A curved beam element in the analysis of flexible multi-body systems using the absolute nodal coordinates

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 parameterized 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 non-incremental 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 to that of the fully parameterized element and the classical large displacement beam element with incremental solution procedures.

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204 Curved Beam Formulation using the Absolute Nodal Coordinates

The Proceedings of the Dynamics & Design Conference ◽

10.1299/jsmedmc.2006._204-1_ ◽

2006 ◽

Vol 2006 (0) ◽

pp. _204-1_-_204-6_

Author(s):

Hiroyuki SUGIYAMA ◽

Yoshihiro SUDA

Keyword(s):

Curved Beam ◽

Absolute Nodal Coordinates ◽

Nodal Coordinates ◽

The Absolute

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A New Thin Spatial Beam Element Using the Absolute Nodal Coordinates: Application to a Rotating Strip#

Mechanics Based Design of Structures and Machines ◽

10.1080/15367730500458267 ◽

2005 ◽

Vol 33 (3-4) ◽

pp. 399-422 ◽

Cited By ~ 15

Author(s):

Wan-Suk Yoo ◽

Oleg Dmitrochenko ◽

Su-Jin Park ◽

O-Kaung Lim

Keyword(s):

Beam Element ◽

Absolute Nodal Coordinates ◽

Spatial Beam ◽

Nodal Coordinates ◽

The Absolute

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Gradient Deficient Curved Beam Element Using the Absolute Nodal Coordinate Formulation

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4000793 ◽

2010 ◽

Vol 5 (2) ◽

Cited By ~ 23

Author(s):

Hiroyuki Sugiyama ◽

Hirohisa Koyama ◽

Hiroki Yamashita

Keyword(s):

Absolute Nodal Coordinate Formulation ◽

Beam Element ◽

Solution Procedure ◽

Large Displacement ◽

Curved Beam ◽

Absolute Nodal Coordinate ◽

Curved Beam Element ◽

Strain Components ◽

The Absolute ◽

Longitudinal Stretch

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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