D modeling
==============


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

POU_D_TGM (multi-fiber 3D beam for nonlinear geometric and material analysis).


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

Number of knots: 11

Number of meshes and type: 10 SEG2


Characteristics of the cross section mesh
-----------------------------------------------------

Number of fibers: 160 (40 in thickness and 4 in width)

Number of meshes and type: 160 QUAD4


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

The incremental analysis is carried out in the pseudo-time interval :math:`\mathrm{[}\mathrm{0 }\mathrm{:}6\mathrm{]}` in 1200 load steps.


History of horizontal rotation :math:`\text{DRY}` (radians) at loaded nodes
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


.. csv-table::

    "**Instant**", "**Moment** :math:`m` ", "**Reference Type**", "**Reference**", "**Tolerance (%)**"
    "0.3", "30. ", "'ANALYTIQUE'", "—0.3000E+00", "0.1"
    "0.6", "60. ", "'ANALYTIQUE'", "—0.6000E+00", "0.1"
    "1.0", "100. ", "'ANALYTIQUE'", "—1.0000E+00", "0.1"
    "3.0", "300. ", "'ANALYTIQUE'", "—3.0000E+00", "0.1"
    "6", "600", "'ANALYTIQUE'", "—6.0000E+00", "0.1"



History of horizontal displacement :math:`\text{DX}(\text{m})` at loaded nodes
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


.. csv-table::

    "**Instant**", "**Moment** :math:`m` ", "**Reference Type**", "**Reference**", "**Tolerance (%)**"
    "0.3", "30. ", "'ANALYTIQUE'", "—1.4932E-01", "2.0"
    "0.6", "60. ", "'ANALYTIQUE'", "—5.8934E-01", "1.0"
    "3.0", "300. ", "'ANALYTIQUE'", "—9.5296", "0.3"
    "6", "600", "'ANALYTIQUE'", "—10.4657", "0.3"



History of vertical displacement :math:`\text{DZ}(\text{m})` at loaded nodes
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


.. csv-table::

    "**Instant**", "**Moment** :math:`m` ", "**Reference Type**", "**Reference**", "**Tolerance (%)**"
    "0.3", "30. ", "'ANALYTIQUE'", "1.4887E+00", "0.1"
    "0.6", "60. ", "'ANALYTIQUE'", "2.9110E+00", "0.1"
    "3.0", "300. ", "'ANALYTIQUE'", "6.6333", "0.5"
    "6", "600", "'ANALYTIQUE'", "6.638286E-02", "0.07"


At the last step of time, the vertical displacement is very low compared to the maximum achieved during the loading path (:math:`\text{DZ}` maximum around :math:`7\text{m}`). A relative comparison with the reference solution is not very relevant (there would then be almost 30% relative error). We would prefer a test in relation to the maximum displacement: :math:`\frac{\mathrm{valeur}\mathrm{calculée}-\mathrm{valeur}\mathrm{de}\mathrm{référence}}{{\mathrm{DZ}}_{\mathrm{max}}}<{\mathrm{tol}}^{\mathrm{relative}}`.

To do this, we test in absolute terms, with an absolute tolerance equal to :math:`{\mathrm{DZ}}_{\mathrm{max}}\mathrm{.}{\mathrm{tol}}^{\mathrm{relative}}`.


.. image:: images/10000000000002FD0000025295F5C86D8625AE6B.png
    :width: 3.8134in
    :height: 2.9693in


.. _refImage_10000000000002 FD0000025295F5C86D8625AE6B .png: