# Sketch-Guided Topology Optimization with Enhanced Diversity for Innovative Structural Design
## 4 Experiments  
### Experiment Settings  
This paper uses the innovative design of automotive wheels as a case study to validate the proposed multi-solution TO framework. The focus of the design is the disk-view 2D structural pattern of the spokes, which can be solved as a 2D structural TO problem. Typical design requirements for wheel hubs include being lightweight and having a high stiffness, using the structural yield (compliance) under specific static loading conditions as the stiffness metric. Accordingly, the TO problem is to minimize compliance under the total material volume constraint. Since the design of automotive wheels also requires aesthetic considerations, a balance between structural performance and aesthetics is desired, making this case highly suitable for validating the TO framework, aiming at enhancing solution diversity and human controllability.  
Specific definitions of the design field and boundary conditions are shown in Figure 2. Structural compliance under both normal force and shear force is used as the stiffness metric. The normal force simulates the weight of the vehicle and wheel hub itself. It distributes on the outer rim within a 30\({}^{\circ}\) central angle range. The shear force simulates the ground friction force on the wheel, acting at the midpoint of the normal force distribution. Within a square domain, density values are set as 1 (solid) for the wheel rim and axleregions, variable (actual design field) for the spoke region, and 0 (void) for the other region. A fixation constraint is applied at the center of the axle.  
The rotational symmetry of the wheel spoke is handled explicitly: the annulus design field is evenly split into several fan units, with one (e.g., the topmost) designated as the reference unit. After sampling grid points for density computation, the points outside the reference unit are mapped to their central symmetric counterparts inside the reference unit, based on angular intervals defined by the fan angle. The counterparts are then taken as the actual input to the density function.  
The content of this section illustrates the following: (1) an experiment for generating innovative structural designs by the TO framework; (2) an experiment for human controllability; (3) an analysis of the impacts of human control on both the design quality and diversity; (4) a comparative analysis with existing methods; and (5) an analysis of adaptive-scale parallel computing. The first experiment is used to verify the ability of the proposed method to enhance structural design exploration, and a qualitative evaluation of the generated results is conducted. The second experiment is used to verify that our method enables designers to control structural features precisely and flexibly. The third experiment is conducted to quantitatively analyze the impacts of human control parameters on design quality and diversity, in order to provide insights for designers to better fine-tune them. The fourth experiment is to verify the superiority of the proposed method over existing ones. The fifth experiment is to verify the usefulness of an adaptive scale in improving computing efficiency. Figure 3 gives a summary of the experiment design.  
Figure 3: Summary of experiment design.  
Figure 2: Definition of design field, boundary, and load conditions.