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


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

The reference solution is a digital solution [:ref:`3 <3>`].


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

The numerical reference results are as follows:


.. csv-table::

    "**Size**", "**DST***
    **(TRIA3)**", "**DST* (QUAD4) **"
    "* Move :math:`w` to point :math:`C` :math:`(L/\mathrm{2,}L/\mathrm{2,0})` ", "—0.07323", "—0.07417", "—0.07417"
    "* Stress :math:`{\sigma }_{\mathrm{xx}}` at point :math:`C` :math:`(L/\mathrm{2,}L/\mathrm{2,}h/2)` (layer 3)", "—0.478", "—0.482"
    "* Stress :math:`{\sigma }_{\mathrm{yy}}` at point :math:`C` :math:`(L/\mathrm{2,}L/\mathrm{2,}h/4)` (layer 2)", "—0.339", "—0.4"
    "* Stress :math:`{\tau }_{\mathrm{xz}}` at point :math:`D` :math:`(\mathrm{0,}L/\mathrm{2,0})` (layer 2)", "—0.0203", "—0.0305"
    "* Stress :math:`{\tau }_{\mathrm{yz}}` at point :math:`B` :math:`(L/\mathrm{2,0}\mathrm{,0})` (layer 2)", "—0.0406", "—0.0204"


* the reference solutions were obtained with a :math:`6\times 6` [:ref:`3 <3>`] mesh.


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

Less than 2%


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


1. BATOZ J.L., DHATT G.: Modeling structures by finite elements, Vol. 2, Beams and Plates, HERMES.


2. PAGANO N.J., Hatfield J.J.: "Elastic behavior of multilayered bidirectional composites", AIAA J., Vol. 10, No. 7, p. 931-933, 1972.


3. LARDEUR P.: Development and evaluation of two new finite elements of composite plates and shells with the influence of transverse shear, Engineering doctoral thesis, Compiègne University of Technology, 1990.