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Documentation

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 :

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
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]SimScaleError (%)
(A)24.624.60.00%
(B)24.624.60.00%
(C)24.624.5990.004%
(D)24.624.599-24.601± 0.004%
(E)24.624.60.00%
(F)24.624.60.00%
(G)24.624.60.00%
(H)24.624.60.00%
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

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