## 4 Topology Optimization of Valve Motion Components Based on Thermal-Fluid-Mechanical Coupling
### Topology Optimization Design
#### 4.3.3 Optimization Calculations  
The iterative accuracy of the topology optimization calculation is 0.1%. By comparing the convergence curves of structural compliance, the optimization convergence under each mass retention rate \(u\) is judged. As shown in Figure 14, the iterative convergence curve of the objective function (i.e., structural compliance) is shown. The horizontal axis represents the number of iterations, and the vertical axis represents the optimization objective function of the valve motion components.  
As the number of iterations increases, the objective function decreases, and the structural compliance value decreases the fastest in steps 0 to 16 before gradually stabilizing from step 17. According to the mass retention rate \(u\) from large to small, the calculation results converge after 24, 22, 27, and 38 iterations of update, respectively, indicating that the stiffness of the valve motion assembly reaches the maximum under satisfying the mass constraint, at which time the unit density of the design area is the optimal force transmission path and material distribution of the valve motion components.  
The retention threshold is set to 0.5. Figures 15 and 16 show the optimization results of the valve motion components at each mass retention rate \(u\). The red part comprises the cells with density 0-0.4, which can be deleted, and the gray part consists of the cells with density 0.6-1, which should be retained.  
Figure 13: Topology optimization domain.  
Figure 16: Comparison of the effective area of material retention.  
Figure 14: Compliance convergence curves.  
Figure 15: Comparison of material removal areas.  
the center of the valve disc because of the large proportion of material removal. As a result, the force transmission path of the structure changes, the stress distribution of the structure also changes, and the structure redistributes units. Elements are added at places with high stress and deleted at places with low stress, and so there will be some ups and downs in the optimization process. When \(u=60\%\) and \(u=40\%\) are optimized, there are no intermittent and sudden changes in the structural force transmission path and stress distribution, and so the optimization process will be relatively stable and easier to converge.  
The materials that can be removed from the back of the valve disc, rocker and connection parts are clearly seen in Figure 15. When \(u\) is reduced, the original valve motion components' nut fixed connection parts have larger optimization spaces under each mass retention rate distribution, while a larger optimization area are generated in the back of the valve disc and rocker parts.  
Figure 16 shows the effective area of material retention. It can be seen that the front side of the valve has a similar optimization trend at each mass retention rate. Additionally, the material is reduced in a spherical shape, forming a spherical surface that reduces the mass and ensures the pressure tolerance. The incompleteness of the valve disc appears at \(u=30\%\), \(u=60\%\) has more topology optimization potential at the back of the valve disc and the connection area, and \(u=50\%\) also has more topological optimization potential at the connection area. In contrast, the optimized solution of \(u=40\%\) has a reasonable material distribution after optimization, which can effectively reduce the structural compliance but also smoothly and efficiently optimize the structure. Finally, the scheme with \(u=40\%\) is selected as the optimal optimization solution.