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

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 :

Mesh used for the SimScale case (A)

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].

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