| In the classical finite element literature beams and plates are not considered as isoparametric elements since infinitesimal rotations are used as nodal coordinates. In order to circumvent this problem in flexible multibody simulations, an intermediate element coordinate system, which has an origin rigidly attached to the origin of the deformable body coordinate system and has axes which are parallel to the axes of the element coordinate system in the undeformed configuration was introduced. Using this intermediate element coordinate system and the fact that conventional beam and plate shape functions can describe an arbitrary rigid body translation, an exact modeling of the rigid body inertia can be obtained.; In this thesis, the absolute nodal co-ordinate dynamic formulation is developed for the large deformations and rotations of three-dimensional plate and beam elements. In this formulation, no infinitesimal or finite rotations are used as nodal co-ordinates, instead global displacements and slopes are used as the plate co-ordinates. The resulting mass matrix is the same constant matrix that appears in linear structural dynamics. The stiffness matrix, on the other hand, is a non-linear function of the nodal co-ordinates of the plate or beam even in the case of a linear elastic problem. It is demonstrated in this thesis that, unlike the incremental finite element formulations, the proposed method leads to an exact modelling of the rigid body inertia when the plate or beam element moves as a rigid body. It is also demonstrated that by using the proposed method the conventional plate element shape function has a complete set of rigid body modes that can describe an exact arbitrary rigid body displacement. As a consequence, an arbitrary rigid body motion of the element results in zero strain. |
