enfr

# Computation of volumogram

31 May 2011

by N. Tardieu, EDF R&D / AMA

A volumogram gives a representation of the component of a field in term of percentage of the volume of the part containing a range of given values.

Thus, if one studies the part presented Figure 1 and that one is interested in the distribution of the von Mises stress, the volumogram is the following:

 Figure 1 : Mesh of the studied bearing
```    INTERVALLE         BORNE_INF      BORNE_SUP       DISTRIBUTION ------------------------------------------------------------------------------------        1              3.47944E-02    4.00516E+01     2.21569E+01        2              4.00516E+01    8.00685E+01     2.26231E+01        3              8.00685E+01    1.20085E+02     1.98340E+01        4              1.20085E+02    1.60102E+02     1.24788E+01        5              1.60102E+02    2.00119E+02     8.81198E+00        6              2.00119E+02    2.40136E+02     5.74077E+00        7              2.40136E+02    2.80153E+02     3.48664E+00        8              2.80153E+02    3.20170E+02     2.12184E+00        9              3.20170E+02    3.60186E+02     1.47352E+00       10              3.60186E+02    4.00203E+02     1.27246E+00```

The range of variation of the von Mises stress extends from 3.47944E-02 to 4.00203E+02 MPa and cutting in 10 intervals:

• the part of the structure which sees this stress varying from 3.47944E-02 to 4.00516E+01 MPa accounts for 22% of the volume of structure;
• the part of the structure which sees this stress varying from 4.00516E+01 to 8.00685E+01 MPa accounts for 22% of the volume of structure;
• etc…
 Figure 2: Distribution of the von Mises stress

The volumogram can be easily visualized in the form of histogram (Figure 3) where it provides a very synthetic vision of the distribution of a field.

 Figure 3 : Representation of the volumogram

The implementation in Code_Aster is very simple thanks to command POST_ELEM, where the user specifies the name of the field, the component to process.

```Table=POST_ELEM(RESULTAT=RESU,      VOLUMOGRAMME=_F(NOM_CHAM='SIEQ_ELGA',      NOM_CMP='VMIS',),);```