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Documentation

Parallelepiped whose Young Modulus is Function of the Temperature

Overview

The aim of this test case is to validate the following functions:

  • Steady-state thermomechanical analysis
  • nonlinear material behavior

The simulation results of SimScale were compared to the results presented in [HPLV100]. Four of the mesh cases were considered; linear and quadratic tetrahedrals, linear and quadratic hexahedrals.

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Geometry

Geometry of the 3D box
ABCDEFGH
x [m]020200020200
y [m]5555-5-5-5-5
z [m]55-5-555-5-5

Analysis type and Domain

Tool Type : Calculix, Code_Aster

Analysis Type : Steady-state thermomechanical

Mesh and Element types :

CaseMesh typeNumber of nodesNumber of 3D elementsElement typeTool type
(A)linear hexahedrals45163D isoparametricCalculiX
(B)quadratic hexahedrals141163D isoparametricCalculiX
(C)linear tetrahedrals44903D isoparametricCalculiX
(D)quadratic tetrahedrals217903D isoparametricCalculiX
(E)linear hexahedrals45163D isoparametricCode_Aster
(F)quadratic hexahedrals141163D isoparametricCode_Aster
(G)linear tetrahedrals44903D isoparametricCode_Aster
(H)quadratic tetrahedrals217903D isoparametricCode_Aster
Mesh used for the SimScale Case A
Mesh used for the SimScale Case C

Simulation Setup

Important

All temperature dependent data is given as a function of °C. This also applies for the data in the different simulations on the SimScale platform (although it says K)!

Material:

  • isotropic: E = 1000/(800 – T) N/m² where T = -35.5 °C to 75 °C, ν

    ν

    = 0.3, ρ

    ρ

    = 2 kg/m³, κ

    κ

    = 1 W/(m °C), α

    α

    = 0 1/°C, Tr

    Tr

    = 20 °C

The temperature dependent Young’s Modulus was calculated using above mentioned formula. The graph below shows the change with respect to temperature:

Young’s modulus change over temperature

Initial Conditions:

  • Initial Temperature Tinitial

    Tinitial

    = 20°C

Constraints:

  • Node nO constrained in x,y and z direction
  • Node nB constrained in x and z direction
  • Node nC constrained in x direction

Loads:

  • Pressure of -1 Pa on face ADHE and BCFG

Temperature:

  • Temperature of 0°C on node nA

Heat flux:

  • Surface heat flux of qs

    qs

    = -2 W/m² on face BCFG

  • Surface heat flux of qs

    qs

    = 2 W/m² on face ADEH

  • Surface heat flux of qs

    qs

    = -3 W/m² on face ABCD

  • Surface heat flux of qs

    qs

    = 3 W/m² on face EFGH

  • Surface heat flux of qs

    qs

    = -4 W/m² on face ABFE

  • Surface heat flux of qs

    qs

    = 4 W/m² on face DCGH

Results

Comparison of temperature on nodes nO and nD obtained with SimScale with the results presented in [HPLV100]. The Error was calculated with respect to [HPLV100] ¹.

Comparison of the temperature on nodes nO and nD [°C]
nodeQuantity [°C][HPLV100] ¹ [°C][HPLV100] ² [°C]Case A [°C]Error [%]Case B [°C]Error [%]Case C [°C]Error [%]Case D [°C]Error [%]Case E [°C]Error [%]Case F [°C]Error [%]Case G [°C]Error [%]Case H [°C]Error [%]
nOT4039.99400400400400400400400400
nDT-35-35-350-350-350-350-350-350-350-350

Comparison of displacements on nodes nA and nD obtained with SimScale with the results presented in [HPLV100]. The Error was calculated with respect to [HPLV100] ¹.

Comparison of the displacements on nodes nA and nD [m]
nodeQuantity [m][HPLV100] ¹ [m][HPLV100] ² [m]Case A [m]Error [%]Case B [m]Error [%]Case C [m]Error [%]Case D [m]Error [%]Case E [m]Error [%]Case F [m]Error [%]Case G [m]Error [%]Case H [m]Error [%]
nAux15.600015.599915.59780.0115.60000.0015.59660.0215.60000.0015.59880.0115.60000.0015.59660.0215.60000.00
uy-0.5700-0.5701-0.378433.61-0.57010.02-0.220561.31-0.56980.04-0.508610.76-0.57010.02-0.220561.31-0.57020.04
uz-0.7700-0.7700-0.510933.65-0.77000.00-0.529231.28-0.77010.01-0.685410.99-0.77000.00-0.529231.28-0.76940.08
nDux16.300016.300016.06241.4616.30000.0016.00571.8116.29990.0016.26100.2416.30000.0016.00571.8116.29980.00
uy-1.7850-1.7850-1.583111.31-1.78510.01-1.443119.15-1.78480.01-1.71673.83-1.78510.01-1.443119.15-1.78520.01
uz-2.0075-2.0075-1.731013.78-2.00750.00-1.735213.56-2.00760.00-1.91374.67-2.00750.00-1.735213.56-2.00690.03

References

[HPLV100](1234567891011) HPLV100 – Parallélépipède dont le module d’Young est fonction de la température

¹ Results by S. ANDRIEUX as mentioned in [HPLV100]: Une solution analytique pour un problème d’élasticité linéaire 3D isotrope avec module d’Young fonction des variables d’espace [V4.90.01]

² Code_Aster results as mentioned in [HPLV100]

Last updated: January 8th, 2021

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