Benchmark solution
=====================

Calculation method
-----------------

The pipe support elements are SEG3.

• The position of the integration points along SEG3 is given in [:ref:`R3.01.01 <R3.01.01>`] "Shape functions and finite element integration points".

*# Coordinates of the Gauss Points along the* *SEG3* *

LongBeam = 3.0

xpg = **pow** (3.0/5.0,0.5)

Points= {1: LongBeam*(1.0-xpg)* 0.5,

2: long beam* 0.5,

3: LongBeam*(1.0+xpg)* 0.5,}

• The coordinates of the integration sub-points depend on the number of layers, the number of sectors, and of course the diameter and thickness of the pipe.

*# Sub-Point Coordinates "Nbfibre = (2*Ncou+1) *(2*Nsect+1)" *

**def** CoordFibre (ifib):

Rint = Rex-Ep

*# coordinate index*

NumAng = ((ifib-1)% (2*Nsect+1))/(2.0*Nsect)

NumNeck = ((ifib-1)/(2 *Insect+1))/(2.0*Nneck)

y = (Rint+EP*NumCoU)*np.cos (2.0*np.PI*nummang)

z = - (Rint+EP*NumCoU)*np.sin (2.0*np.pi*nummang)

**return** y, z

where:

◦ Rext and Ep are the outer radius and the thickness of the pipe, respectively, specified in command AFFE_CARA_ELEM.

◦ Nsect and Ncu are the number of sectors and layers, respectively, specified in the AFFE_CARA_ELEM command.

CARA **= AFFE_CARA_ELEM (**

**MODELE =** MODELE,

**POUTRE =_F (GROUP_MA =( 'POUTRE '**, **' POUTRE0')**, **

**SECTION =' CERCLE '**, **CARA =( 'R'**, **'EP')**, **VALE =( 0.5**, **0.2)**, **0.2)**,

**TUYAU_NSEC =** **8**, **TUYAU_NCOU =** **3**, **)**, **)**,

**)**

For pipe :math:`P0P1` the coordinates :math:`(x,y,z)` of the fiber 'ifib' for the point 'ipt' are given by:

x = Points [ipt]

y, z = CoordFibre (ifib)


Reference quantities and results
------------------------

The values are assigned to the sub-points, by:

• CALC_CHAM_ELEM: calculating the coordinates of the sub-points.

• CREA_CHAMP, option AFFE: creating a function field.

• CREA_CHAMP, option EVAL: evaluation of functions at the coordinates of the sub-points.

• CREA_CHAMP, option ASSE: definition of the constraint field.

• CREA_RESU: creation of a result containing the constraint field.

The sizes are then tested using TEST_TABLE.


Uncertainties about the solution
----------------------------

None, exact solution.