Modeling A
==============


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

POU_D_E beam element and DIS_TR discrete element


.. image:: images/1000078C0000170C00000C9CD7E72108490208A3.svg
    :width: 297
    :height: 162


.. _RefImage_1000078C0000170C00000C9CD7E72108490208A3.svg:

Cutting: beam :math:`\mathrm{AB}`: 20 meshes SEG2.

Boundary conditions:

At the :math:`A` end node

DDL_IMPO: (NOEUD: A DX: 0., DY: 0., DY: 0., DZ: 0., DRX: 0., DRY: 0., DRZ: 0.)


.. csv-table::

    "Nodal mass in :math:`B` with an eccentricity", ":math:`\mathit{ey}\mathrm{=}0.` ", "Case 1"
    "", ":math:`\mathrm{ey}=1.` ", "Case 2"



.. csv-table::

    "Node names:", "Points", ":math:`A\mathrm{=}\mathit{N100}` "," :math:`B=\mathrm{N200}`"



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


.. csv-table::

    "Number of knots:", "21"
    "Number of meshes and types:", "20 SEG2"



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


.. csv-table::

    "**Case**", "**Nature of the clean mode**", "**Frequency**
    **Reference**", ":math:`\mathrm{Hz}`
    **Aster**", "**% difference**"
    "", "flexure 1.2", "1.65", "1.65", "1.6554", "0.33"
    "", "flex 3.4", "16.07", "16.07", "16.0712", "0."
    "CAS 1", "flexure 5.6", "50.02", "50.0240", "0."
    "", "traction 1", "76.47", "76.4727", "76.4727", "0."
    ":math:`\mathrm{yc}=0.` ", "twist 1", "80.47", "80.47", "80.4688", "0."
    "", "flexure 7.8", "103.20", "103.20444", "0."
    "", ":math:`{f}_{z}+{t}_{o}` 1", "1.636", "1.636", "1.6363", "0."
    "", ":math:`{f}_{y}+{t}_{r}` 2", "1.642", "1.642", "1.6416", "0."
    "CAS 2"," :math:`{f}_{y}+{t}_{r}` 3", "13.46", "13.46", "13.4551", "0."
    "", ":math:`{f}_{z}+{t}_{o}` 4", "13.59", "13.59", "13.5919", "0."
    ":math:`\mathrm{yc}=1.` "," :math:`{f}_{z}+{t}_{o}` 5", "28.90", "28.90", "28.8972", "0."
    "", ":math:`{f}_{y}+{t}_{r}` 6", "31.96", "31.96", "31.9594", "0."
    "", ":math:`{f}_{z}+{t}_{o}` 7", "61.61", "61.61", "61.6091", "0."
    "", ":math:`{f}_{y}+{t}_{r}` 8", "63.93", "63.93", "63.9289", "0."
    "Fashion", ":math:`{\theta }_{\mathit{xB}}` ", "0.03", "3.039 10—2", "1.321"
    "1"," :math:`{w}_{C}\mathrm{/}{w}_{B}` ", "1.030", "1.030", "1.030", "0."
    "2"," :math:`{u}_{C}\mathrm{/}{v}_{B}` ", "—0.148", "—0.148", "0."
    "3"," :math:`{u}_{C}/{v}_{B}` ", "—2.882", "—2.880", "0.07"
    "4"," :math:`{w}_{C}\mathrm{/}{w}_{B}` ", "—0.922", "—0.923", "0.108"
    "5"," :math:`{\theta }_{\mathit{xB}}` ", "—1.922", "—1.92268", "0.036"



.. csv-table::

    "with:", ":math:`{f}_{z}+{t}_{o}\mathrm{=}\mathit{flexion}x,z+\mathit{torsion}` "," :math:`{f}_{y}+{t}_{r}\mathrm{=}\mathit{flexion}x,y+\mathit{traction}`"



notes
---------

Calculations made by:


.. code-block:: text
 CALC_MODES
OPTION = 'PLUS_PETITE'
CALC_FREQ =_F (NMAX_FREQ = n) Case 1: n=10, Case 2: n=8
SOLVEUR_MODAL =_F (METHODE = 'TRI_DIAG')

In the test, you cannot check the values of the :math:`\frac{{u}_{C}}{{v}_{B}}` ratios for modes 2 and 3 (except manually). As for the values of :math:`\frac{{w}_{C}}{{w}_{B}}`, the technique is as follows: if we impose :math:`{w}_{B}\mathrm{=}1` (command NORM_MODE), we then have :math:`\frac{{w}_{C}}{{w}_{B}}\mathrm{=}1+{\theta }_{\mathit{xB}}` and we can check the values of :math:`{\theta }_{\mathit{xB}}`.

**Contents of the results file:**

Case 1:11 first natural frequencies, eigenvectors and modal parameters.

Case 2:9 first natural frequencies, eigenvectors and modal parameters.