Designing for Deflection
Fall 2021
For my engineering design class, I was challenged to design a beam that would deflect exactly 0.5 inches under 200 pounds of force applied under predetermined load conditions. I first designed and analyzed a beam using SOLIDWORKS and FEA, compared those results to an analytical strain energy calculation, then had the design fabricated and tested in real life.
Design Process
The initial beam design used semi-circular patterns on the left side of the beam. This shape was causing high stress concentrations in the design, I flattened the semi-circle to a line with some fillets on each end. I continued the process by reducing the overall stress by spreading it out over the entire beam structure by taking existing line segments, cutting them in half, then adding a fillet between the halves. I incrementally adjusted the thickness until yielding was minimized. I then worked to increase deflection to the desired amount. This involved slowly lowering the thickness of any parts that could handle more stress until the beam reached the desired deflection. Running the FEA for each of these changes was a very slow process, and in the future I would like to learn ways to do this more efficiently. In order to ensure the mesh size was not affecting the results, I performed a mesh analysis, testing and analyzing the results from 18 different mesh sizes.
Analytical Calculations
While the FEA gave me the results I was looking for, my professor emphasized throughout the semester that simulations cannot be blindly trusted. In order to cross-check my results to see if they were viable, I used Castigliano's theorem to find the deflection of the beam by hand. I had to simplify the geometry in order to make a free-body-diagram I could realistically work with. I used upper and lower bounds of each dimension to get a range instead of a single final value. The FEA resulting deflection was within this range.
Real Life Testing
I had the beam fabricated out of Al 6061-T6511 using a water jet and then tested on an Instron 5800R machine applying 200 lbf to the structure. According to the graph, the testing resulted in a stiff diagonal line, showing that there was no yielding. The final deflection was 0.506 inches for 200 lbf applied. These results show that the design was very successful. In the future, I would work on the design to make it lighter. Adding cutouts to reduce the bulk would have made for a better design.
