Study on the geometrical nonlinearity and order reduction for the dynamics of a spatial curved beam

Abstract

For a multi-flexible-body system that will undergo large displacement and small deformation, methods based on the floating frame of reference, in which the nodal coordinates are defined with respect to their floating reference systems, could be used; accordingly, component mode synthesis methods are often applied to reduce the order of the dynamics equations of the flexible bodies. The occurrence of major prestressing forces makes it necessary to consider the geometrical nonlinearity relating to the strain-displacement relationship. Besides the substructuring techniques, two other strategies have been proposed for floating frame of reference methods to account for such geometrical nonlinearity: the first strategy is based on the augmentation of the expressions for the strain energy and is applicable for a general flexible body; while the second strategy relies on distinguishing the contribution of the foreshortening effect from that of the conventional strain in modeling the longitudinal displacement, but it is specialized only for beams. The second strategy has been demonstrated in existing literature by planar straight beams and is reported to be much more efficient computationally compared with the first strategy. In this paper, the second strategy is extended for the dynamics modeling and simulation of a spatial curved beam undergoing large displacement and small deformation. The computational results are verified by comparing with those obtained from ABAQUS software. Comparison with the first strategy shows its superiority with respect to the computational efficiency and accuracy.