Figure 1: Thermal Conditions

During re-entry of the Apollo Command Module into the earth’s atmosphere, the system undergoes both a thermal load and after deploying its parachutes, it undergoes a mechanical load. In this project, we use two finite element programs to analyze the effect of these loads on a 2-D cross section of the titanium module.

We used the material properties for titanium (Table 1) and the provided numerical data (Table 2) which correspond to the constants labeled in Figures 1 and 2.



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Table 1

Table 2

Figure 2: Mechanical Conditions

Results

Figure 3 shows the temperature distribution of the mesh when only the boundary condition Tg = 100◦C is prescribed to the tubes.
Figure 4 shows the temperature distribution in the steady state condition after convection coefficients and initial boundary temperatures are applied.
Figure 5 shows the Transient heat solution with sample step sizes. These steps were generated using dt = dt^1.6. Because the thermal solution approaches steady state as t → ∞, an exponential scale allows us to continue to observe the heating behavior as temperatures increase. 

Figure 3: Stationary Heat Solution with Constant Temperature

Figure 4: Steady State Temp Distribution

Figure 5: Transient Heat Solution with Sample Step Sizes

Figure 6 shows the undeformed and deformed mesh along with the stress parabola applied along border AB.
​Figure 7 shows the von Mises yield criterion stress distribution in the mesh. A maximum of about 4.15 ∗ 106[Pa] at the bottom center is displayed in dark red. A minimum of about .01∗106[Pa] is displayed in blue at the top, along the right and left edge, and at the bottom right and left corners. 

Figure 6: Deformation with Stress Parabola Applied

Figure 7: von Mises Yield Criterion Stress Distribution [Pa]

Acknowledgements

Team Members:
Andy Meyers, Theo Fedronic, Heather Hughes

Professor:
Ralf Denzer

Instructors:
Sally Issa, Philip Oppermann 

​Lund University
Department of Mechanical Engineering 

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