This validation case belongs to thermomechanics, with the case of a thick hollow thermoelastic cylinder under temperature gradient conditions. The aim of this test case is to validate the following parameters:
Thermomechanical solver
The simulation results of SimScale were compared to the analytical results presented in [HPLA100]\(^1\).
It represents a quarter section of a hollow cylinder with an internal radius of 19.5 \(m\) and an external radius of 20.5 \(m\), length of 10.0 \(m\). Face ABCD coincides with the XZ plane, face EFGH with the YZ plane and face CHGD with the XY plane.
Fixed temperature value of \(T\) = -0.5 \(°C\) on the internal face (BEHC)
Fixed temperature value of \(T\) = 0.5 \(°C\) on the external face (AGDF)
Temperatures (Cases B, D) – Radial expansion
Fixed temperature value of \(T\) = 0.1 \(°C\) on the internal face (BEHC)
Fixed temperature value of \(T\) = 0.1 \(°C\) on the external face (AGDF)
Reference Solution
The reference solution for the thermoelastic cylinder is of the analytical type, as presented in [HPLA100]\(^1\). It is given in terms of the longitudinal stress onthe internal and external faces:
Cases A and C, internal face: \( \sigma_{ZZ}\) = 1.4321427 \( MPa \)
Cases A and C, external face: \( \sigma_{ZZ}\) = -1.4250001 \( MPa \)
Cases B and D, internal face: \( \sigma_{ZZ}\) = -0.2 \( MPa \)
Cases B and D, external face: \( \sigma_{ZZ} \) = -0.2 \( MPa \)
Result Comparison
Comparison of the computed stresses with the reference solution is presented, at the representative points:
CASE
POINT
SIMSCALE \( \sigma_{ZZ} \) \([Pa]\)
REFERENCE \( \sigma_{ZZ} \) \([Pa]\)
ERROR
A
C
1.1593Ee6
1.4321e6
19.1 %
D
-1.1943e6
-1.4250e6
16.2 %
B
C
-2.0010e5
-2.0e5
0.0 %
D
-1.9993e5
-2.0e5
0.0 %
C
C
1.4342e6
1.4321e6
-0.1 %
D
-1.4228e6
-1.4250e6
0.2 %
D
C
-2.0000e5
-2.0e5
0.0 %
D
-2.0000e5
-2.0e5
0.0 %
Table 2: Results comparison and computed errors for cases A through D
It is found that general results agree with the reference solution. As usual, the first order tetrahedral mesh gives bad accuracy on the bending case, although for the pure expansion it gives good results. It is expected that a finer mesh will improve the accuracy of the solution.
Illustration of the stress distribution for the bending case of the thermoelastic cylinder is shown below:
Figure 4: Longitudinal stress distribution from case C
This website uses cookies so that we can provide you with the best user experience possible. Cookie information is stored in your browser and performs functions such as recognising you when you return to our website and helping our team to understand which sections of the website you find most interesting and useful.
Strictly Necessary Cookies
Strictly Necessary Cookie should be enabled at all times so that we can save your preferences for cookie settings.
If you disable this cookie, we will not be able to save your preferences. This means that every time you visit this website you will need to enable or disable cookies again.