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.