Nonlinear Dynamics

, Volume 93, Issue 2, pp 413–441 | Cite as

Topology optimization of a flexible multibody system with variable-length bodies described by ALE–ANCF

  • Jialiang Sun
  • Qiang Tian
  • Haiyan Hu
  • Niels L. Pedersen
Original Paper


Recent years have witnessed the application of topology optimization to flexible multibody systems (FMBS) so as to enhance their dynamic performances. In this study, an explicit topology optimization approach is proposed for an FMBS with variable-length bodies via the moving morphable components (MMC). Using the arbitrary Lagrangian–Eulerian (ALE) formulation, the thin plate elements of the absolute nodal coordinate formulation (ANCF) are used to describe the platelike bodies with variable length. For the thin plate element of ALE–ANCF, the elastic force and additional inertial force, as well as their Jacobians, are analytically deduced. In order to account for the variable design domain, the sets of equivalent static loads are reanalyzed by introducing the actual and virtual design domains so as to transform the topology optimization problem of dynamic response into a static one. Finally, the novel MMC-based topology optimization method is employed to solve the corresponding static topology optimization problem by explicitly evolving the shapes and orientations of a set of structural components. The effect of the minimum feature size on the optimization of an FMBS is studied. Three numerical examples are presented to validate the accuracy of the thin plate element of ALE–ANCF and the efficiency of the proposed topology optimization approach, respectively.


Flexible multibody dynamics Arbitrary Lagrangian–Eulerian formulation Absolute nodal coordinate formulation Topology optimization Moving morphable components 



This work was supported in part by the National Natural Science Foundation of China under Grants 11290151 and 11472042. It was also supported in part by Postgraduate Research & Practice Innovation Program of Jiangsu Province under Grants KYCX17_0226 and by China Scholarship Council under Grants 201706830011.

Compliance with ethical standards

Conflict of interest

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Jialiang Sun
    • 1
  • Qiang Tian
    • 2
  • Haiyan Hu
    • 1
    • 2
  • Niels L. Pedersen
    • 3
  1. 1.State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.MOE Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace EngineeringBeijing Institute of TechnologyBeijingChina
  3. 3.Department of Mechanical EngineeringSolid Mechanics, Technical University of DenmarkKongens LyngbyDenmark

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