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

Test No. VTL04Determine stresses at the top and bottom of a constrained straight bar under linear temperature field.


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

Figure 1.

Figure 2.


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.

Figure 3. Temperature distribution
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).

Figure 4. Bar deformation and stress X distribution
  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.