# Bimetallic Strip Under Thermal Load¶

## Overview¶

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

- thermomechanical solver with different materials

The simulation results of SimScale were compared to the analytical results derived from [Roark]. The mesh used was created locally consisting of quadratic hexahedral elements and uploaded to the SimScale platform.

## Geometry¶

The bimetallic strip has a length of \(l = 10 m\), width of \(w = 1 m\) and total height of \(h = 0.1 m\) with each strip thickness of \(t_a = t_b = 0.05 m\).

## Analysis type and Domain¶

**Tool Type** : CalculiX

**Analysis Type** : Thermomechanical

**Mesh and Element types** :

Mesh type | Number of nodes | Number of 3D elements | Element type |
---|---|---|---|

quadratic hexahedral | 3652 | 600 | 3D isoparametric |

## Simulation Setup¶

Material:

Upper strip:

- isotropic: \(E_a\) = 200 GPa, \(\nu\) = 0, \(\rho\) = 7870 kg/m³, \(\kappa\) = 60 W/(mK), \(\gamma_a\) = 1e-5 1/K, Reference temperature = 300 K

Lower strip:

- isotropic: \(E_b\) = 200 GPa, \(\nu\) = 0, \(\rho\) = 7870 kg/m³, \(\kappa\) = 60 W/(mK), \(\gamma_b\) = 2e-5 1/K, Reference temperature = 300 K

Initial Conditions:

- uniform: \(T_o\) = 300 K

Constraints:

- Node N1 fixed in all directions
- Node N2 fixed in x and y direction
- Node N3 fixed in y direction

Temperature:

- \(T\) = 400 K on face ABCD and EFGH

Contact:

- Bonded contact with automatic ‘Position tolerance’ between two strips.

## Reference Solution¶

The equation (1), (2), (3) and (4) used to solve the problem is derived in [Roark]. Equations (2) and (3) are the displacements of the bimetallic strip in x and z direction respectively. Whereas, equation (4) is the normal stress in x direction at the bottom surface.