1. Reference problem#
1.1. Geometry#
Figure 1.1-a: Diagram of thermal loads and geometry (A and B models)
Figure 1.1-b: Isovalues of the thermal field on the initial thermal mesh (A and B models)
It is a cracked metal « cylinder head » (steel 1 6MND5, \(E\mathrm{=}{210.10}^{3}\mathit{Mpa}\),, \(\nu \mathrm{=}0.2\), \(\rho {C}_{p}\mathrm{=}{\mathrm{526,10}}^{4}J\mathrm{/}{m}^{3}°C\) , \(\lambda \mathrm{=}\mathrm{33,5}W\mathrm{/}m°C\)).
In both models (A and B), an isotropic transient linear thermal calculation (THER_LINEAIRE or THER_NON_LINE) is performed in lumped modeling (PLAN_DIAG) on a thermal mesh TRIA3/SEG2.
In the second modeling, this calculation is linked with an elastic calculation (MECA_STATIQUE or STAT_NON_LINE) in plane stress modeling (C_PLAN) on a mechanical mesh in TRIA6/SEG3.
Figure 1.1-c: Schematic of thermo-mechanical loads and geometry (modeling B)
Figure 1.1-d: Decay in deformation potential energy during the free adaptation process of meshes (B modeling)
Figure 1.1-e: Deformed mechanical mesh (B modeling)
The various key areas of the calculation are designated: GM38 for the entire volume part in TRIA, GM33 for the outgoing heat flow, GM36 /37 for the exchange conditions, GM39 /40 for the embedment, GM34 for the distributed pressure and GM35 for the distributed pressure and at which the average temperature will be measured.
1.2. Material properties#
Throughout the structure (GROUP_MAGM38), the following material characteristics are applied:
\(\begin{array}{c}E\mathrm{=}21000\mathit{MPa}\\ \nu \mathrm{=}0.2\\ \rho C\mathrm{-}p\mathrm{=}526{10}^{4}J\mathrm{/}{m}^{3}°C\\ \lambda \mathrm{=}\mathrm{33,5}W\mathrm{/}m°C\end{array}\)
1.3. Boundary conditions and loads#
The breakdown of loads by zone can be summarised in the form of the following table:
Loads |
|
GM33 |
FLUN = \(\mathrm{-}400W\mathrm{/}{m}^{2}\) |
GM36 |
COEF_H = \(1000W\mathrm{/}{m}^{2}°C\) TEMP_EXT = \(350°C\) |
GM37 |
COEF_H = \(5000W\mathrm{/}{m}^{2}°C\) TEMP_EXT = \(150°C\) |
GM39 /40 |
DX=DY=0. |
GM34 |
PRES = \(\mathrm{-}0.1N\) |