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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
    Modal Representation of Stress in Flexible Multibody Simulation (1999)
    Springer
    Nonlinear dynamics 20 (1999), S. 381-399 
    Details
    ISSN: 1573-269X
    Keywords: multibody simulation ; flexible body modelling ; modal coordinates ; representation of stress
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An application of the floating frame of reference formulation together with the nodal approach using quasi-comparison functions as shape functions allows an efficient analysis of stress in the flexible bodies of a multibody system. This is demonstrated using two simple examples. They are chosen to demonstrate the effects of various choices of shape functions and associated body reference frames. In the floating frame of reference formulation the equations of motion are linearized assuming the deformations to be small. The quasi-comparison functions, i.e. shape functions, can be selected in ways to increase the range of validity of the linearized equations of motion. The latter goal is achieved as well by so-called substructuring techniques. Combining both of the methodologies, one obtains efficient models for flexible multibody simulation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008322210909
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  • 3
    Electronic Resource
    Electronic Resource
    Representation of geometric stiffening in multibody system simulation (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1833-1850 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Geometric, rotational or dynamic stiffening is a well and long known phenomenon in the analysis of flexible bodies. In multibody dynamics the effect has attracted attention only recently. The objective of this paper is to contribute to the understanding of the modelling of geometric stiffening in multibody system simulation. Today's methods for modelling the effect assume that the (applied) stresses in a flexible system body are zero in its reference configuration, in which it performs large overall motions. The corresponding inertial loads are shown to be balanced by constraint stresses. This can be seen easily when formulating the system equations of motion for non-zero reference stresses. As a result one obtains an efficient alternative to compute the geometric stiffening terms. The method increases the generality of flexible body models for multibody system simulation.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320818
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