An explicit–implicit method for flexible–rigid multibody systems

Lim, H.C.; Taylor, Robert L.

doi:10.1016/s0168-874x(01)00073-7

Cited by 6 publications

(2 citation statements)

References 14 publications

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“…The use of rotational quaternions in beam and multibody theories has been mostly limited to construct numerically stable and efficient local computational algorithms that avoid singularity problems and accelerate computations (see, e.g. [6], [9], [14], [20], [23], [27], [31]). Zupan and Saje [36] studied the effect of the choice of the parametrization of rotations when integrating rotations from angular velocities using various methods.…”

Section: Introductionmentioning

confidence: 99%

Quaternion-based dynamics of geometrically nonlinear spatial beams using the Runge–Kutta method

Zupan

Saje

Zupan

2012

Finite Elements in Analysis and Design

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The rotational quaternions are the unique four dimensional representation of rotations in three dimensional Euclidean space. In the present paper on the dynamics of non-linear spatial beams, they are used as the basic rotational parameters in formulating the finite-element approach of geometrically exact beam-like structures. The classical concept of parametrizing the rotation matrix by the rotational vector is completely abandoned so that the only rotational parameters are the rotational quaternions representing both rotations and rotational strains in the beam. Because the quaternions are the elements of a four dimensional linear space, their use is an advantage compared to the elements of the special orthogonal group SO(3). This makes possible, e.g. to interpolate the rotational quaternions in a standard additive way and to apply standard Runge-Kutta time integration methods. The present finite-element realization of such a quaternion-based beam theory introduces some further ideas including the use of collocation, the weak form of the consistency equations and the symmetrically integrated boundary conditions which enhances the accuracy or efficiency of the solution and avoids the differential-algebraic type of the discretized governing equations often met in classical formulations. The main advantage of the proposed dynamics formulation is probably its simple implementation into the standard Runge-Kutta procedures. Thus several benefits of the Runge-Kutta methods such as the absence of the analytical linearization of the discrete governing equations, the local error control and the adaptive time steps are automatically incorporated in the present procedure.

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Section: Introductionmentioning

confidence: 99%

Quaternion-based dynamics of geometrically nonlinear spatial beams using the Runge–Kutta method

Zupan

Saje

Zupan

2012

Finite Elements in Analysis and Design

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“…If one uses classical rotation parameters, such as Euler angles or spin vector, it is difficult to determine stability conditions for an explicit integration scheme. This motivated us to introduce a new set of parameters, based on the so-called 'four-mass' concept [8,9], to describe global rigid motion. The position and orientation of the local frame are given by four points whose distances to one another are kept constant during the simulation.…”

Section: Introductionmentioning

confidence: 99%

Local modal reduction in explicit dynamics with domain decomposition. Part 1: extension to subdomains undergoing finite rigid rotations

Faucher

Combescure

2004

Numerical Meth Engineering

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SUMMARYWe present an extension of the dual Schur multidomain method with local linear modal reduction previously introduced by Gravouil, Combescure, Herry and Faucher to the case of modal reduction on geometrically non-linear vibrating subdomains. This first part of a two-part paper describes a new formalism, based on an original set of parameters, to represent a subdomain's finite rigid-body motion. Special attention is paid to the stability issues with time integration using the central difference scheme. The method is validated on an academic example and its efficiency is demonstrated on a large-scale example.

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An Improved Contact Algorithm for Multi‐Material Continuum Codes

Walls

Littlefield

2013

Materials Under Extreme Loadings

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An explicit–implicit method for flexible–rigid multibody systems

Cited by 6 publications

References 14 publications

Quaternion-based dynamics of geometrically nonlinear spatial beams using the Runge–Kutta method

Quaternion-based dynamics of geometrically nonlinear spatial beams using the Runge–Kutta method

Local modal reduction in explicit dynamics with domain decomposition. Part 1: extension to subdomains undergoing finite rigid rotations

An Improved Contact Algorithm for Multi‐Material Continuum Codes

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