A study of flexible multibody system with finite shell elements

Two finite element formulations are discussed for the dynamic analysis and simulation of flexible multibody systems. One is floating reference frame formulation and the other is absolute nodal coordinate formulation. The floating reference frame formulation is the most widely used method for the dynamic analysis of flexible multibody systems since such a formulation allows easy addition of general constraint and force functions. The one of advantages of floating reference frame formulation is one can use stiffness matrix and elastic nodal coordinates that used in any kind of classical finite element without modification. However, complex inertia shape integrals appear in the components of the mass matrix and the quadratic velocity vector that represent the non-linear inertia coupling between the reference motion and the elastic deformation. The use of this method, however, is limited to small deformation problems because of the nature of the generalized coordinates used.; In this study, a recently developed computational finite element procedure is also discussed for the computer-aided analysis of flexible multibody systems. This procedure, which is based on the absolute nodal coordinate formulation, lead to an optimum sparse matrix structure and allow for easy addition of kinematic constraints and external forcing functions, there by maintaining the main advantages of the algorithms based on the floating reference formulation. Furthermore this procedure can be used for the large deformation analysis of flexible multibody systems, and as such, it does not suffer from the limitations of the floating reference frame formulation. In the absolute nodal coordinate formulation, global displacement coordinates and slopes are used to describe the element deformation. Infinitesimal or finite rotations are not used as nodal coordinates. The absolute nodal coordinate formulation leads to a constant mass matrix, and as a result, the vector of Coriolis and centrifugal forces is identically equal to zero. To avoid 'Poisson Thickness Locking', a non-linear finite shell element formulation accounting for the thickness stretching is presented for large elastic deformation and large rigid body rotation problems. This is achieved by enriching the strain field of the element by an additional linear component thickness strain by the EAS method. The extra thickness strain parameters are independently interpolated for each element. The 'internal' strain parameters do not have to be compatible across the element boundaries so that they can be eliminated on the element level.