# SS-V: 4030 Coupled Thermal-Structural Analysis - Constrained Straight Bar Under Linear Temperature Field

Test No. VTL04 Determine stresses at the top and bottom of a constrained straight bar under linear temperature field.

## Definition

A straight 1 x 1 x 10 mm bar (Figure 1) is constrained at ends and is thermally loaded. A uniform temperature of 100 degress Celsius is applied to the top of the bar, and a uniform temperature of -100 degrees Celsius is applied to the bottom of the bar. The rest of the bar surfaces are insulated.

The material properties are:

**Properties****Value**- Modulus of Elasticity
- 2.1e+11 pa
- Poisson's Ratio
- 0.3
- Coefficient of thermal expansion
- 1.2e-5 m/m-C
- Thermal conductivity
- 43 W/m-K

## Results

The bar is simulated using a 3D solid model. The
temperature distribution is obtained in thermal analysis (Figure 3). Temperature changes
linearly across the bar from 100 degrees Celsius at the top to -100 degrees Celsius
at the bottom.

The obtained temperature field was used as input for structural
analysis. In order to make use of the reference data obtained for a 1D model of the
bar, the following constraints are applied: sliding supports are applied to end
surfaces of the bar and two vertices at one end of the bar are constrained in order
to eliminate rigid body motion of the bar (Figure 2).

Ref Solution * | SimSolid | % Difference | |
---|---|---|---|

Stress at the top/bottom of the bar (compression/tension) [pa] | 2.520E+08 | 2.516E+08 | -0.17% |

* Ref Solution is a 1D model

^{1}W.C. Young, R.G. Budynas, Roark’s Formulas for Stress and Strain, Seventh Edition, McGraw-Hill Book Co.,Inc., 2001, p. 759.