Conclusion and tips for use
====================================

In the following table, a summary of the possibilities offered by plate and shell models is described.


.. csv-table::

    "**Modeling**", "**DKT**", "**DST, Q4G**", "**DKTG, Q4GG**", "**COQUE_3D**", "**COQUE_AXIS**", "****", "****", "****", "**GRILLE_***"
    "Area of application", "", "", "", "", "", ""
    "Linear statics:
    Isotropic material", "**X**", "**X**", "**X**", "**X**", "**X**", "**X**", "**X**"
    "Orthotropic, composite material", "**X**", "**X**", "", "", "", "", ""
    "Static non-linear material", "**X**", "", "**X**", "**X**", "**X**", "**X**", "**X**"
    "Geometric nonlinear statics", "", "", "", "", "**X**", ""
    "Dynamic analysis", "**X**", "**X**", "**X**", "**X**", "**X**", "**X**", "**X**"
    "Euler buckling", "**X**", "", "", "**X**", "", "**X**", "**X**"


In the figure below the field of use of the plates and shells is schematised.


.. image:: images/Object_41.svg
    :width: 642
    :height: 274


.. _RefImage_Object_41.svg:

Figure 5-a: Fields of use of plates and shells

Some recommendations concerning the area of use of these elements:


* *Thin structures* **:**: **for these structures, whose h/L ratio is less than 1/20, transverse shear effects can be overlooked and Kirchhoff's theory applies. It is recommended to use plate elements DKT - DKQ or curved shell elements (COQUE_3D, _ AXIS) for this type of structure.**It is advisable to use preferably the elements**** DKT and DKQ ** which give very good results on movements and more approximate on constraints (recommended for vibration analyses). Even if a large number of these elements must be used, the execution times are still reasonable compared to those of the curved elements. It is recommended not to exceed a ratio H/L=1/500 in order to avoid problems associated with digital locks.


* *Thick structures:* for these structures, plate elements DST, DSQ and Q4G will be used that take into account transverse shear with a shear correction factor :math:`k\mathrm{=}5\mathrm{/}6` (Reissner theory) or **preferably curved shell elements**. The shear correction factor makes it possible to go from a Hencky-Mindlin-Naghdi theory for :math:`k\mathrm{=}1`, to a Reissner theory for :math:`k\mathrm{=}5\mathrm{/}6`. The shear coefficient is only adjustable for curved shell elements but it is recommended that you do not change its value by default.

**When modelling** **Q4G has been preferred, a small mesh sensitivity study** should be carried out. In fact, the tests show that this modeling requires a sufficiently fine mesh in the directions under stress in order to obtain low errors.

The elements DKT, DKQ, DST, DSQ and Q4G are plane elements, they do not take into account the curvature of the structures, so it is necessary to refine the mesh in the case where the curvature is important if we want to avoid parasitic flexions.

The variation in the geometry metric (i.e. its radius of curvature) as a function of its thickness is taken into account:


* automatically for modeling COQUE_3D.


* user defined for modeling COQUE_AXIS.

The optimal mechanical element in statics according to all the test cases in paragraph [:ref:`§2.5 <§2.5>`] is the 9-node shell element **MEC3QU9H**, which makes it possible to obtain good movements and good constraints thanks to its P2 membrane interpolation. It is a versatile element that can be used both to represent very thin structures (:math:`h/L\le 1/100`) and thicker ones. Since, moreover, **the shell element with 7 nodes** **MEC3TR7Hest is less performance**, it is **recommended that the user mesh their shell structure with the largest possible number of quadrangles**.


* *Material nonlinearity:* nonlinear behaviors (plasticity, etc.) under plane stresses are available for curved shell elements (COQUE_3D, COQUE_AXIS) and DKT - DKQ plate elements only. The plastic behavior does not take the terms transverse shear that are treated elastically, because the transverse shear is decoupled from the plastic behavior. For a good representation of the progression of plasticity through thickness, it is recommended to use for numerical integration 3 to 5 layers in the thickness for a number of gauss points equal to 3, 5 and 11 respectively.


* *Geometric nonlinearity* **:**: ** geometric nonlinearities (large displacements, large rotations) under plane stresses are available for COQUE_3D curved shell elements only.


* *Euler buckling* **:**: ** this type of analysis is available with curved shell elements COQUE_3D and plate elements DKT and DKTG.

Elements corresponding to mechanical elements exist thermally; thermomechanical couplings are therefore available both for plate and shell elements. For the time being, these couplings are not possible for multilayer materials.