Modal reduction procedures for flexible multibody dynamics
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Modal reduction procedures for flexible multibody dynamics Valentin Sonneville1 · Matteo Scapolan1 · Minghe Shan1 · Olivier A. Bauchau1
Received: 3 July 2020 / Accepted: 18 November 2020 © The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature 2020
Abstract Through a critical review of the various component mode synthesis techniques developed in the past, it is shown that both Craig–Bampton’s and Herting’s methods are particular cases of the mode-acceleration method and furthermore, Rubin’s method is equivalent to Herting’s method. Consequently, the mode-acceleration method is the approach of choice due to its simplicity and because unlike the other methods, it imposes no restriction on the selection of the modes. Next, a general approach to the modal reduction of geometrically nonlinear structures is developed within the framework of the motion formalism, based on the small deformation assumption. The floating frame of reference is defined unequivocally by imposing six linear constraints on the deformation measures, which are defined as the vectorial parameterization of the relative motion tensor that brings the fictitious rigidbody configuration to its deformed counterpart. This approach yields deformation measures that are both objective and tensorial, unlike their classical counterparts that share the first property only. Derivatives are expressed in the material frame, leading to computationally advantageous properties: tangent matrices are functions of the deformation measures only and become nearly constant during the simulation. Numerical examples demonstrate the accuracy, robustness, and numerical efficiency of the proposed approach. With a small number of modal elements, the formulation is able to capture geometrically nonlinear effects accurately, even in the presence of inherently nonlinear phenomena such as buckling. Keywords Flexible multibody systems · Finite element analysis · Component mode synthesis
B O.A. Bauchau
[email protected] V. Sonneville [email protected] M. Scapolan [email protected] M. Shan [email protected]
1
Department of Aerospace Engineering, University of Maryland, College Park, Maryland 20742, USA
V. Sonneville et al.
1 Introduction Multibody systems often involve components that present complex three-dimensional geometries and undergo small deformation. For those components, two questions must be answered: (1) what is the impact of the flexibility of the component on the dynamic response of the overall system and (2) what is the three-dimensional stress field in such component? The prediction of the three-dimensional stress fields in these complex components requires the use of three-dimensional finite element models, often involving fine mesh sizes to capture complex geometries, intricate material property distributions, and the resulting threedimensional strain fields that determine structural flexibility. Fine mesh sizes result in a set of algebraic equations that is prohibitively large for direct dynamic simulation and leads to the appearance of
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