Analysis of large flexible body deformation in multibody systems using absolute coordinates

To consider large deformation problems in multibody system simulations a finite element approach, called absolute nodal coordinate. formulation, has been proposed. In this formulation absolute nodal coordinates and their material derivatives are applied to represent both deformation and rigid body motion. The choice of nodal variables allows a fully nonlinear representation of rigid body motion and can provide the exact rigid body inertia in the case of large rotations. The methodology is especially suited for but not limited to modeling of beams, cables and shells in multibody dynamics. This paper summarizes the absolute nodal coordinate formulation for a 3D Euler-Bernoulli beam model, in particular the definition of nodal variables, corresponding generalized elastic and inertia forces and equations of motion. The element stiffness matrix is a nonlinear function of the nodal variables even in the case of linearized strain/displacement relations. Nonlinear strain/displacement relations can be calculated from the global displacements using quadrature formulae. Computational examples are given which demonstrate the capabilities of the applied methodology. Consequences of the choice of shape. functions on the representation of internal forces are discussed. Linearized strain/displacement modeling is compared to the nonlinear approach and significant advantages of the latter, when using the absolute nodal coordinate formulation, are outlined.