The aim of this test case is to validate the following functions:
The simulation results of SimScale were compared to the analytical results in [Roark]. The meshes used in (A) and (B) were created with the parametrized-tetrahedralization-tool on the SimScale platform and the meshes used in (C) and (D) were meshed with Salome.
The bar has a cross section of 0.05 x 0.05 m2 and a length of l = 1.0 m.
Tool Type : Calculix, Code_Aster
Analysis Type : Thermomechanical
Mesh and Element types :
|Case||Mesh type||Number of nodes||Element type||Tool type|
|(A)||linear tetrahedral||84||3D isoparametric||Calculix|
|(B)||quadratic tetrahedral||369||3D isoparametric||Calculix|
|(C)||linear hexahedral||369||3D isoparametric||Calculix|
|(D)||quadratic hexahedral||1221||3D isoparametric||Calculix|
|(E)||linear tetrahedral||84||3D isoparametric||Code_Aster|
|(F)||quadratic tetrahedral||369||3D isoparametric||Code_Aster|
|(G)||linear hexahedral||369||3D isoparametric||Code_Aster|
|(H)||quadratic hexahedral||1221||3D isoparametric||Code_Aster|
Constraints (Boundary Conditions):
$$\sigma = \Delta T \gamma E$$
The equation used to solve the problem is derived in [Roark]. Inserting the values described in the previous chapter results in the unit stress σ = 24.6 Mpa in the whole beam.
Comparison of the unit stress σ in the beam obtained with SimScale with the results derived from the equations presented in [Roark].
Note: The worst results was obtained with mesh (D). This was due to an interpolation error and is shown in the picture below.
|[Roark]||(1, 2, 3, 4) (2011)”Roark’s Formulas For Stress And Strain, Eighth Edition”, W. C. Young, R. G. Budynas, A. M. Sadegh|