Modeling A
==============


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


.. image:: images/Object_9.svg
    :width: 209
    :height: 265


.. _RefImage_Object_9.svg:

Along the beam, we have :math:`\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0`.

At the base, all degrees of freedom are blocked.


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

The mesh consists of 21 nodes and 20 Timoshenko beam elements.


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

**Natural bending frequencies**


.. csv-table::

    "Mode number", "1", "2", "3", "3", "3", "4", "5", "6", "7", "8", "9", "9", "10"
    "Castem", "0.70", "5.04", "5.04", "14.69", "14.69", "28.78", "46.19", "66.82", "92.74", "125.15", "125.15", "163.91", "163.91", "208.81"
    "DYNAM2D/DRAM ", "0.70", "5.04", "5.04", "14.67", "14.67", "28.75", "46.18", "66.86", "92.77", "125.05", "125.05", "125.05", "163.38", "163.38", "208.81"
    "PERMAS (1)", "0.70", "5.04", "5.04", "14.69", "14.69", "28.78", "46.19", "66.82", "92.74", "125.15", "125.15", "125.15", "163.91", "163.91", "208.81"
    "NASTRAN ", "0.70", "5.04", "5.04", "14.67", "14.67", "28.75", "46.18", "66.86", "92.78", "125.05", "125.05", "163.48", "163.48", "207.70"
    "SYSTUS (1)", "0.72", "5.13", "5.13", "14.91", "14.91", "29.19", "46.83", "67.65", "93.64", "125.95", "125.95", "125.95", "164.39", "208.61"
    "ABAQUS ", "0.70", "5.02", "5.02", "14.57", "14.57", "28.42", "45.40", "65.17", "89.26", "118.50", "118.50", ""
    "MECHANICA ", "0.70", "5.03", "5.03", "14.62", "14.62", "28.54", "45.63", "65.60", "90.21", "120.43", "120.43", "155.88", "155.88", "196.01"
    "CASTOR ", "0.70", "5.03", "5.03", "14.59", "14.59", "28.46", "45.48", "65.35", "89.88", "120.24", "120.24", "154.40", "154.40", "194.06"
    "SYSTUS (2)", "0.70", "5.03", "5.03", "14.59", "14.59", "28.42", "", "", "", ""
    "PERMAS (2)", "0.70", "5.03", "5.03", "14.60", "14.60", "28.48", "45.50", "65.29", "89.59", ", "119.41", "119.41", "119.41", "14.60", ""
    "Average values", "0.70", "5.04", "5.04", "14.66", "14.66", "28.66", "45.89", "66.27", "91.51", "122.77", "122.77", "157.79", "157.79", "204.69"
    "ASTER ", "0.70", "5.03", "5.03", "14.59", "14.59", "28.43", "45.38", "65.07", "89.17", "118.67", "118.67", "153.24", "153.24", "192.40"
    "Variance*Aster*", "0.00", "0.26", "0.26", "0.26", "0.48", "0.79", "1.12", "1.81", "2.56", "3.34", "3.34", "2.88", "2.88", "6.00"
    "Average values in%", "", "", "", "", "", "", "", "", "", "", ""


**Movement** :math:`(m)` **: with** :math:`\mathrm{Fx}=1000`


.. csv-table::

    "CASTEM "," DYNAM2D "," PERMAS (1)", "PERMAS (1)", "(2)", "SYSTUS (1)", "ABAQUS ", "Average value", "ASTER ", "Variance (%) Value
    average/ ASTER"
    "0.039", "0.038", "0.041", "0.041", "0.038", "0.038", "0.034", "0.0344", "—9.4", "—9.4"



notes
---------

Definitive problems between internal forces and constraints do not allow the results of ASTER to be compared with other codes (bending moment and shear force).