## 5 Comparative Analysis between the Two Weight Optimization Methods
### Comparison of Elapsed Time with the Same Mesh Density  
Based on this component, to carry out a comparison of subsequent mesh refinement, the model used the mesh division method to divide the global mesh and further refined the constraint position. Solid 187 element was used. In the mesh generation step of finite element analysis, the integer or an integer-like method is usually used to refine the mesh size. In this paper, when the mesh was bigger than 1 mm, the global mesh was gradually refined in a 1 mm step value from the default mesh size. For mesh sizes smaller than 1 mm, the global mesh size was gradually refined in a step value of 0.1 mm. A total of 12 types of mesh densities were established using an iterative solver. For the topology optimization calculation, there were 725,215 meshes and 1,232,924 nodes at most. Under this mesh condition, the final optimized material removal rate was 49.74%, which was still 12.24% lower than the manual setting method. Taking the global mesh size as an independent variable, as shown in Figure 17, and the number of meshes as the independent variable, as show in Figure 18, when it was bounded by a mesh size of 0.7 mm, the total number of meshes was 136,639. Once the mesh size was less than 0.7 mm, the calculation time of the topology optimization simulation increased significantly. Figures 17 and 18 also indicate the difference between static stress calculation and topology optimization calculation in time consumption. Figure 16: Maximum equivalent stress of all results from static analysis. Figure 17: Elapsed time of simulation in different global mesh size. To better present the difference in time consumption between the two simulation calculations under the same mesh size, the time consumption of the two simulations were compared to obtain the time consumption ratio, as indicated in Figure 19a. As shown in Figure 19, compared with static calculation, the time of the topology optimization calculation increased exponentially, and this increasing trend further expanded with the refinement of the meshes. Figure 19b shows the single iterative calculation efficiency of topology optimization. When the mesh size was greater than 2 mm, the average single iterative calculation time of topology optimization was faster than static calculation. However, when the mesh size was  
Figure 19: Time ratio. (**a**) Time ratio of two optimization methods under the same mesh size; (**b**) time ratio of average single iterative calculation time of topology optimization to static analysis under the same mesh size; (**c**) comparison of topology optimization under all mesh sizes and static analysis under 3 mm mesh. Figure 18: Elapsed time of simulation in increased mesh elements. smaller 0.9 mm, the single average iteration time was noticeably longer than the calculation time of the static module. It was also observed from the curve that the average iteration time of topology optimization under the same mesh size was longer than static calculation with the refinement of the meshes, and this trend also continuously expanded. The 3 mm mesh size was a special size, because the judgment of mesh independence could be concluded at this situation. In practical application, this means that the static calculation was terminated. The static calculation time at this mesh size was compared with all the cases of topology optimization calculation, as shown in Figure 19c. This comparison aimed at analyzing the time of topology optimization and whether it was necessary to further carry out the static calculation. However, the topology simulation still needs further calculation to compare the time consumed. It could be seen that after the 0.7 mm mesh size, the time consumed reached as many as hundreds of times. Meanwhile, the weight of the members was reduced after the analysis results of the static stress of the structure were obtained. It was only necessary to carry out a Boolean operation with the reinforced filling structure along the direction of the maximum stress after the shelling of the model.