# Topology Optimization of Anisotropic Materials with Smooth Fiber Orientation
## 3 Numerical Results
### Analysis of Structural Stiffness and Fiber Continuity  
In this section, according to the boundary conditions set in Section 3.1, three schemes are used for optimization. Scheme (1) does not consider the fiber angle constraint and uses the traditional filtering method; scheme (2) considers the fiber angle constraint and uses the traditional filtering method; and scheme (3) considers the fiber angle constraint and uses the adaptive filtering method. Figure 7 shows the optimization results and data of each boundary condition under different schemes. The data are the overall structural compliance and the fiber continuity rate, which are represented by C and FCR, respectively. Among them, the compliance is the reciprocal of the stiffness, and the smaller the compliance, the greater  
Figure 6: Boundary conditions: (**a**) cantilever beam; (**b**) double-load cantilever beam; (**c**) double-hole cantilever beam; (**d**) bridge girder; (**e**) double-load bridge beam; (**f**) L-shaped beam. Figure 8: Comparison of the fiber continuity rates of different optimization schemes under different boundary conditions (a–f) Correspond to the six boundary conditions in Figure 6, respectively. Figure 9: Comparison of structural compliance of different optimization schemes under different boundary conditions (a–f) Correspond to the six boundary conditions in Figure 6, respectively. Figure 11: Trend of the fiber continuity rate of the double-load cantilever beam with different schemes. Figure 10: The optimization results of the double-load cantilever beam with different schemes correspond to the results of **(b-1-b-3)** in Figure 7, which shows a detailed analysis. Figure 12: Trend of structural compliance of the double-load cantilever beam with different schemes. Figure 13: The optimization results of different schemes are adopted for the bridge girder, corresponding to the results of (**d-1–d-3**) in Figure 7, which shows a detailed analysis. As shown in Figure 7, the six examples are analyzed from the data. The structural compliance of scheme (1) is small, but the fiber continuity rate is low. After considering the fiber angle constraint, that is, scheme (2), the fiber continuity rate is significantly improved, which can be maintained at about 98%, but the compliance is greatly increased; on the basis of considering the fiber angle constraint, the adaptive filter is introduced, that is, scheme (3). The fiber continuity rate is still maintained at about 98%, or even higher, and the structural compliance is also greatly reduced compared with scheme (2). This means that the concurrent optimization method combining the fiber angle constraint strategy and the adaptive filtering technology is effective. It not only improves the fiber continuity rate but also ensures the overall structural stiffness to a certain extent. Figure 8 intuitively shows the comparison of fiber continuity with different optimization schemes under different boundary conditions. After the fiber angle constraint, the fiber continuity rate increased significantly to about 98%. Furthermore, after introducing the adaptive filtering technology on the basis of the fiber angle constraint, the fiber continuity rate is still maintained at about 98% or even higher. Figure 9 intuitively shows the structural compliance comparison of different optimization schemes under different boundary conditions. After the fiber angle constraint, the compliance increases significantly, indicating that while improving fiber continuity, the overall structure's resistance to force decreases significantly, and the mechanical properties deteriorate. After the further introduction of adaptive filtering technology, we observed a significant decrease in structural compliance, which indicates that the mechanical properties have been improved to a certain extent. Although the compliance at this time is still slightly higher than the level in scheme (1), in the process of pursuing fiber continuity, the original optimal fiber angle distribution must be adjusted.