2. Reference solution

2.1. Calculation method used for the reference solution

This test is taken from a study, carried out by Department MMC, which focused on the modeling of industrial piping. It led to comparisons between*code_aster* and the SYSPIPE code from FRAMATOME. The reference solution is numerical (comparison between design results and code_aster results for mechanical loads) and fatigue results obtained by a EXCEL procedure.

2.2. Benchmark results

The final result of the fatigue calculation, on the node at the entrance of the first bend after the component exits, provides a global use factor: \(u\mathrm{=}0.00648\).

This result is based on the results of mechanical and thermal calculations carried out on the line. In order to validate the entire calculation chain, it is ensured that the results of the mechanical calculations are identical to those of reference. These are summarized here:

Natural frequencies of the empty line (embedded at both ends) with springs and at the temperature of \(20°C\):

NUMERO	FREQUENCE (\(\mathit{Hz}\)) Circus/Aster calculation
1	5.059
2	6.023
3	6.866
4	8.204
5	9.733
6	9.987
7	16.535
8	17.329
9	18.282
10	19.004
11	20.271

Torsional and flexural moments for each mechanical load:

Thermal calculations:

The results available in the note were carried out on a 3D modeling of the elbow located after the output of the component. The results are provided for analysis segments located in the right part and in the elbow:

: average value of \(T(i)\mathrm{-}T(j)\) on the ligament

: variation of a linear distribution of T (i, j).

These quantities are maximized for all of the pairs of moments \(i\) and \(j\):

Thermal transient	\(°C\)	\(°C\)	right part	elbow
2	0.741	0.125	1.043	1.445
6	15.48	2.84	5.99	5.69

2.3. Uncertainty about the solution

Numerical solution, obtained with identical data and comparable elements. We can therefore estimate the precision to \(\text{1\%}\) for the mechanical solution.