**process weibull#
Description#
This post computation provides the means for doing a Weibull analysis on a structure. Two modes of operation are available:
eigenstress(211)#\[\sigma'= \left( \frac{\sigma_1^M-\sigma_0}{\sigma_u} \right)^m\]independent(212)#\[\sigma'= \left( \frac{\sigma_1^M-\sigma_0}{\sigma_u} \right)^m + \left( \frac{\sigma_2^M-\sigma_0}{\sigma_u} \right)^m + \left( \frac{\sigma_3^M-\sigma_0}{\sigma_u} \right)^m\]
The Weibull stress is then defined as:
where \(\sigma_1^M\), \(\sigma_2^M\) and \(\sigma_3^M\) are
the post-computation results from a local fmax applied successively
to the three principal stresses \(\sigma_1\), \(\sigma_2\) and
\(\sigma_3\), in descending order. These sub-posts are run
automatically by the weibull processor.
\(V_0\), \(\sigma_u\), \(\sigma_0\) and \(m\) are material parameters.
The probability of failure \(P_r\) is is given by:
In addition to the output of \(\sigma_W\) and \(P_r\). the
values of \(\sigma'\) are stored at each Gauss point under a name
constructed by adding _wb to the variable name.
Syntax#
**process weibull
\(~\,\) *var name
\(~\,\) *mode eigenstress | independant
\(~\,\) *coefmin value1
\(~\,\) *coefmax value2
\(~\,\) *file namef
If the user has only specified a single map (with output_number),
the history is reconstructed from the values read after the options
*coefmin and *coefmax. \(\sigma_1^M\) varies linearly over
100 maps of value1 * \(\sigma_1\) to
value2* \(\sigma_1\) (where \(\sigma_1\) is calculated at
the specified map).
With the option *file, the history is read in the file namef, of
the form:
0.01 10
0.02 15
0.03 20
0.04 40
0.05 60
...
where the first column represents the time and the second the value of \(\sigma_1\).
These two methods presented for the mode eigenstress extend to the
mode independant as well.
Example#
**output_number 10
**process weibull
*var sig
*mode independent
*coefmin 0.5
*coefmax 2.5
% material file
**process weibull
V0 10.
m 20.
sigma_u 1200.
sigma_0 0.