Abstract: 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.

Abstract: For determining the behavior of a flexible system submitted to predetermined displacement boundary conditions, a process uses geometrically non-linear finite element analysis. The process has a plurality of incremental steps within a total Lagrangian formalism with co-rotational update. In each incremental step, one computes for a finite element of the flexible system a displacement vector, having translational and rotational components, at the nodes of the finite element. This computation of the displacement vector is carried out by minimizing the energy of the flexible system when the system is submitted to a fraction of the predetermined displacement. For a given finite element, the co-rotational update is carried out by computing an updated elementary frame of reference, without considering the bending rotational components of the displacement vectors computed at the nodes of the finite element. The properties of this co-rotational update make all computations similar, hence simpler and easier.

Abstract: For determining the behavior of a flexible system submitted to predetermined displacement boundary conditions, a process uses geometrically non-linear finite element analysis. The process has a plurality of incremental steps within a total Lagrangian formalism with co-rotational update. In each incremental step, one computes for a finite element of the flexible system a displacement vector, having translational and rotational components, at the nodes of the finite element. This computation of the displacement vector is carried out by minimizing the energy of the flexible system when the system is submitted to a fraction of the predetermined displacement. For a given finite element, the co-rotational update is carried out by computing an updated elementary frame of reference, without considering the bending rotational components of the displacement vectors computed at the nodes of the finite element. The properties of this co-rotational update make all computations similar, hence simpler and easier.

Abstract: A process of using finite element analysis for determining the behaviour 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 node of the system. 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, for which similar steps of computing for a finite element and timely minimizing of the system's energy are performed. 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.