Adaptive model reduction technique for large-scale dynamical systems with frequency-dependent damping

Xie, Xiaofeng; Zheng, Hui; Jonckheere, Stijn; Walle, Axel van de; Pluymers, Bert; Desmet, Wim

doi:10.1016/j.cma.2017.12.023

Cited by 49 publications

(40 citation statements)

References 25 publications

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“…Mode selection is crucial to the accuracy of the MOR algorithms. 21,63,64 In order to forecast and control the truncation errors in the simulation process, an adaptive mode selection method based on two criteria is proposed as follows. Assuming that the lth subsystem performs the new local linearization at moment t = t N+1 , one derives the corresponding total energy as Π(ėe) =…”

Section: Adaptive Algorithmmentioning

confidence: 99%

“…The model is often intractable for the computation memory and time limitations. 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.…”

mentioning

confidence: 99%

“…36,55 The MOR algorithms have been used to deal with the vibrating structures with material damping in frequency domain. 21,22,36,43,56 A comparison 57 was made for various MOR algorithms adapted to structures with frequency-dependent damping, aiming at improving the modal strain energy. The main characteristics of viscoelastic materials strongly depend on temperature and frequency, 58 thus results in challenges due to the broad ranges of mechanical properties, mainly stiffness and damping.…”

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confidence: 99%

“…33 An adaptive MOR algorithm based on Taylor's theorem with frequency-dependent damping systems was proposed in the field of structural dynamics. 21 A two-step condensation method 59 was proposed based on the floating frame of reference formulation (FFRF) with approximated expressions for the influence of the residual modes recently. The necessity of using the modes of current equilibrium configuration in large deformations and overall rotations has been discussed in the third paragraph of the introduction.…”

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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: Adaptive Algorithmmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

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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“…Model order reduction (MOR) is a field considerably developed in computational simulations in engineering; such field has relevant applications in many other fields, like dynamics as explained in related works, multiscale analysis, and fluids analysis . Related to the development of the MOR itself, several MOR with offline analysis are described in other works, or in online analysis as developed in previous works; several of them achieving meaningful results related to the processing time.…”

Section: Introductionmentioning

confidence: 99%

Model order reduction with Galerkin projection applied to nonlinear optimization with infeasible primal‐dual interior point method

Nigro

Simões²,

Pimenta

et al. 2019

Numerical Meth Engineering

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Summary It is not new that model order reduction (MOR) methods are employed in almost all fields of engineering to reduce the processing time of complex computational simulations. At the same time, interior point methods (IPMs), a method to deal with inequality constraint problems (which is little explored in engineering), can be applied in many fields such as plasticity theory, contact mechanics, micromechanics, and topology optimization. In this work, a MOR based in Galerkin projection is coupled with the infeasible primal‐dual IPM. Such research concentrates on how to develop a Galerkin projection in one field with the interior point method; the combination of both methods, coupled with Schur complement, permits to solve this MOR similar to problems without constraints, leading to new approaches to adaptive strategies. Moreover, this research develops an analysis of error from the Galerkin projection related to the primal and dual variables. Finally, this work also suggests an adaptive strategy to alternate the Galerkin projection operator, between primal and dual variable, according to the error during the processing of a problem.

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“Advanced” Methods for the Vibro‐acoustic Response of Naval Structures

LEBLOND

2022

Fluid–Structure Interaction

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Adaptive model reduction technique for large-scale dynamical systems with frequency-dependent damping

Cited by 49 publications

References 25 publications

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

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

Model order reduction with Galerkin projection applied to nonlinear optimization with infeasible primal‐dual interior point method

“Advanced” Methods for the Vibro‐acoustic Response of Naval Structures

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