2. Benchmark solution#

2.1. Calculation method#

The pipe support elements are SEG3.

The position of the integration points along SEG3 is given in [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 \(P0P1\) the coordinates \((x,y,z)\) of the fiber “ifib” for the point “ipt” are given by:

x = Points [ipt]

y, z = CoordFibre (ifib)

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.

None, exact solution.