An absolute nodal coordinate formulation for the dynamic analysis of flexible multibody systems

The floating frame of reference formulation is currently the most widely used approach in flexible multibody simulations. The use of this approach, however, has been limited to small deformation problems. In this investigation, the use of the new absolute nodal coordinate formulation in the small and large deformation analysis of flexible multibody systems that consist of interconnected bodies is discussed. While in the floating frame of reference formulation a mixed set of absolute reference and local elastic coordinates are used, in the absolute nodal coordinate formulation only absolute coordinates are used. In the absolute nodal coordinate formulation. new interpretation of the nodal coordinates of the finite elements is used. No infinitesimal or finite rotations are used as nodal coordinates for beams and plates, instead global slopes are used to define the element nodal coordinates. Using this interpretation of the element coordinates beams and plates can be considered as isoparametric elements, and as a result, exact modeling of the rigid body dynamics can be obtained using the element shape function and the absolute nodal coordinates. Unlike the floating frame of reference approach, no coordinate transformation is required in order to determine the element inertia. The mass matrix of the finite elements is a constant matrix, and therefore, the centrifugal and Coriolis forces are equal to zero when the absolute nodal coordinate formulation is used. The generalized elastic forces, however, become highly nonlinear function of the system coordinates, and as such, little is to be gained from the use of the small strain assumptions. Another advantage of using the absolute nodal coordinate formulation in the dynamic simulation of multibody systems is its simplicity in imposing some of the joint constraints. The results obtained in this investigation shows an excellent agreement with the results obtained using the floating frame of reference formulation when large rotation-small deformation problems are considered.