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:
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INTERVALLE BORNE_INF BORNE_SUP DISTRIBUTION
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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+00The 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…
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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.
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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',),);