D modeling
==============


Characteristics of modeling
-----------------------------------

DKT + substructure of GUYAN


.. image:: images/1000439000000EC800001389956FDEAF3A224200.svg
    :width: 190
    :height: 252


.. _RefImage_1000439000000EC800001389956FDEAF3A224200.svg:

**Boundary conditions:** Free plate

Condensation of mass matrices and stiffness on the nodes:

:math:`(A,B,C,D,G,H,I,J,K,L,M,N,O)`.


Characteristics of the mesh
----------------------------

Number of knots: 145

Number of meshes and types: 256 TRIA3


Tested sizes and results
------------------------------


.. csv-table::

    "**Order of**", "**Frequency**", "**(** :math:`\mathrm{Hz}` **)**", "", ""
    "**clean mode i**", "**Reference**", "**Aster**", "**% difference**", "**Tolerance**"


2°: Free plate


.. csv-table::

    "7", "33.7119", "33.8758", "—0.48", ""
    "8", "49.4558", "49.5240", "—0.14", "1.1 10—2"
    "9", "61.0513", "61.6240", "—0.94", ""



notes
---------

We are trying to calculate the first 3 non-zero natural frequencies of the problem of the free plate on its edges.

If we condense the matrices onto the nodes alone:

:math:`(A,B,C,D,G,H,I,J,K)`

The accuracy of the frequencies is then only :math:`\text{2\%}`.

To obtain the desired results with the expected precision (:math:`\text{1\%}`), the points :math:`(L,M,N,O)` must be added.