A structural decomposition method based on symbol operation for solving differential algebraic equations (DAEs) is developed. Constrained dynamical systems are represented in terms of DAEs. State-space methods are universal for solving DAEs in general forms, but for complex systems with multiple degrees-of-freedom, these methods will become difficult and time consuming because they involve detecting Jacobian singularities and reselecting the state variables. Therefore, we adopted a strategy of dividing and conquering. A large-scale system with multiple degrees-of-freedom can be divided into several subsystems based on the topology. Next, the problem of selecting all of the state variables from the whole system can be transformed into selecting one or several from each subsystem successively. At the same time, Jacobian singularities can also be easily detected in each subsystem. To decompose the original dynamical system completely, as the algebraic constraint equations are underdetermined, we proposed a principle of minimum variable reference degree to achieve the bipartite matching. Subsequently, the subsystems are determined by aggregating the strongly connected components in the algebraic constraint equations. After that determination, the free variables remain; therefore, a merging algorithm is proposed to allocate these variables into each subsystem optimally. Several examples are given to show that the proposed method is not only easy to implement but also efficient.

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# A Method for Solving Large-Scale Multiloop Constrained Dynamical Systems Using Structural Decomposition

Tao Xiong

,
Tao Xiong

National Engineering Research Center of CAD

Software Information Technology,

School of Mechanical Science and Engineering,

Huazhong University of Science and Technology,

Wuhan 430074, China

e-mail: xiongtao39@hust.edu.cn

Software Information Technology,

School of Mechanical Science and Engineering,

Huazhong University of Science and Technology,

Wuhan 430074, China

e-mail: xiongtao39@hust.edu.cn

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Jianwan Ding

,
Jianwan Ding

National Engineering Research Center of CAD

Software Information Technology,

School of Mechanical Science and Engineering,

Huazhong University of Science and Technology,

Wuhan 430074, China

e-mail: dingjw@hust.edu.cn

Software Information Technology,

School of Mechanical Science and Engineering,

Huazhong University of Science and Technology,

Wuhan 430074, China

e-mail: dingjw@hust.edu.cn

1

Corresponding author.
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Yizhong Wu

,
Yizhong Wu

National Engineering Research Center of CAD

Software Information Technology,

School of Mechanical Science and Engineering,

Huazhong University of Science and Technology,

Wuhan 430074, China

e-mail: cad.wyz@mail.hust.edu.cn

Software Information Technology,

School of Mechanical Science and Engineering,

Huazhong University of Science and Technology,

Wuhan 430074, China

e-mail: cad.wyz@mail.hust.edu.cn

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Liping Chen

,
Liping Chen

National Engineering Research Center of CAD

Software Information Technology,

School of Mechanical Science and Engineering,

Huazhong University of Science and Technology,

Wuhan 430074, China

e-mail: chenlp@tongyuan.cc

Software Information Technology,

School of Mechanical Science and Engineering,

Huazhong University of Science and Technology,

Wuhan 430074, China

e-mail: chenlp@tongyuan.cc

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Wenjie Hou

Wenjie Hou

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Tao Xiong

Software Information Technology,

School of Mechanical Science and Engineering,

Huazhong University of Science and Technology,

Wuhan 430074, China

e-mail: xiongtao39@hust.edu.cn

Jianwan Ding

Software Information Technology,

School of Mechanical Science and Engineering,

Huazhong University of Science and Technology,

Wuhan 430074, China

e-mail: dingjw@hust.edu.cn

Yizhong Wu

Software Information Technology,

School of Mechanical Science and Engineering,

Huazhong University of Science and Technology,

Wuhan 430074, China

e-mail: cad.wyz@mail.hust.edu.cn

Liping Chen

Software Information Technology,

School of Mechanical Science and Engineering,

Huazhong University of Science and Technology,

Wuhan 430074, China

e-mail: chenlp@tongyuan.cc

Wenjie Hou

1

Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 9, 2015; final manuscript received June 14, 2016; published online December 5, 2016. Assoc. Editor: Jozsef Kovecses.

*J. Comput. Nonlinear Dynam*. May 2017, 12(3): 031005 (13 pages)

**Published Online:**December 5, 2016

Article history

Received:

November 9, 2015

Revised:

June 14, 2016

Citation

Xiong, T., Ding, J., Wu, Y., Chen, L., and Hou, W. (December 5, 2016). "A Method for Solving Large-Scale Multiloop Constrained Dynamical Systems Using Structural Decomposition." ASME. *J. Comput. Nonlinear Dynam*. May 2017; 12(3): 031005. https://doi.org/10.1115/1.4034044

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