A finite element approach to kinetic energy discretization of deformable bodies in quasi-rigid motion

In this paper a finite element technique for the discretization of kinetic energy of bodies subjected to large rigid motion and small deformation (which we refer to as quasi-rigid motion) is presented. First, on the basis of a separation between the rigid displacement and the deformation, the relevant kinematic relationships are derived. A standard assumed-mode approach is used to describe the deformation displacement field by a linear combination of known functions. Then, the computation of the kinetic energy leads to the definition of a set of tensors, which are configuration-independent (like the mass matrix in a linear setting) and fully characterize the body non-linear dynamic behaviour introduced by large rotation. A computer code has been developed, in order to extend an existing FE package, for the computation of these tensors. Details of the technique, including storage requirements and suggestions for model reduction, are given. Finally, two examples are presented: (i) the result of the computation of one of the introduced tensors; (ii) the development of the non-linear model of a rotating beam.