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Fixed Beam Under Changing Temperature


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 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 :

CaseMesh typeNumber of nodesElement typeTool type
(A)linear tetrahedral843D isoparametricCalculix
(B)quadratic tetrahedral3693D isoparametricCalculix
(C)linear hexahedral3693D isoparametricCalculix
(D)quadratic hexahedral12213D isoparametricCalculix
(E)linear tetrahedral843D isoparametricCode_Aster
(F)quadratic tetrahedral3693D isoparametricCode_Aster
(G)linear hexahedral3693D isoparametricCode_Aster
(H)quadratic hexahedral12213D isoparametricCode_Aster
Mesh used for the SimScale case (A)

Mesh used for the SimScale case (A)

Mesh used for the SimScale case (C)

Mesh used for the SimScale case (C)

Simulation Setup


  • 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


  • 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.


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]SimScaleError (%)
(D)24.624.599-24.601± 0.004%
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)


[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

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part of: Fixed Beam Under Gravitational Load

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