Model order reduction of multibody system dynamics based on stiffness evaluation in the absolute nodal coordinate formulation

Kim, Euiyoung; Kim, Hyunil; Cho, Maenghyo

doi:10.1007/s11071-016-3161-y

Cited by 26 publications

(9 citation statements)

References 14 publications

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“…The superscript [0] here stands for the initial value of the corresponding vector in the Newton-Raphson iteration of a simulation time. Substituting Equation (28) into Equation (27), one gets…”

Section: A Condensed Algorithm In the Subsystemmentioning

confidence: 99%

“…33 Modal base updated process is a simple problem of solving eigenvectors using the current mass M and stiffness matrices G in Equation 7. Once the modal bases of a subsystem are updated, it is necessary to update the subsystem matrices of reduced order in Equations (24), (26), (27), (30), and (32), the assembled matrices in Equation 34, so as to obtain the new dynamic equations of reduced order based on a new modal base in Equation (33). The initial conditions in the generalized-α method should also be represented in the new modal bases.…”

Section: Reduced Order Computation Algorithm For Fmbs Dynamicsmentioning

confidence: 99%

“…21 Therefore, many approaches have been developed so far to speed up the computation. Among them, there are the parallel algorithms associated with computer resources, 22,23 and the model order reduction (MOR) algorithms with energy equivalence, [24][25][26][27][28][29][30][31][32][33] or their combinations. In addition, the dynamic substructuring algorithms 23,24,30,31,34 have been develop to obtain the global dynamic response of a complicated structural system by decomposing a large-scale problem into several small ones and solving those small ones independently.…”

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confidence: 99%

“…38 In most existing studies on the MOR of flexible multibody dynamics, the modes are derived from the configuration of a corresponding rigid-body configuration with zero energy or initial configuration. [24][25][26][27] Mode shapes and mode frequencies are based on linear description of small deformations and determined from solving an eigenvalue problem. 33,35,39 Thus, previous studies neglected the influence of the dynamic deformations of flexible bodies on the quasi-static equilibrium configurations.…”

mentioning

confidence: 99%

“…33,35,39 Thus, previous studies neglected the influence of the dynamic deformations of flexible bodies on the quasi-static equilibrium configurations. Although these studies [24][25][26][27] have updated the stiffness or mass matrices of the large deformed bodies, called nonlinear method, 27 a common feature of them is that they have nothing to do with the description of dynamic configurations. The continuous use of modal bases derived from the initial configuration leads to poor convergence or even divergence.…”

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confidence: 99%

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A condensed algorithm for adaptive component mode synthesis of viscoelastic flexible multibody dynamics

Tang

Tian

2020

Numerical Meth Engineering

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A condensed algorithm for adaptive component mode synthesis is proposed to compute the dynamics of viscoelastic flexible multibody systems efficiently and accurately. As studied, the continuous use of modes derived from the initial configuration will lead to poor convergence when dealing with geometric nonlinearity caused by large deformations and overall rotations. The modal reduction at a series of quasi-static equilibrium configurations should be updated accordingly. According to the loss rate of system energy in the updating process of modal bases, an adaptive mode selection is proposed to reserve the optimal modal bases with their modal number automatically so as to achieve a high-accuracy simulation. In the proposed condensed iteration algorithm, the order of reduced dynamic equations in the Newton-Raphson is far less than the number of the unknowns to be discrete in generalized-α scheme. Using an analytical mapping between the two parts of unknowns, the new algorithm solves a small part of the unknowns iteratively and solves the others noniteratively. Therefore, the saving of time cost comes not only from the proposed adaptive component mode synthesis, but also from the proposed condensed iteration algorithm. The modal bases of subsystems are updated by a series of frame-like quasi-static equilibrium configurations independently, in conjunction with the Craig-Bampton method. Thus, the challenges in the model reduced of extensive ranges of stiffness and damping are removed via the successively updated modal bases. Finally, three numerical tests are made to illuminate the high accuracy and efficiency of the new algorithm proposed. K E Y W O R D S absolute nodal coordinate formulation, condensed algorithm for adaptive component mode synthesis, flexible multibody dynamics, modal reductions, viscoelastic damping 1 INTRODUCTION The past few decades have witnessed the development 1-4 of the computational dynamics of flexible multibody systems (FMBS). The geometrically exact beam formulation (GEBF) 2,3 and the absolute nodal coordinate formulation (ANCF) 4 are two promising formulations to handle the complexities of both large deformations and overall rotations. Simo and Vu-Quoc 2,3 developed the GEBF based on Reissner's theory, and the main problem of the GEBF is how to handle the

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Section: A Condensed Algorithm In the Subsystemmentioning

confidence: 99%