Difference between revisions of "Contrib:KeesWouters/beam/macropoutre"

Revision as of 18:34, 26 March 2011

back to my main page:
Contrib:KeesWouters
Back to: Use of beam elements
Contrib:KeesWouters/beam

Software compatibility

march 2011 - SalomeMeca 2010 (Code Aster 10.2) - Ubuntu Meerkat 10.10 64bits.

Using the macro MACR_CARA_POUTRE to define cross section quanties of a beam

This is just another simple example of the use of beams for static calculations. The main focus is on varying obtaining the cross section quantities of the beam by using the macro MACR_CARA_POUTRE. Based on a 2D mesh of the cross section of the beam, most of the required quantities for beam analysis are derived. Here (Contrib:KeesWouters/beam/orientation) an equivalent analysis has been carried out based on a rectangular beam cross section. Here we use an L shaped cross section. Length of the beam is 1.41 [m].

Geometry, mesh, material properties and loads

We need to define two meshes now: one for the cross section of the beam and one for the configuration of the beams. The configuration of the beams: this mesh consists of about thirty beam elements distributed along the x axis.
Note that this has the curious effect that the coordinates of the nodes are defined by a single coordinate. A mesh along the y axis yields a 2D coordinate (x equal to zero). No prices for further guessing.
I decided to read the configuration mesh from unit 20, defined by ASTK:

#Read MED mesh file
BeamMesh=LIRE_MAILLAGE(UNITE=20,
                       FORMAT='MED',
                       NOM_MED='Mbeam1',
                       INFO_MED=2,
                       INFO=2,);

The cross section of the L shaped beam is read from unit 21, also defined by ASTK:

XL=LIRE_MAILLAGE(UNITE=21,
                       FORMAT='MED',
                       NOM_MED='AMesh',
                       INFO_MED=2,
                       INFO=2,);

In the pictures below the configuration and cross section meshes are shown.

*

The boundary conditions are: fully clamped at x = 0, free at the opposite end. The load consist of a shear force of 1 [N] in y direction at the end node:

#Define boundary conditions
BndCnd=AFFE_CHAR_MECA(MODELE=BeamMod,
                     DDL_IMPO=(_F(GROUP_NO='P1',DX=0.0, DY=0.0, DZ=0.0,
                                  DRX=0.0,DRY=0.0,DRZ=0.0,),),
                     FORCE_NODALE=_F(GROUP_NO='P2',FX=0.0,FY=1.0,FZ=0.0),);

Using the macro MACR_CARA_POUTRE

As seen previously, the cross section of the L shaped beam is read from unit 21, also defined by ASTK:

XL=LIRE_MAILLAGE(UNITE=21,
                       FORMAT='MED',
                       NOM_MED='AMesh',
                       INFO_MED=2,
                       INFO=2,);

The result structure XL is used by the macro MACR_CARA_POUTRE to retrieve the cross section quantities of it:

Bsection=MACR_CARA_POUTRE(MAILLAGE=XL,
                         INFO=2,
                         ORIG_INER=(0.0,0.0),);

The result Bsection is an Aster (table Bsection:<table_sdaster(7f166f039810,'Bsection')> with a number of components. The table can be written to a file to be examined:

IMPR_TABLE(TABLE=Bsection,
           FORMAT='TABLEAU',
           UNITE=26, 
           SEPARATEUR=' * ',
           TITRE='xsection of L-beam');

#
# -------------------------------------------------------------------------#
#xsection of L-beam
#ASTER 10.02.00 CONCEPT Bsection CALCULE LE 26/03/2011 A 15:57:43 DE  TYPE
#TABLE_SDASTER
* LIEU         * ENTITE       * AIRE_M       * CDG_X_M      * CDG_Y_M      
* IX_G_M       * IY_G_M       * IXY_G_M      * Y_MAX        * Z_MAX       
* Y_MIN        * Z_MIN        * R_MAX        * AIRE         * CDG_X       
* CDG_Y        * IX_G         * IY_G         * IXY_G        * IY_PRIN_G   
* IZ_PRIN_G    * ALPHA        * X_P          * Y_P          * IX_P        
* IY_P         * IXY_P        * IXR2         * IYR2         * IYR2_PRIN_G 
* IZR2_PRIN_G  * IXR2_P       * IYR2_P       * MAILLAGE

* .... list of Nones (with index 1, next usefull quantities have index 2)

