A process of using finite element analysis for determining the behavior of a system, submitted to predetermined load and displacement boundary conditions with a degree of freedom relative to a local coordinate system released at one system node. For a geometrically non-linear solution scheme, a plurality of incremental steps are carried, for which computing for a finite element of the system a displacement vector at the nodes of the finite element is performed by minimizing the energy of the system. For a geometrically linear solution scheme, a single solving step is carried. The step of minimizing is carried out, for a node having a released degree of freedom, in a local frame of reference, and the released degree of freedom at the node is expressed along one axis of such frame. Hybrid reference frames allow expressing and considering in the formulation the constraints of the non-released degrees of freedom simply.