A FINITE-ELEMENT APPROACH TO THE CHAOTIC MOTION OF GEOMETRICALLY EXACT RODS UNDERGOING INPLANE DEFORMATIONS

The paper is concerned with a hybrid finite element formulation for th e geometrically exact dynamics of rods with applications to chaotic mo tion. The rod theory is developed for in-plane motions using the direc t approach where the rod is treated as a one-dimensional Cosserat line . Shear deformation is included in the formulation. Within the element s, a linear distribution of the kinematical fields is combined with a constant distribution of the normal and shear forces. For time integra tion, the mid-point rule is employed. Various numerical examples of ch aotic motion of straight and initially curved rods are presented provi ng the powerfulness and applicability of the finite element formulatio n.