# Topology and Response Surface Optimization of a Bicycle Crank Arm with Multiple Load Cases
## 3 Results and Discussion
### Topology Optimization Result
#### 3.1.1 Geometry Creation  
After the optimization has reached its steady-state condition above, the next step of the research is creating a manufacturable geometry. From Figure 7d, it can be seen that the optimized geometry is still rough and difficult to be manufactured. Therefore, the geometry should be redrawn again using CAD in the SpaceClaim software to avoid the complexity and achieve manufacturability. This process is called the geometry creation. This process involves neglectable mass elimination, curve fitting and smoothening, radius creation, as well as symmetrical aspects consideration. By considering all those aspects, the final geometry can be created, as seen in Figure 8 below.  
Now, the optimized geometry has a simpler shape and less complexity. It also clearly shows that the optimization method gives significant mass reduction which is emphasized by the presence of holes on the crank arm. The holes significantly reduce the initial mass of the crank arm roughly by 0.1 kg from its original mass of 0.30 kg, which now turns into 0.2 kg. This mass reduction and holes geometry could become the basic approach for lightweight structure creation of the bike crank arm which has never been done before. It is also one of the most important aspects to be discussed since it is related closely to the stress distribution of both before and after the optimization process as the stress distribution is an envelope for all the load cases.  
From the stress distribution result of the optimized design in Figure 9, it is found that the multiple loads' application on the crank arm results in nonsymmetrical stress distribution. This is caused by the direction of the multiforces that are dominantly in the negative \(y\)-direction for all given angles. Proportionally, the moment also moves towards the negative \(y\)-direction, as well. This makes the lower part of the crank arm experiencing higher compression stress than the upper part tension stress. We can also see from the result that the compression stress occurs almost throughout the lower part of the crank while the tension stress occurs only up to the middle part of the crank arm.  
Figure 8: The final geometry of the topology optimized design.  
Figure 9: Stress distribution of the topology optimized design.  
From the maximum stress point of view, it can be seen that the optimized design gives significant differences in von Mises stress compared to the original design. The stress has been increased from 33.2 to 85.0 MPa. Similar to the previous result from [PERSON] et al. [20] and [PERSON] et al. [23] where the narrowing cross-sectional area obtained from the topological optimization hole significantly increases the stress concentration of the crank. Even though the maximum stress is increased, the value is still considerably far below the material yield strength also known as being still in the safety elastic region. Nevertheless, this will be improved by implementing the response surface optimization which will be discussed in the next section.