6. Thermomechanical chaining

6.1. Description

For the resolution of chained thermomechanical problems, thermal shell finite elements [R3.11.01] must be used for thermal calculation, whose temperature field is retrieved as the input data of Code_Aster for mechanical calculation. There must therefore be compatibility between the thermal field given by the thermal shells and that recovered by the mechanical shells. The latter is defined by the knowledge of the 3 fields TEMP_SUP, TEMP_MIL and TEMP_INF given in lower, middle and upper shell skins.

The table below shows the compatibilities between mechanical shell and thermal shell elements.

Modeling THERMIQUE	Mesh	Finished Element	for use with	Mesh	Finished Element	Finished Element	Modeling MECANIQUE
COQUE	QUAD9	THCOQU9	///////////	QUAD9	MEC3QU9H	COQUE_3D
COQUE	TRIA7	THCOTR7	///////////	TRIA7	MEC3TR7H	COQUE_3D

Notes:

• The nodes of thermal shell elements and mechanical shells must match. The meshes for thermal and mechanical engineering will therefore have the same number and the same type of meshes.

• Surface thermal shell elements are treated as plane elements by projecting the initial geometry onto the plane defined by the first 3 vertices.

Thermomechanical chaining is also possible if one knows through experimental measurements the variation of the temperature field in the thickness of the structure or of certain parts of the structure. In this case we work with a temperature map defined a priory; the temperature field is no longer given by the three values TEMP_INF, TEMP_MIL and TEMP_SUP of the thermal calculation obtained by EVOL_THER. It can be much richer and contain an arbitrary number of discretization points in the thickness of the shell. The operator DEFI_NAPPE makes it possible to create such temperature profiles from the data provided by the user. These profiles are affected by the CREA_CHAMP command (cf. test case HSNS100B). It should be noted that for mechanical calculation, it is not necessary for the number of integration points in the thickness to be equal to the number of points of discretization of the temperature field in the thickness. The temperature field is automatically interpolated at the points of integration into the thickness of the shell elements.

6.2. Test case

The test cases for thermomechanical chaining between thermal shell elements and mechanical shell elements are HPLA100C (elements MEC3QU9H) and HPLA100D (elements MEC3TR7H). It is a thermoelastic hollow cylinder weighing in uniform rotation [V7.01.100] subjected to a phenomenon of thermal expansion where the temperature fields are calculated with THER_LINEAIRE by a stationary calculation.

Thermal expansion is worth: \(T(\rho )\mathrm{-}{T}_{\text{ref}}(\rho )\mathrm{=}0\text{.}5({T}_{s}+{T}_{i})+2\text{.}({T}_{s}+{T}_{i})(r\mathrm{-}R)\mathrm{/}h\)

with:

• \({T}_{s}\mathrm{=}0\text{.}5°C,{T}_{i}\text{=-}0\text{.}5°C,{T}_{\text{ref}}\mathrm{=}0\text{.}°C\)

• \({T}_{s}\mathrm{=}0\text{.}1°C,{T}_{i}\mathrm{=}0\text{.}1°C,{T}_{\text{ref}}\mathrm{=}0\text{.}°C\)

We test the stresses, the efforts and the flexing moments in \(L\) and \(M\). The reference results are analytical. Very good results are obtained regardless of the type of element considered.