In this investigation, a gradient deficient beam element of the absolute nodal coordinate formulation is generalized to a curved beam for the analysis of multibody systems, and the performance of the proposed element is discussed by comparing with the fully parametrized curved beam element and the classical large displacement beam element with incremental solution procedures. Strain components are defined with respect to the initially curved configuration and described by the arc-length coordinate. The Green strain is used for the longitudinal stretch, while the material measure of curvature is used for bending. It is shown that strains of the curved beam can be expressed with respect to those defined in the element coordinate system using the gradient transformation, and the effect of strains at the initially curved configuration is eliminated using one-dimensional Almansi strain. This property can be effectively used with a nonincremental solution procedure employed for the absolute nodal coordinate formulation. Several numerical examples are presented in order to demonstrate the performance of the gradient deficient curved beam element developed in this investigation. It is shown that the use of the proposed element leads to better element convergence as compared with the fully parametrized element and the classical large displacement beam element with incremental solution procedures.
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April 2010
Research Papers
Gradient Deficient Curved Beam Element Using the Absolute Nodal Coordinate Formulation
Hiroyuki Sugiyama,
Hiroyuki Sugiyama
Department of Mechanical Engineering,
e-mail: hsugiy1@rs.kagu.tus.ac.jp
Tokyo University of Science
, Tokyo 102-0073, Japan
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Hirohisa Koyama,
Hirohisa Koyama
Department of Mechanical Engineering,
Tokyo University of Science
, Tokyo 102-0073, Japan
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Hiroki Yamashita
Hiroki Yamashita
Department of Mechanical Engineering,
Tokyo University of Science
, Tokyo 102-0073, Japan
Search for other works by this author on:
Hiroyuki Sugiyama
Department of Mechanical Engineering,
Tokyo University of Science
, Tokyo 102-0073, Japane-mail: hsugiy1@rs.kagu.tus.ac.jp
Hirohisa Koyama
Department of Mechanical Engineering,
Tokyo University of Science
, Tokyo 102-0073, Japan
Hiroki Yamashita
Department of Mechanical Engineering,
Tokyo University of Science
, Tokyo 102-0073, JapanJ. Comput. Nonlinear Dynam. Apr 2010, 5(2): 021001 (8 pages)
Published Online: February 9, 2010
Article history
Received:
January 27, 2009
Revised:
August 18, 2009
Online:
February 9, 2010
Published:
February 9, 2010
Citation
Sugiyama, H., Koyama, H., and Yamashita, H. (February 9, 2010). "Gradient Deficient Curved Beam Element Using the Absolute Nodal Coordinate Formulation." ASME. J. Comput. Nonlinear Dynam. April 2010; 5(2): 021001. https://doi.org/10.1115/1.4000793
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