Benchmark solution
=====================


Calculation method used for the reference solution
--------------------------------------------------------

Analytical solution [:ref:`bib1 <bib1>`].


Benchmark results
----------------------

The baseline results are as follows:


.. csv-table::

    "**Load case**", "**Stress**", "**Value (Mpa)**", "**Comments**"
    ":math:`\mathrm{Mxx}=1` "," :math:`\mathrm{SIXX}(z=–h/2)`
    Layer 1", "—6.82", "Stress :math:`{\sigma }_{\mathrm{xx}}` on the lower skin of layer 1"
    "", ":math:`\mathrm{SIXX}(z=–h/4)` layer 2", "—0.135", ":math:`{\sigma }_{\mathrm{xx}}` stress on the lower skin of layer 2"
    ":math:`\mathrm{Myy}=1` "," :math:`\mathrm{SIYY}(z=–h/2)`
    Layer 1", "—1.5", "Stress :math:`{\sigma }_{\mathrm{yy}}` on the lower skin of layer 1"
    "", ":math:`\mathrm{SIYY}(z=–h/4)` layer 2", "—18.76", ":math:`{\sigma }_{\mathrm{yy}}` stress on the lower skin of layer 2"
    ":math:`\mathit{QY}=1` "," :math:`\mathrm{SIYZ}(z=–h/4)`
    Layer 2", "0.28125", "Stress :math:`{\sigma }_{\mathrm{yz}}` on the lower skin of layer 2"
    "", ":math:`\mathrm{SIYZ}(z=0)`
    Layer 2", "2.62625", "Stress :math:`{\sigma }_{\mathrm{yz}}` on the middle skin of layer 2"
    ":math:`\mathrm{QX}=1` "," :math:`\mathrm{SIXZ}(z=–h/4)`
    Layer 2", "1.279", "Stress :math:`{\sigma }_{\mathrm{xz}}` on the lower skin of layer 2"
    "", ":math:`\mathrm{SIXZ}(z=0)`
    Layer 2", "1.296", "Stress :math:`{\sigma }_{\mathrm{xz}}` on the middle skin of layer 2"


The shape of the distribution of the stresses in the thickness of the plate is as follows:

0.135

1.279

1.296

2.626

0.281

.. image:: images/1000000000000316000002DE1C3BA841A619A3DB.png
    :width: 3.8453in
    :height: 3.572in


.. _RefImage_1000000000000316000002DE1C3BA841A619A3DB.png:


Uncertainties about the solution
----------------------------

Null (analytical solution).


Bibliographical references
---------------------------


1. Dhatt-Batoz "Modeling of structures by finite elements, Volume 2" Pages 246-250 Hermes edition.