Curved Beam Formulation in the Large Deformation Analysis of Flexible Multibody Systems

Abstract

This paper is concerned with the development of a curved beam element in the analysis of large deformation multibody system dynamics. The absolute nodal coordinate formulation which has been used in the large deformation analysis of multibody systems is generalized to the curved beam element which does not suffer from some of existing numerical problems. Using the position vector gradient coordinates used in the absolute nodal coordinate formulation, the rotation and deformation field within the element can be uniquely defined, and this formulation leads to a constant mass matrix for fully nonlinear dynamics problems. In existing beam elements in this formulation, however, since the elastic forces are defined using the Green-Lagrange strain tensor as a volume element, locking phenomenon associated with the shear and membrane forces leads to erroneously stiffer bending characteristics. In order to avoid this drawback, Hellinger-Reissner variational principle is applied to modify the shear stress distribution, while the assumed strain method is employed to avoid the membrane locking associated with the cross-section deformation. Numerical examples are presented in order to demonstrate the performance of the curved beam formulation developed in this investigation.