5. Summary of results

Modeling A, carried out in 3D with linear meshes (PENTA15, HEXA8), gives results where four values (out of 22) exceed the tolerance set initially. The maximum difference obtained is 1.24% for a tolerance of 1%. This exceeding of the tolerance is observed for temperature values close to 0.

In addition, modeling B, carried out in AXIS with linear cells (TRIA3), gives satisfactory results, the maximum difference obtained is 0.25%.

Modeling AXIS is more appropriate for modeling this cylindrical bar than 3D modeling. Circumferential 3D cutting is not dense enough to represent the cylinder, and finer cutting would improve the results.

The results obtained by 3D modeling are considered to be acceptable taking into account the mesh used.

The analytical solution, which is an approximate solution, assumes that the \(r/L\) ratio is much greater than 1. For this numerical test, the \(r/L\) ratio was taken to be equal to 100.