B modeling
==============

Characteristics of modeling
-----------------------------------

The beam arch was modelled in a polygonal line of :math:`2\times 20` SEG2.

Boundary conditions:

     DDL_IMPO = _F (GROUP_NO ='Beam', DX= 0.0, DRY = 0.0, DRZ = 0.)

                 _F (NOEUD =( 'A', 'G), DX= 0.0, DY= 0.0, DZ= 0.)

except for load case 2

                     (NOEUD ='A', DX= 0.0, DY= 1.0, DY= 1.0, DZ= 1.0)

                     (NOEUD ='G', DX= 0.0, DY=-1.0, DY=-1.0, DZ= 1.0)

load case 1

     FORCE_NODALE = _F (NOEUD =( 'C', 'D'), Fz = -1000.0)

load case 3: Charging at temperature via command AFFE_MATERIAU

     AFFE_VARC =_F (NOM_VARC =' TEMP ', VALE_REF =0., EVOL = TEMP,

                     TOUT =' OUI ', NOM_CHAM =' TEMP',),)

Charging case 4

 PESANTEUR =_F (GRAVITE =9.81,

                 DIRECTION =( 0.,0., -1.))

Node name: :math:`A,B,C,D,E,F`


Characteristics of the mesh
----------------------------

Number of knots: 45

Number of meshes and types: 44 SEG2


Tested sizes and results
------------------------------

.. csv-table::

    "**Case**", "**Point**", "**movement**
    **(** :math:`m` **)**", "**Reference**", "**Reference**", "**Aster**", "**%diff**", "**tolerance**"
    "", "", "", "", "", "", ""
    "", ":math:`B` "," :math:`{v}_{B}` ", "—8.120E-3", "—8.1209E-3", "0.01", "1.E-3"
    "1", "", ":math:`{w}_{B}` ", "—1.000E-2", "—1.000E-2", "0.00", ""
    "", "", "", "", "", "", ""
    "Forces", ":math:`C` "," :math:`{v}_{C}` ", "7.389E-3", "7.3863E-3", "—0.04", ""
    "nodal", ":math:`D` "," :math:`{w}_{D}` "," ", "—2.553E-2", "—2.5528E-2", "—0.01", ""
    "", ":math:`B` "," :math:`{v}_{B}` ", "9.858E-1", "9.858E-1", "9.8585E-1", "—0.00", "1.E-3"
    "2", "", ":math:`{w}_{B}` ", "1.000", "1.000", "1.0000", "—0.00", ""
    "", "", "", "", "", "", ""
    "Displacement", ":math:`C` "," :math:`{v}_{C}` "," ", "1.738E-1", "1.7374E-1", "—0.04", ""
    "imposed", ":math:`D` "," :math:`{w}_{D}` "," ", "1.812", "1.8121", "0. ", ""
    "", ":math:`B` "," :math:`{v}_{B}` ", "—5.660E-6", "—5.6612E-6", "0.02", "1.E-3"
    "3", "", ":math:`{w}_{B}` ", "", "", "", ""
    "", "", "", "", "", "", ""
    "Expansion", ":math:`C` "," :math:`{v}_{C}` "," ", "—1.305E-4", "—1.3051E-4", "0.01", ""
    "", ":math:`D` "," :math:`{w}_{D}` ", "5.248E-4", "5.2484E-4", "0.01", ""
    "", "", "", "", "", "", ""
    "", ":math:`B` "," :math:`{v}_{B}` ", "—3.111E-3", "—3.1145E-3", "0.11", "5.E-3"
    "4", "", ":math:`{w}_{B}` ", "—4.552E-3", "—4.5521E-3", "0.00", ""
    "Gravity", ":math:`C` "," :math:`{v}_{C}` "," ", "1.180E-3", "1.1409E-3", "—3.31", "5.E-2"
    "", ":math:`D` "," :math:`{w}_{D}` ", "—8.850E-3", "—8.850E-3", "—0.40", "5.E-3"



notes
---------

The modeling of the elbow by straight elements requires a very fine mesh, for sufficient precision (especially for distributed loading).