I was wondering if we could model rigid body motion of bodies using finite element models. Particularly I'm interested to know if we can model motion of objects with no constraints or with some degrees of freedom (such as only rotation). Though I've used word 'rigid body' to convey the situations closest to what I'm considering, In reality there will be stress, considering non-uniform application of force on surface/body or because of rotation they undergo, and these are not small enough to ignore.
Finite element method is used to change the boundary value problem, with an infinite number of unknowns, into a system of algebraic equations with a finite number of degrees of freedom (DOFs).
For example, the response of the deformable body, which conveniently is described by partial diffrenetial equation (PDE), using finite element method is transformed into a system of algebraic equations with the finite number of DOFs.
If you write equations for rigid body or system of rigid bodies, you do not have PDE; you have immediately a system of algebraic equations. Thus no need for finite element method.
The problem with the system only rigid bodies is that is very often over-constrained, since only you have equations of equilibrium to work with. However, this is another story.