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.
Multibody system dynamics Absolute nodal coordinate formulation Flexible deformation Spline representation Rational finite element
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Sanborn GG, Shabana AA. On the integration of computer aided design and analysis using the finite element absolute nodal coordinate formulation. Multibody Syst Dyn. 2009;22(2):181–97.CrossRefzbMATHGoogle Scholar
Lan P, Shabana AA. Rational finite elements and flexible body dynamics. J Vib Acoust. 2010;132(4):0410071–9.CrossRefGoogle Scholar
Yamashita H, Sugiyama H. Numerical convergence of finite element solutions of nonrational B-spline element and absolute nodal coordinate formulation. Nonlinear Dyn. 2012;67(1):177–89.MathSciNetCrossRefzbMATHGoogle Scholar
Mikkola AM, Shabana AA, Sanchez-Rebollo C, et al. Comparison between ANCF and B-spline surfaces. Multibody Syst Dyn. 2013;30(2):119–38.MathSciNetCrossRefGoogle Scholar
Belytschko T, Liu WK, Moran B, et al. Nonlinear finite elements for continua and structures. 2nd ed. New York: Wiley; 2014. p. 346–53.Google Scholar
Mikkola AM, Shabana AA. A non-incremental finite element procedure for the analysis of large deformation of plates and shells in mechanical system applications. Multibody Syst Dyn. 2003;9(3):283–309.MathSciNetCrossRefzbMATHGoogle Scholar
Dmitrochenko ON, Pogorelov DY. Generalization of plate finite elements for absolute nodal coordinate formulation. Multibody Syst Dyn. 2003;10(1):17–43.CrossRefzbMATHGoogle Scholar
Dufva K, Shabana AA. Analysis of thin plate structures using the absolute nodal coordinate formulation. Proc Inst Mech Eng Part K J Multibody Dyn. 2005;219(4):345–55.Google Scholar
Olshevskiy A, Dmitrochenko O, Kim CW. Three-dimensional solid brick element using slopes in the absolute nodal coordinate formulation. J Comput Nonlinear Dyn. 2014;9(2):021001.CrossRefGoogle Scholar