* .9000014
* .9000014     * TOUT         *  1.54334E-03 *  1.14339E-02 *  3.95862E-02 
*  1.53931E-06 *  2.14464E-07 * -2.96934E-07 *  6.14691E-02 *  1.94603E-02
* -4.67767E-02 * -3.03799E-02 *  6.14862E-02 *  1.54334E-03 *  1.14339E-02
*  3.95862E-02 *  1.53931E-06 *  2.14464E-07 * -2.96934E-07 *  1.50958E-07
*  1.60282E-06 *  1.02072E+02 *  0.00000E+00 *  0.00000E+00 *  3.95783E-06
*  4.16232E-07 *  4.01622E-07 *  1.10571E-08 *  6.24183E-09 * -8.41633E-09
*  9.50713E-09 *  2.99290E-07 *  3.76498E-08 * -  

Now suppose you need the area of the cross section AIRE/AIRE_M. This is the third entry (and equal to entry 14 AIRE) of the table. The numerical value is 1.54334E-03 [mm2].
Other interesting quantities are:

• CDG_X_M and CDG_X_M:
  • centre of gravity CoG/CDG in x and y direction
• Y_MIN/MAX and Z_MIN/Max:
  • minimum and maximum distance from CDG in the main coordinate system 0YZ. The origin coincides with CoG/CDG and is rotated by alpha
• ALPHA:
  • rotation (in [deg]) from global x axis of the mesh to local Y axis of the main coordinate system. In this case alpha = 102 [deg], see also second picture.
• IY_PRIN_G and IZ_PRIN_G:
  • main <how is this called in english?> lijntraagheidsmomenten

For normal static analysis we only need the torsion stiffness of the beam. This is not provided by the table.

Using the results inside the command file - I

Having it print out in a file is nice, having directly access by a Python command is much nicer. You can use eg:

alpha  = Bsection['ALPHA',      2]
Ixx    = Bsection['IY_PRIN_G',  2]
Iyy    = Bsection['IZ_PRIN_G',  2]
Area   = Bsection['AIRE_M',     2]
CoGX   = Bsection['CDG_X',      2]
CoGY   = Bsection['CDG_Y',      2]
IxR20  = Bsection['IYR2_PRIN_G',2]
IyR20  = Bsection['IZR2_PRIN_G',2]

print 'alpha0: etc: ',alpha,Iyy,Izz,Area,CoGx,CoGy,IxR20,IyR20

A few remarks:

• index 2 is used because the first index is normally filled with None
• the output of the table in the main coordinate system O(CoG,Ymain,Zmain). You need to interpreted the results accordingly.
• the first index is the name also found in the table output
• a number of values are None. Eg the torsion stiffness 'CT' is None and thus has not been computed by the macro.

Using the results inside the command file - II

It is also possible to define a Python variable that extracts the data from the Bsection table.

BSvar    = Bsection.EXTR_TABLE()

BSvalues = BSvar.values()

Again a few remarks:

• Note the the last index of BSvalues['AY'][1] is now 1 because Python counts from zero.
• the following types are obtained from:
  • print type(BSvalues)............<type 'dict'>
  • print type(BSvar)..............<class 'Utilitai.Table.Table'>
  • print type(BSvar.values).......<type 'instancemethod'>
  • print BSvalues['IYR2'][0]......None
  • print BSvalues['IYR2'][1]......6.24183205019e-09

Here eg we can extract the following data from BSvalues. BSvalues is a Python dictionary:

Jx   = BSvalues['CT'][1]
Axy  = BSvalues['AIRE'][1]
alpha= BSvalues['ALPHA'][1]    ## angle of main principle axes
CoGx = BSvalues['CDG_X'][1]
CoGy = BSvalues['CDG_Y'][1]
Iyy  = BSvalues['IY_PRIN_G'][1]
Izz  = BSvalues['IZ_PRIN_G'][1]

Unfortunately the torsion stiffness Jx is also not defined here.

General way to define the orientation of the beam

The geometry and mesh are generated in Salome in the standard way. In Code Aster the mesh is read, including nodes number, node coordinates, element types and element connectivity. We use linear seg2 elements for the beams.
Of each element we can

• determine the nodes by the connectivity matrix,
• determine the x coordinates of the nodes and
• generate the orientation of the beam

by Python commands.

*

*

Define a beam element by standard commands

After reading the mesh file the following two commands define the beam elements in a standard way:

#Assign to the Model
BeamMod=AFFE_MODELE(MAILLAGE=BeamMesh,
                   AFFE=_F(##TOUT='OUI',
                           GROUP_MA='beam1',
                           PHENOMENE='MECANIQUE',
                           MODELISATION='POU_D_T',),);