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


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.


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 (real distributed effort: zero imaginary part)**


.. 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: traction (complex distributed effort: zero real part)**


.. csv-table::

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


**Problem 3: traction + damping (real distributed effort: zero imaginary part)**


.. 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", "(2.9879 103, —1.897 102)", "'ANALYTIQUE'", "0.05"


**Problem 4: flexure + damping (complex distributed force: zero real part)**


.. csv-table::

    "**Point/Size**", "", "", "**Reference value**", "**Reference type**", "**Precision (%)**"
    "displacement", "B", "DX", "(3.363 10—3, 5.296 10—5)", "'ANALYTIQUE'", "0.05"
    "speed", "B", "DX", "(-3.327 10—3, 2.113 10—4)", "'ANALYTIQUE'", "0.05"
    "acceleration", "B", "DX", "(-1.327 10—2, -2.091 10—1)", "'ANALYTIQUE'", "DX", "0.05"
    "generalized effort", "B", "N", "N", "(1.897 102, 2.9879 103)", "'ANALYTIQUE'", "0.05"


When the distributed force is applied as an imaginary part of the load, the reference solution is obtained from that of modeling A by exchanging the real part and the imaginary part and by changing the sign of the new real parts.