2. Benchmark solution#
2.1. Thermo-elastic solution#
The reference solution is digital. It is obtained with Code_Aster for a fine mesh (20 elements in the thickness). The TP is carried out with a very coarse mesh (3 elements in the thickness), so it is not surprising to obtain results that are quite far from the reference solution.
Indeed, the aim of the TP is to show:
for the thermal calculation, the effects of exceeding the maximum, the instability of the explicit diagram and the contribution of the diagonalization of the thermal mass matrix,
for mechanical calculation, the stresses due to the incompatibility of thermal deformations, even if the cylinder is free, then the incremental aspects of the calculation with STAT_NON_LINE.
The values tested are:
Instant ( \(s\) ) |
Max temperature ( \(\mathit{Tmax}\) ) en \(°C\) |
Number of nodes reached by \(\mathit{Tmax}\) and node numbers |
Min temperature |
Min temperature ( \(\mathit{Tmin}\) ) in \(°C\) |
Number of nodes |
0 |
100 |
63 knots |
100 |
63 |
|
0,1 |
100 |
1 node: \(\mathit{N26}\) |
69,5309 |
1 node: \(\mathit{N62}\) |
|
4 |
100 |
1 node: \(\mathit{N1}\) |
8.5 182 |
1 node: \(\mathit{N62}\) |
|
10 |
100 |
1 node: \(\mathit{N2}\) |
5,56755 |
1 node: \(\mathit{N62}\) |
|
100 |
95,1712 |
1 node: \(\mathit{N3}\) |
1,81091 |
1 node: \(\mathit{N62}\) |
The maximum and minimum values of constraints \(\mathit{SIYY}\) at the times \(t\mathrm{=}\mathrm{0s}\) and \(t\mathrm{=}\mathrm{11s}\)
Unflanged case
Instant ( \(s\) ) |
Maximum Stress \(\mathit{SIYY}\) max |
Number of meshes reached by \(\mathit{SIYY}\) max and mesh number |
Minimum constraint \(\mathit{SIYY}\) min |
Number of stitches reached by \(\mathit{SIYY}\) min and mesh number |
11 |
364.875 |
1 stitch: \(\mathit{M21}\) |
—320,094 |
1 stitch: \(\mathit{M2}\) |
Case bridged with MECA_STATIQUE and STAT_NON_LINE with \(\mathit{TREF}\mathrm{=}0\) (and an initial state \(T\mathrm{=}0°C\)),
Instant ( \(s\) ) |
Stress maximum |
|||
\(\mathit{SIYY}\) max » |
Number of meshes reached by \(\mathit{SIYY}\) max and mesh number |
Stress minimal \(\mathit{SIYY}\) min |
Number of meshes reached by \(\mathit{SIYY}\) min and mesh number |
|
0 |
—200 |
1 stitch: \(\mathit{M40}\) |
—200 |
1 stitch: \(\mathit{M1}\) |
11 |
—61.5003 |
1 stitch: \(\mathit{M1}\) |
—702.563 |
1 stitch: \(\mathit{M22}\) |
Case bridged with MECA_STATIQUE and STAT_NON_LINE with \(\mathit{TREF}\mathrm{=}100°C\) (and an initial state \(T\mathrm{=}100°C\)),
Instant ( \(s\) ) |
Maximum Stress \(\mathit{SIYY}\) max |
Number of meshes reached by \(\mathit{SIYY}\) max and mesh number |
Minimum constraint \(\mathit{SIYY}\) min |
Number of stitches reached by \(\mathit{SIYY}\) min and mesh number |
11 |
138.5 |
1 stitch: \(\mathit{M21}\) |
—502.563 |
1 stitch: \(\mathit{M2}\) |
2.2. Bibliographical reference#
Validation documentation [V7.01.100].