Reference problem
=====================


Geometry
---------


.. image:: images/1000040E00001AAA0000099DCB49F5AAB14B8B7C.svg
    :width: 257
    :height: 93


.. _RefImage_1000040E00001AAA0000099DCB49F5AAB14B8B7C.svg:

Beam :math:`\mathit{PA}`:

Section: :math:`0.1\mathrm{mm}\times 0.1\mathrm{mm}`

Length: :math:`3.0m`

Beam :math:`\mathit{PB}`:

Section: :math:`0.001\mathrm{mm}\times 0.001\mathrm{mm}`

Length: :math:`2.0m`

Mass ratio between :math:`\mathrm{PB}` and :math:`\mathrm{PA}`: :math:`0.33E–04`


Material properties
-----------------------


.. csv-table::

    "Young's module beams :math:`A` and :math:`B`:", ":math:`E=2.1E+11N/{m}^{2}`"
    "Poisson ratio beams :math:`A` and :math:`B`:", ":math:`\nu =0.3`"
    "Density beam :math:`\mathrm{PA}`:", ":math:`{\rho }_{A}=2000\mathrm{kg}/{m}^{3}`"
    "Density beam :math:`\mathit{PB}`:", ":math:`{\rho }_{B}=1000\mathrm{kg}/{m}^{3}`"



Boundary conditions and loads
-------------------------------------

The movement is authorized in plan :math:`(\mathrm{DX},\mathrm{DY})`.

Beam :math:`\mathrm{PA}` is embedded in the support.

Beam :math:`\mathrm{PB}` is connected to Beam :math:`\mathrm{PA}` by three points. In each, the movements in the :math:`\mathrm{DX}` and :math:`\mathrm{DY}` directions of the :math:`\mathrm{PA}` node and the :math:`\mathrm{PB}` node are identical. The rotations are not linked.

The interspectral matrix that transmits the movements from structure :math:`\mathrm{PA}` to structure :math:`\mathrm{PB}` in the chained calculation is of dimension 6 (6 degrees of freedom of transmission).