Reference Coordinate System of Nonlinear Beam Element Based on the Geometrically Exact Formulation under Large Spatial Rotations and Deformations

Abstract

Analysis of slender beam structures in a three-dimensional space is widely applicable in mechanical and civil engineering. This paper presents a new procedure to determine the reference coordinate system of a beam element under large rotation and elastic deformation based on a newly introduced physical concept: the zero twist sectional condition, which means that a non-twisted section between two nodes always exists and this section can reasonably be regarded as a reference coordinate system to calculate the internal element forces. This method can avoid the disagreement of the reference coordinates which might occur under large spatial rotations and deformations. Numerical examples given in the paper prove that this procedure guarantees the numerical exactness of the inherent formulation and improves the numerical efficiency, especially under large spatial rotations.

Analysis of slender beam structures in a three-dimensional space is widely applicable in mechanical and civil engineering. This paper presents a new procedure to determine the reference coordinate system of a beam element under large rotation and elastic deformation based on a newly introduced physical concept: the zero twist sectional condition, which means that a non-twisted section between two nodes always exists and this section can reasonably be regarded as a reference coordinate system to calculate the internal element forces. This method can avoid the disagreement of the reference coordinates which might occur under large spatial rotations and deformations. Numerical examples given in the paper prove that this procedure guarantees the numerical exactness of the inherent formulation and improves the numerical efficiency, especially under large spatial rotations.

Keywords

Reference Coordinate System, Element Coordinate System, Large Rotation, Beam Finite Element, Geometric Nonlinearity, Geometrically Exact Beam Formulation

Reference Coordinate System, Element Coordinate System, Large Rotation, Beam Finite Element, Geometric Nonlinearity, Geometrically Exact Beam Formulation

Cite this paper

nullK. Lee, S. Chang, J. Park and S. Kim, "Reference Coordinate System of Nonlinear Beam Element Based on the Geometrically Exact Formulation under Large Spatial Rotations and Deformations,"*Engineering*, Vol. 3 No. 1, 2011, pp. 1-16. doi: 10.4236/eng.2011.31001.

nullK. Lee, S. Chang, J. Park and S. Kim, "Reference Coordinate System of Nonlinear Beam Element Based on the Geometrically Exact Formulation under Large Spatial Rotations and Deformations,"

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