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


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


.. image:: images/100002B400001688000006836B505E07D12DEE4F.svg
    :width: 290
    :height: 84


.. _RefImage_100002B400001688000006836B505E07D12DEE4F.svg:

The beam consists of a single mesh.

The modeling used for the beam is that of Euler-Bernoulli (POU_D_E).

The :math:`A` end is embedded:


.. code-block:: text
 DX = DY = DZ = 0. DRX = DRY = DRZ = 0.

The velocities and accelerations are obtained in the following manner in harmony:

:math:`v(B)=i\mathrm{\omega }u(B)`

:math:`a(B)=-{\mathrm{\omega }}^{2}u(B)`


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

Number of knots: 2

Number of meshes and types: 1 mesh of type SEG 2

The characteristic points of the mesh are as follows:


Quantities tested (real/imaginary shape)
-----------------------------------------

**Problem 1: Traction**


.. csv-table::

    "**Point/Size**", "", "", "**Reference value**", "**Reference type**", "**Precision (%)**"
    "displacement", "B", "DX", "(5.318 10—5, 0. )", "'ANALYTIQUE'", "0.05"
    "speed", "B", "DX", "(0., 3.341 10—3)", "'ANALYTIQUE'", "0.05"
    "acceleration", "B", "DX", "(—2.099 10—1, 0. )", "'ANALYTIQUE'", "0.05"
    "generalized effort", "B", "N", "N", "(3000., 0. )", "'ANALYTIQUE'", "0.05"


**Problem 2: flexion**


.. csv-table::

    "**Point/Size**", "", "", "**Reference value**", "**Reference type**", "**Precision (%)**"
    "displacement", "B", "DY", "(1.828 10—2, 0. )", "'ANALYTIQUE'", "0.05"
    "", "", "DRZ ", "(1.82 10—2, 0. )", "'ANALYTIQUE'", "0.05"
    "speed", "B", "DY", "(0., 1.1489)", "'ANALYTIQUE'", "0.05"
    "", "", "DRZ ", "(0., 1.1438)", "'ANALYTIQUE'", "0.05"
    "acceleration", "B", "DY", "(—72.19, 0. )", "'ANALYTIQUE'", "0.05"
    "", "", "DRZ ", "(—71.86, 0. )", "'ANALYTIQUE'", "0.05"
    "generalized effort", "B", "VY", "(3000., 0. )", "'ANALYTIQUE'", "0.05"


**Problem 3: traction + dampening**


.. csv-table::

    "**Point/Size**", "", "", "**Reference value**", "**Reference type**", "**Precision (%)**"
    "displacement", "B", "DX", "(5.296 10—5, —3.363 10—6)", "'ANALYTIQUE'", "DX", "0.05"
    "speed", "B", "DX", "(2.113 10—4, 3.327 10—3)", "'ANALYTIQUE'", "0.05"
    "acceleration", "B", "DX", "(—2.091 10—1, 1.327 10—2)", "'ANALYTIQUE'", "0.05"
    "generalized effort", "B", "N", "N", "(2.9879103, —1.897 102)", "'ANALYTIQUE'", "0.05"


**Problem 4: flexure + dampening**


.. csv-table::

    "**Point/Size**", "", "", "**Reference value**", "**Reference type**", "**Precision (%)**"
    "displacement", "B", "DY", "(1.746 10—2, —4.469 10—3)", "'ANALYTIQUE'", "0.05"
    "", "", "DRZ ", ", "(1.757910—2, —3.402 10—3)", "'ANALYTIQUE'", "0.05"
    "speed", "B", "DY", "(2.808 10—1, 1.097)", "'ANALYTIQUE'", "0.05"
    "", "", "DRZ ", "(2.138 10—1, 1.1045)", "'ANALYTIQUE'", "0.05"
    "acceleration", "B", "DY", "(—68.95, 17.64)", "'ANALYTIQUE'", "0.05"
    "", "", "DRZ ", "(—69.4, 13.43)", "'ANALYTIQUE'", "0.05"
    "generalized effort", "B", "VY", "(3.0215103, 1.212 102)", "'ANALYTIQUE'", "0.05"
    "", "", "MFZ ", "(—1.567 102, —8.583 102)", "'ANALYTIQUE'", "0.05"