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    Fixed Beam Under Changing Temperature

    Overview

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

    • thermomechanical analysis

    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.

    Import validation project into workspace

    Geometry

    FixedBeamUnderChangingTemperature-geometry
    Geometry of the beam

    Geometry of the beam

    The bar has a cross section of 0.05 x 0.05 m2 and a length of l = 1.0 m.

    Analysis type and Domain

    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
    FixedBeamUnderChangingTemperature-mesh-a
    Mesh used for the SimScale case (A)

    Mesh used for the SimScale case (A)

    FixedBeamUnderChangingTemperature-mesh-c
    Mesh used for the SimScale case (C)

    Mesh used for the SimScale case (C)

    Simulation Setup

    Material:

    • isotropic: E = 205 GPa, ν = 0.3
    • thermal expansion coefficient γ = 12E-6 1/K

    Constraints (Boundary Conditions):

    • Fixed x-translation of face ABCD and face A’B’C’D’
    • Additional points were fixed to restrain the remaining translations and rotations

    Loads:

    • Temperature change ΔT = 10 K on the outer surface

    Reference Solution

    $$\sigma = \Delta T \gamma E$$
    The equation (1) 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.

    Results

    Comparison of the unit stress σ in the beam obtained with SimScale with the results derived from the equations presented in [Roark].

    Comparison of the unit stress σ in [MPa]
    Case [Roark] SimScale Error (%)
    (A) 24.6 24.6 0.00%
    (B) 24.6 24.6 0.00%
    (C) 24.6 24.599 0.004%
    (D) 24.6 24.599-24.601 ± 0.004%
    (E) 24.6 24.6 0.00%
    (F) 24.6 24.6 0.00%
    (G) 24.6 24.6 0.00%
    (H) 24.6 24.6 0.00%
    FixedBeamUnderChangingTemperature-quadratichexa-results
    Stress filed obtained with mesh (D)

    Note: The worst results was obtained with mesh (D). This was due to an interpolation error and is shown in the picture below.

    Stress filed obtained with mesh (D)

    References

    [Roark] (1234) (2011)”Roark’s Formulas For Stress And Strain, Eighth Edition”, W. C. Young, R. G. Budynas, A. M. Sadegh

    Last updated: January 29th, 2019

    What's Next

    part of: Fixed Beam Under Gravitational Load

    Contents