# Computation of volumogram

*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:

` 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…

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.

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',),);