For the modeling of large deformations in multibody dynamics problems, the absolute nodal coordinate formulation (ANCF) is advantageous since in general, the ANCF leads to a constant mass matrix. The proposed ANCF beam finite elements in this approach use the transverse slope vectors for the parameterization of the orientation of the cross section and do not employ an axial nodal slope vector. The geometric description, the degrees of freedom, and a continuum-mechanics-based and a structural-mechanics-based formulation for the elastic forces of the beam finite elements, as well as their usage in several static problems, have been presented in a previous work. A comparison to results provided in the literature to analytical solution and to the solution found by commercial finite element software shows accuracy and high order convergence in statics. The main subject of the present paper is to show the usability of the beam finite elements in dynamic and buckling applications.
Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Buckling and Nonlinear Dynamic Examples
Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received December 20, 2012; final manuscript received April 11, 2013; published online October 15, 2013. Assoc. Editor: Hiroyuki Sugiyama.
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Nachbagauer, K., and Gerstmayr, J. (October 15, 2013). "Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Buckling and Nonlinear Dynamic Examples." ASME. J. Comput. Nonlinear Dynam. January 2014; 9(1): 011013. https://doi.org/10.1115/1.4025282
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