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


Calculation method
-----------------

The reference results are either non-regression values, or the analytical solutions in motion and under pressure, given by the following formulas :ref:`[1] <[1]>`:

 :math:`U1=\frac{{({x}^{2}-1)}^{2}({y}^{2}-1)y}{4}` and :math:`U2=\frac{{({y}^{2}-1)}^{2}(1-{x}^{2})x}{4}`



 :math:`P=5{x}^{3}(y-1)+{y}^{3}`


.. _RefHeading__12997_1909213516:


Reference quantities and results
-----------------------------------

The analytical solution gives:


.. csv-table::

    "**Location**", "**Instant**", "**Component** (DEPL)", "Value"
    "Node PT_ben :math:`(\mathrm{0.5,}0.5)` "," :math:`t=1s` "," ", "DX", ":math:`-0.052734375\mathit{mm}`"
    "Node PT_ben :math:`(\mathrm{0.5,}0.5)` "," :math:`t=1s` "," ", "DY", ":math:`0.052734375\mathit{mm}`"
    "PT_Ben :math:`(\mathrm{0.5,}0.5)` node "," :math:`t=1s` "," "," PRES "," :math:`-0.1875\mathit{Pa}`"



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

This analytical reference solution is accurate.


Bibliographical reference
-------------------------


.. _[1]:

[:ref:`1 <1>`] *An analysis of some mixed-enhanced finite element for plane linear elasticity*, F. Auricchio, L. Beirao da Veiga, C. Lovadina, C. Lovadina, A. Reali. Compute. Methods Appl. Mech. Engrg. 194 (2005) 2947- 2968