204 Curved Beam Formulation using the Absolute Nodal Coordinates

Abstract

This paper is eoncerned with the develepment of a curved bearn element in thc arralysis of large deforrnation multibody system dynamics ． The absolute nodal coordinate formuiation which has been used in the 1 e deb ation ana ［ ysis of multibody systems is generalized to the curved beam element which d。es not suffer from some of existing numerical problcms ， Using the position vector grad 童 ent coordinates used in the abso 正 ute nodal coordinate ft ) rmulatiQn ， the rQtation and defbrmation 且eld within the e 正 ement can be uniquely defined ， and this fbrmulation leads to a constant mass matrix fbr 血 lly nonlinear dynamics problems ， In existing beam elements in this fommulation ， howeveら since the elastic fbrces are defined using the Green ・ Lagrange strain tensor as a volume element ， locking phenornenon associated with the shear and membrane forces leads to erroneously stiffer bending characteristics ． In order to avoid this drawback ， He 〃inger − Rei∬ ner variational pr 加 ¢ ρ ' e is applied to modify the shear stress distribulion ， whi ［ e the a ∬ umed ∫ 醐 ゴ η methed is employed to avoid the membrane

Numerical investigation of the slope discontinuities in large deformation finite element formulations

“…Furthermore, as explained in the second section of this paper, the transformation of the elements that employ finite rotations is not straightforward as compared to the fully parameterized finite elements of the absolute nodal coordinate formulation (ANCF) [8,9,[12][13][14]. This formulation has been proposed to model system components that undergo large translational and rotational displacements, as well as large deformations [1,2,7,11,19]. Global position vectors and global gradient vectors are used as nodal coordinates in this non-incremental finite element method.…”