Model order reduction based on successively local linearizations for flexible multibody dynamics

This paper presents a novel system-level model order reduction scheme for flexible multibody simulation, namely the system-level affine projection (SLAP). Contrary to existing system-level model order reduction approaches for multibody systems simulation, this methodology allows to obtain a constant reduced order basis which can be obtained in a noninvasive fashion with respect to the original flexible multibody model. It is shown that this scheme enables an automatic joint constraint elimination which can be obtained at low computational cost through exploitation of the component level modes typically employed in flexible multibody simulation. The equations of motion are derived such that the computational cost of the resulting SLAP model is independent of the original model size. This approach results in a set of ordinary differential equations with a constant mass matrix and nonlinear internal forces. This structure makes the resulting model suitable for a range of estimation, control, and design applications. The proposed approach is validated numerically on a flexible four-bar mechanism and shows good accuracy for a very low-order SLAP model. K E Y W O R D S flexible multibody, model reduction, nonlinear INTRODUCTIONOver the past decades flexible multibody simulation has demonstrated itself as a powerful framework for the dynamic analysis of mechanical systems consisting of multiple components. For many industrial applications, the small deformation assumption in particular has led to the development of range of efficient descriptions like the floating-frame-of-reference component mode synthesis (FFR-CMS) 1,2 and generalized component mode synthesis approaches (GCMS), 3,4 and more recently the flexible natural coordinate formulation (FNCF). 5 The possibility of these methods for effectively describing the system-level dynamics at a feasible computational cost, in contrast to more general nonlinear finite element approaches, has led to an increasing interest in exploiting (flexible) multibody simulation paradigms in a range of novel frameworks like:• model-based state-estimation 6-8 and• model-based control and design. 9However, the broad application of these general frameworks for multibody system models faces two main difficulties:Int J Numer Methods Eng. 2020;121:3083-3107. wileyonlinelibrary.com/journal/nme

Section: Introductionmentioning

confidence: 99%

A noninvasive system‐level model order reduction scheme for flexible multibody simulation

Naets

Devos

Humer

et al. 2020

“…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%

“…[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. 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.…”

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confidence: 99%

“…The continuous use of modal bases derived from the initial configuration leads to poor convergence or even divergence. 24,33 Therefore, some reduction techniques, such as the modal derivatives (MD) [28][29][30] and global modal parameterization (GMP) 31,32 method, account for the nonlinear effects on the modes. However, the computation of MDs greatly amplified the problem size from (n) to (n 2 ).…”

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confidence: 99%

“…However, the computation of MDs greatly amplified the problem size from (n) to (n 2 ). 30,33 Such a feature makes it time-consuming to select the updated MDs for capturing the nonlinear behavior. In addition, the modes from the MD are no longer orthogonal to each other.…”

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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

Self Cite

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

An adaptive model order reduction method for nonlinear seismic analysis of civil structures based on the elastic–plastic states

Fang

Wang

2021

As an approach to evaluating the seismic performance of civil structures, nonlinear seismic analysis faces a challenge in terms of computational efficiency for high-fidelity simulations of large-scale finite element models. In this article, an adaptive model order reduction (AMOR) method is proposed for alleviating the computational burden of nonlinear seismic analysis based on elastic-plastic states. The elastic-plastic states are classified as the initial-elastic, plastic-deforming, and residual-elastic states. The finite element model of a civil structure is automatically partitioned into linear and nonlinear substructures according to the time-varying spatial distribution of the plastic deformation zone, and the Craig-Bampton method was employed to construct the reduced governing equations in each elastic-plastic state. An elastic-plastic-triggered reanalysis method was proposed to conduct a seamless transformation of the reduced governing equations between different elastic-plastic states. In the back-off step, the reduced response vectors are projected back to the physical coordinate space. In the reanalysis step, the response vectors are initialized, partitioned, and transformed onto the hybrid coordinate space spanned by reduced-order bases. Compared with a conventional time step integration method, the AMOR method yields comparative results with a higher computational efficiency.