimum number of non-zero coefficients for the unknown accelerations and constraint forces in order to be able to exploit efficient sparse matrix algorithms. This paper describes procedures for the computer implementation of the absolute nodal coordinate formulation' for flexible multibody applications. In the absolute nodal coordinate formulation, no infinitesimal or finite rotations are used as nodal coordinates. The configuration of the finite element is defined using global displacement coordinates and slopes. By using this mixed set of coordinates, beam and plate elements can be treated as isoparametric elements. As a consequence, the dynamic formulation of these widely used elements using the absolute nodal coordinate formulation leads to a constant mass matrix. It is the objective of this study to develop computational procedures that exploit this feature. In one of these procedures, an optimum sparse matrix structure is obtained for the deformable bodies using the QR decomposition. Using the fact that the element mass matrix is constant, a QR decomposition of a modified constant connectivity Jacobian matrix is obtained for the deformable body. A constant velocity transformation is used to obtain an identity generalized inertia matrix associated with the second derivatives of the generalized coordinates, thereby minimizing the number of non-zero entries of the coefficient matrix that appears in the augmented Lagrangian formulation of the equations of motion of the flexible multibody systems. An alternate computational procedure based on Cholesky decomposition is also presented in this paper. This alternate procedure, which has the same computational advantages as the one based on the QR decomposition, leads to a square velocity transformation matrix. The computational procedures proposed in this investigation can be used for the treatment of large deformation problems in flexible multibody systems. They have also the advantages of the algorithms based on the floating frame of reference formulations since they allow for easy addition of general nonlinear constraint and force functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008072517368
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  • 4
    Electronic Resource
    Electronic Resource
    In Memory of Dr. Richard Schwertassek August 14, 1940–April 5, 2000 (2000)
    Springer
    Nonlinear dynamics 22 (2000), S. 315-316 
    Details
    ISSN: 1573-269X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008365123888
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  • 5
    Electronic Resource
    Electronic Resource
    Three-dimensional absolute nodal co-ordinate formulation: plate problem (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 2775-2790 
    Details
    ISSN: 0029-5981
    Keywords: large rotation ; large deformation ; finite element ; plate element ; multibody dynamics ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this investigation, an absolute nodal co-ordinate dynamic formulation is developed for the large deformations and rotations of three-dimensional plate elements. In this formulation, no infinitesimal or finite rotations are used as nodal co-ordinates, instead global displacements and slopes are used as the plate coordinates. Using this interpretation of the plate coordinates the new method does not require the use of co-ordinate transformation to define the global inertia properties of the plates. The resulting mass matrix is the same constant matrix that appears in linear structural dynamics. The stiffness matrix, on the other hand, is a non-linear function of the nodal co-ordinates of the plate even in the case of a linear elastic problem. It is demonstrated in this paper that, unlike the incremental finite element formulations, the proposed method leads to an exact modelling of the rigid body inertia when the plate element moves as a rigid body. It is also demonstrated that by using the proposed method the conventional plate element shape function has a complete set of rigid body modes that can describe an exact arbitrary rigid body displacement. Using this fact, plate elements in the proposed new formulation can be considered as isoparametric elements. As a consequence, an arbitrary rigid body motion of the element results in zero strain. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Book
    Book
    Dynamics of multibody systems / (2005)
    Cambridge [u.a.] :Cambridge Univ. Press,
    Details
    Title: Dynamics of multibody systems /
    Author: Shabana, Ahmed A.
    Edition: 3. ed.,
    Publisher: Cambridge [u.a.] :Cambridge Univ. Press,
    Year of publication: 2005
    Pages: X, 374 S. : graph. Darst.
    ISBN: 0-521-85011-8
    Type of Medium: Book
    Language: English
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  • 7
    Unknown
    Dynamics of multibody systems (2005)
    Cambridge ; New York : Cambridge University Press
    Details
    Keywords: Dynamics. ; Kinematics.
    Pages: x, 374 p.
    Edition: 3rd ed
    ISBN: 0-511-11583-0
    URL: http://www.netLibrary.com/urlapi.asp?action=summary&v=1&bookid=138999
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    E-Book (German National Licenses)
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