Use
===========




Modeling
------------

For each connection, the user must define under the keyword factor LIAISON_ELEM of AFFE_CHAR_MECA:


.. csv-table::

    ":math:`S`:", "the trace of the right section of the beam on the shell: it does it with the keywords MAILLE_1et /or GROUP_MA_1c 'in other words, it gives the list of line cells (assigned to shell modeling 'edge' elements) that represent this section geometrically."
    ":math:`\text{P}`:", "a node (keyword NOEUD_1ou GROUP_NO_1) carrying the 6 classical beam degrees of freedom: DX, DY, DZ, DRX, DRY, DRZ"
    ":math:`V`:", "the vector defining the axis of the beam, oriented from the shell to the beam, and defined by its coordinates using the AXE_POUTRE keyword: (v1, v2, v3)"


**Note:**


**the node* :math:`\text{P}` *can be a beam element node or a discrete element node,*


* *the list of shell edge meshes, defined by* *MAILLEou* * *GROUP_MAdoit represent* **exactly the right section of the beam. This is an important constraint for meshing.*




Examples and tests
-----------------




Quiz SSLX101
~~~~~~~~~~~~

It is a straight beam subjected to unit forces in :math:`\text{B}` (traction, bending and torsional moments). A section of thin tube with a thickness of :math:`\text{h}\ll \text{R}` is taken.


.. image:: images/Object_80.svg
    :width: 375
    :height: 126


.. _RefImage_Object_80.svg:

The embedding in :math:`\text{O}` is achieved using a connection between the edge of the shell and a point element located in :math:`\text{O}`. This element is embedded (translations and rotations zero).

This makes it possible to obtain a stress state in the shell that is very similar to a "beam" solution: there is no disturbance in the stress field. The solution differs from the analytical solution (solution RDM) by 3%, this being solely due to the fineness of the mesh in shell elements.




Flexion of a plate
~~~~~~~~~~~~~~~~~~~~~~

Let us consider a sufficiently long thin plate, of length :math:`\mathrm{2L}`, of width :math:`\text{b}`, of width, of thickness :math:`\text{h}`, modeled by a shell element :math:`\text{OA}` and a beam element on :math:`\text{AB}`:


.. image:: images/Object_81.svg
    :width: 375
    :height: 126


.. _RefImage_Object_81.svg:


* The 1st link condition is written as:

:math:`bhU(A)=h{\int }_{\text{CD}}U(y)\text{dy}`

the displacement of point :math:`\text{A}` (belonging to the beam) is the average of the movements of the edge :math:`\text{CD}` of the plate.


* The 2nd connection condition is written as:

:math:`I(\Omega )=h{\int }_{\text{CD}}\mathrm{AQ}\wedge U(Q)\text{ds}+\frac{{h}^{3}}{\text{12}}{\int }_{\text{CD}}\theta (Q)\text{ds}`

In the case of a bend around :math:`y`, the only non-zero term is: :math:`\frac{{h}^{3}}{\text{12}}{\int }_{-\frac{b}{2}}^{b/2}\theta (y)\text{dy}`

Indeed, :math:`h{\int }_{\text{CD}}\mathrm{AQ}\wedge U(Q)\text{ds}=h({\int }_{-\frac{b}{2}}^{\frac{b}{2}}{U}_{z}\text{ydy})\text{.}x=0`

For a bend around :math:`y`, the link is therefore written:

:math:`{I}_{y}{\theta }_{y}(A)=\frac{b{h}^{3}}{\text{12}}{\theta }_{y}` because :math:`{\theta }_{y}` is constant on CD.

This application is implemented in test SSLX100B: 3D_shell_beam mix.