Multibody System Dynamics

, Volume 35, Issue 4, pp 321–351 | Cite as

Three new triangular shell elements of ANCF represented by Bézier triangles

  • Hanjiang Chang
  • Cheng Liu
  • Qiang Tian
  • Haiyan Hu
  • Aki Mikkola


The past few years have witnessed rapid advances in the integration of Computer-Aided Design (CAD) and Finite Element Analysis (FEA), such as the Isogeometric Analysis (IGA) method and the Integration of Computer Aided Design and Analysis (I-CAD-A) technique. Recent studies indicated that the geometry description used in the Absolute Nodal Coordinate Formulation (ANCF) is consistent with the geometry description in CAD systems, making it an attractive approach for I-CAD-A. ANCF as an accurate, non-incremental finite element method to deal with the dynamics of those systems subject to large motions and large deformations has developed towards practical application in the field of flexible multibody systems. The objective of this study is to enrich the family of ANCF elements with three new triangular shell elements: the thin triangular element, the low order thick triangular element and the high order thick triangular element, which are represented by Bézier triangles. The linear mapping relationship between the geometrical representation of the Bézier triangle and that of the proposed thin triangular element is established. The invertible property of the linear mapping relationship clearly indicates that the proposed thin triangular element can be also used to perform the I-CAD-A. The conditions of the approximate \(G^{1}\) continuity between the proposed adjacent elements are also deduced in order to construct a smooth surface. Finally, several static and dynamic numerical examples are employed to validate the correctness and effectiveness of the proposed triangular shell elements.


I-CAD-A Absolute Nodal Coordinate Formulation (ANCF) Triangle shell element Bézier triangle Approximate \(G^{1}\) continuity 



This work was supported in part by National Natural Science Foundations of China under Grants 11290151, 11221202 and 11302025. The work was also supported in part by Excellent Young Scholar Research Fund from Beijing Institute of Technology, and supported in part by the Beijing Higher Education Young Elite Teacher Project under Grant YETP1201.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Hanjiang Chang
    • 1
  • Cheng Liu
    • 1
  • Qiang Tian
    • 1
  • Haiyan Hu
    • 1
  • Aki Mikkola
    • 2
  1. 1.MOE Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace EngineeringBeijing Institute of TechnologyBeijingChina
  2. 2.Department of Mechanical EngineeringLappeenranta University of TechnologyLappeenrantaFinland

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