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

Abstract In this investigation, a curved beam element is developed for the analysis of large deformation of flexible multi-body systems using the absolute nodal coordinate formulation. In the existing beam element in this formulation, because the elastic forces are defined using the Green-Lagrange strain tensor as a volume element, locking phenomenon associated with the shear and cross-section deformation leads to erroneously stiffer bending characteristics. In order to circumvent this drawback, the Hellinger-Reissner variational principle is applied to modify the shear stress distribution, whereas the assumed strain method is employed to alleviate the locking associated with the cross-section deformation. The consistent tangent stiffness matrices are derived for the curved beam element and used with implicit integration methods. Numerical examples are presented in order to demonstrate the performance of the curved beam element developed in this investigation.

[1]  T. R. Kane,et al.  Dynamics of a cantilever beam attached to a moving base , 1987 .

[2]  E. Hairer,et al.  Stiff and differential-algebraic problems , 1991 .

[3]  Hiroyuki Sugiyama,et al.  On the Use of Implicit Integration Methods and the Absolute Nodal Coordinate Formulation in the Analysis of Elasto-Plastic Deformation Problems , 2004 .

[4]  E. Haug,et al.  Geometric non‐linear substructuring for dynamics of flexible mechanical systems , 1988 .

[5]  R. Y. Yakoub,et al.  Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory , 2001 .

[6]  H Sugiyama,et al.  Finite element analysis of the geometric stiffening effect. Part 2: Non-linear elasticity , 2005 .

[7]  Aki Mikkola,et al.  Three-Dimensional Beam Element Based on a Cross-Sectional Coordinate System Approach , 2006 .

[8]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[9]  R. Y. Yakoub,et al.  Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Implementation and Applications , 2001 .

[10]  J. C. Simo,et al.  A three-dimensional finite-strain rod model. Part II: Computational aspects , 1986 .

[11]  Daniel García-Vallejo,et al.  Modeling of Belt-Drives Using a Large Deformation Finite Element Formulation , 2006 .

[12]  R. D. Wood,et al.  Nonlinear Continuum Mechanics for Finite Element Analysis , 1997 .

[13]  Hiroyuki Sugiyama,et al.  Formulation of Three-Dimensional Joint Constraints Using the Absolute Nodal Coordinates , 2003 .

[14]  Arend L. Schwab,et al.  Comparison of Three-Dimensional Flexible Beam Elements for Dynamic Analysis: Finite Element Method and Absolute Nodal Coordinate Formulation , 2005 .

[15]  A. Shabana,et al.  Use of the Finite Element Absolute Nodal Coordinate Formulation in Modeling Slope Discontinuity , 2003 .

[16]  Aki Mikkola,et al.  A Non-Incremental Nonlinear Finite Element Solution for Cable Problems , 2003 .

[17]  A. Mikkola,et al.  Description of Elastic Forces in Absolute Nodal Coordinate Formulation , 2003 .

[18]  J H Kim,et al.  An analytical approach to predicting particle deposit by fouling in the axial compressor of the industrial gas turbine , 2005 .

[19]  Johannes Gerstmayr,et al.  Deformation modes in the finite element absolute nodal coordinate formulation , 2006 .