There are two basic modes of failure for the Dome: the failure of the rebar by breaking, or deflection of the rebar - which causes the mud to fail. Therefore, the most essential task in the design/analysis of the Dome was to create an accurate computer simulated model using finite element analysis (FEA). The simulated model allowed for prediction of the Domes failure modes. Moreover, it predicted deflections and stresses within the rebar given different loading conditions. These stresses and deflections were used to assess whether or not the Dome would survive or fail during an earthquake or windstorm.
Two of the most accurate types of three-dimensional FEA are tetra4 and tetra10, where the four and ten refer to the number of nodes per element, so tetra10 would be more accurate than tetra4. Therefore, in order to perform the finite element analysis, the team chose to use Unigraphics. Unigraphics has a high-end 3D solver that can perform tetra10 analysis with relative ease. This means that the results that were obtained are more accurate than the results that could have been obtained by other programs, which only have tetra4 ability.
One disadvantage in using the 3D model was that it created thousands of finite elements that caused the computer to crash if there were too many. For this reason, the diameter of the rebar (in the model) needed to be modified to compensate for the number of finite elements. Larger diameter rebar required fewer elements, but to compensate for the larger diameter, the material properties needed to be changed. By changing the material properties, 12mm rebar was simulated by 60mm rebar, which meant that two different types of models produced the same stresses and deflections. In addition, the idea of including the mud into the FEA model had been considered, unfortunately, due to the limitation of the number of finite elements, this task proved impossible.
Once the model was completed, the loading conditions that might have caused failure in the Dome were applied. First, in order to test the accuracy of the model, we applied a 180lb point load to the actual Dome and measured its deflection to be 2.0. We then applied that same load to the finite element model, and it predicted a deflection of 1.994. That test proved that the model was accurate. One thing that should be noted is that during the preliminary testing of our finite element model, we found that the stresses that were being caused by the loading were insignificant. This meant that the Dome was not likely to fail due to high stresses in the rebar. In fact, the stresses caused in the rebar were approximately 150psi for most loading conditions, which is well below the elastic limit. So, the rest of the testing done was based upon the second failure criterion of the Dome deflecting enough that it caused the mud to fail.
We then applied the earthquake loading conditions. Using the fact that a 7.0 on the Richter scale earthquake produces a 150 cm/s2 acceleration, we applied this acceleration to the Dome using gravity loading.
The results of the earthquake loading showed that during an earthquake, the Dome would only deflect about 6/100, which is well below the failure point of the mud. This led us to the conclusion that the Dome would not fail during an earthquake.
Next, we applied the loadings found from the CFD analysis. The CFD showed that in the event of high winds, there would be two forces acting on the Dome. There would be one pressure force pushing on the outside of the Dome, and one pressure force acting from the inside of the Dome. By applying both of those to the Dome at the same time, we came up with following results
The Dome will not deflect more than about 1 Ύ, which is about Ό below the worst-case scenario failure point for the mud. This means that the Dome would not fail under a Class 5 hurricane wind loading.
The results of the FEA show that the Dome will not fail given the extreme loading conditions that we applied. The 6/100 deflection caused by the earthquake loading was significantly low, also the 1 Ύ deflection caused by the wind loading was not high enough to fail the mud shell. Therefore, team Habitat must give the Dome its approval, given that the Dome is built to the specifications listed in the conclusions section of the document.