Acta Mechanica Solida Sinica

, Volume 31, Issue 2, pp 207–228 | Cite as

Modeling Method and Application of Rational Finite Element Based on Absolute Nodal Coordinate Formulation

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Abstract

In multibody system dynamics, the absolute nodal coordinate formulation (ANCF) uses power functions as interpolating polynomials to describe the displacement field. It can get accurate results for flexible bodies that undergo large deformation and large rotation. However, the power functions are irrational representation which cannot describe the complex shapes precisely, especially for circular and conic sections. Different from the ANCF representation, the rational absolute nodal coordinate formulation (RANCF) utilizes rational basis functions to describe geometric shapes, which allows the accurate representation of complicated displacement and deformation in dynamics modeling. In this paper, the relationships between the rational surface and volume and the RANCF finite element are provided, and the generalized transformation matrices are established correspondingly. Using these transformation matrices, a new four-node three-dimensional RANCF plate element and a new eight-node three-dimensional RANCF solid element are proposed based on the RANCF. Numerical examples are given to demonstrate the applicability of the proposed elements. It is shown that the proposed elements can depict the geometric characteristics and structure configurations precisely, and lead to better convergence in comparison with the ANCF finite elements for the dynamic analysis of flexible bodies.

Keywords

Multibody system dynamics Absolute nodal coordinate formulation Flexible deformation Spline representation Rational finite element 

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2018

Authors and Affiliations

  1. 1.Beijing Key Laboratory of Intelligent Space Robotic Systems Technology and ApplicationsBeijing Institute of Spacecraft System EngineeringBeijingChina
  2. 2.Department of Aerospace EngineeringHarbin Institute of TechnologyHarbinChina

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