1. Discretization

1.1. Degrees of freedom

For the three three-dimensional beam models, the degrees of freedom of discretization are, at each node of the support mesh, the six displacement components (three translations and three rotations). These knots are supposed to describe a segment of the average fiber of the beam.

For three-dimensional member modeling, the degrees of freedom of discretization are, at each node of the support mesh, the three translational displacement components.

Finished element	Degrees of freedom (at each vertex node)
POU_D_T	DX	DY	DZ	DRX	DRY	DRZ
POU_D_E	DX	DY	DZ	DRX	DRY	DRZ
BARRE	DX	DY	DZ

1.2. Stiffness matrix support mesh

Finite element support meshes, in displacement formulation, are segments with two nodes SEG2:

Modeling	Mesh	Finished Element	Remarks
POU_D_T	SEG2	MECA_POU_D_T
POU_D_E	SEG2	MECA_POU_D_E
BARRE	SEG2	MECA_BARRE

1.3. Cargo support mesh

All the loads applicable to the beam and member elements are treated by direct discretization on the support mesh of the element in displacement formulation.

No load support mesh is therefore required for the edge of the beam or bar elements.

1.4. Main characteristics of the models

Modeling POU_D_E (Euler’s Right Beam) corresponds to the Euler-Bernouilli hypothesis, i.e. the sections remain straight and perpendicular to the average fiber (high slenderness hypothesis).

Modeling POU_D_T (Timoshenko Right Beam) takes into account the effects of transverse shear.

Modeling BARRE only treats axial forces and deformations.

The warped beam is treated in [U3.11.04].