In this paper, a rational absolute nodal coordinate formulation (RANCF) thin plate element is developed and its use in the analysis of curved geometry is demonstrated. RANCF finite elements are the rational counterpart of the nonrational absolute nodal coordinate formulation (ANCF) finite elements which employ rational polynomials as basis or blending functions. RANCF finite elements can be used in the accurate geometric modeling and analysis of flexible continuum bodies with complex geometrical shapes that cannot be correctly described using nonrational finite elements. In this investigation, the weights, which enter into the formulation of the RANCF finite element and form an additional set of geometric parameters, are assumed to be nonzero constants in order to accurately represent the initial geometry and at the same time preserve the desirable ANCF features, including a constant mass matrix and zero centrifugal and Coriolis generalized inertia forces. A procedure for defining the control points and weights of a Bezier surface defined in a parametric form is used in order to be able to efficiently create RANCF/ANCF FE meshes in a straightforward manner. This procedure leads to a set of linear algebraic equations whose solution defines the RANCF coordinates and weights without the need for an iterative procedure. In order to be able to correctly describe the ANCF and RANCF gradient deficient FE geometry, a square matrix of position vector gradients is formulated and used to calculate the FE elastic forces. As discussed in this paper, the proposed finite element allows for describing exactly circular and conic sections and can be effectively used in the geometry and analysis modeling of multibody system (MBS) components including tires. The proposed RANCF finite element is compared with other nonrational ANCF plate elements. Several numerical examples are presented in order to demonstrate the use of the proposed RANCF thin plate element. In particular, the FE models of a set of rational surfaces, which include conic sections and tires, are developed.
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September 2016
Research-Article
Rational ANCF Thin Plate Finite Element
Carmine M. Pappalardo,
Carmine M. Pappalardo
Department of Industrial Engineering,
University of Salerno,
Fisciano (Salerno) 84084, Italy
University of Salerno,
Fisciano (Salerno) 84084, Italy
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Zuqing Yu,
Zuqing Yu
Department of Mechanic and
Electronic Engineering,
Harbin Institute of Technology,
Harbin 150001,
Heilongjiang, China
Electronic Engineering,
Harbin Institute of Technology,
Harbin 150001,
Heilongjiang, China
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Xiaoshun Zhang,
Xiaoshun Zhang
School of Science,
Nanjing University of Science and Technology,
Nanjing 210094, China
Nanjing University of Science and Technology,
Nanjing 210094, China
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Ahmed A. Shabana
Ahmed A. Shabana
Department of Mechanical and
Industrial Engineering,
University of Illinois at Chicago,
Chicago, IL 60607
Industrial Engineering,
University of Illinois at Chicago,
Chicago, IL 60607
Search for other works by this author on:
Carmine M. Pappalardo
Department of Industrial Engineering,
University of Salerno,
Fisciano (Salerno) 84084, Italy
University of Salerno,
Fisciano (Salerno) 84084, Italy
Zuqing Yu
Department of Mechanic and
Electronic Engineering,
Harbin Institute of Technology,
Harbin 150001,
Heilongjiang, China
Electronic Engineering,
Harbin Institute of Technology,
Harbin 150001,
Heilongjiang, China
Xiaoshun Zhang
School of Science,
Nanjing University of Science and Technology,
Nanjing 210094, China
Nanjing University of Science and Technology,
Nanjing 210094, China
Ahmed A. Shabana
Department of Mechanical and
Industrial Engineering,
University of Illinois at Chicago,
Chicago, IL 60607
Industrial Engineering,
University of Illinois at Chicago,
Chicago, IL 60607
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received August 22, 2015; final manuscript received December 12, 2015; published online February 3, 2016. Assoc. Editor: Ahmet S. Yigit.
J. Comput. Nonlinear Dynam. Sep 2016, 11(5): 051009 (15 pages)
Published Online: February 3, 2016
Article history
Received:
August 22, 2015
Revised:
December 12, 2015
Citation
Pappalardo, C. M., Yu, Z., Zhang, X., and Shabana, A. A. (February 3, 2016). "Rational ANCF Thin Plate Finite Element." ASME. J. Comput. Nonlinear Dynam. September 2016; 11(5): 051009. https://doi.org/10.1115/1.4032385
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