1. Discretization

1.1. Degrees of freedom

The degrees of freedom are, for each node of the support mesh:

• the six displacement components of the average fiber (three translations and three rotations),

• three degrees of freedom corresponding to modes 0 and 1,

• for each Fourier mode 6 degrees of freedom (\(U\) corresponds to warping, \(V\) to orthoradial displacement, \(W\) to radial displacement).

Finished element	Degrees of freedom (at each vertex node)						Remarks
TUYAU_3M	DX	DY	DZ	DRX	DRY	DRZ
	W0	WI1	WO1
	UI2	VI2	WI2	UO2	VO2	WO2	Fashion 2
	UI3	VI3	WI3	UO3	VO3	WO3	Fashion 3
TUYAU_6M	DX	DY	DZ	DRX	DRY	DRZ
	W0	WI1	WO1
	UI2	VI2	WI2	UO2	VO2	WO2	Fashion 2
	UI3	VI3	WI3	UO3	VO3	WO3	Fashion 3
	UI4	VI4	WI4	UO4	VO4	WO4	Mode 4
	UI5	VI5	WI5	UO5	VO5	WO5	Fashion 5
	UI6	VI6	WI6	UO6	VO6	WO6	Fashion 6

1.2. Support mesh for stiffness matrices

Finite element support meshes, in displacement formulation, are segments with 3 or 4 knots.

Modeling	Mesh	Finished Element	Remarks
TUYAU_3M	SEG3	MET3SEG3
	SEG4	MET3SEG4
TUYAU_6M	SEG3	MET6SEG3