## 2 Materials and Methods
### Topology Optimization
The modified SIMP approach offers several advantages over the classical SIMP formulation, including independency between the minimum values of the materials' elastic modulus and superior penalization power [22]. However, topological optimization methods are likely to encounter numerical difficulties, such as mesh dependency, checkerboard patterns, and local minima [23]. To mitigate such issues, researchers have proposed the use of regularization techniques [24]. One of the most common approaches is the use of density filters [25]. On the other hand, the compliance function in the level-set method relies on the response type or constraint. Static structural analysis supports a combination of force-based and displacement-based loading, as well as thermal loading. The compliance function can be described as follows:  
\[ \begin{split} J(\Omega)&=\frac{1}{2}\left[\int_{ \Omega}A\left(e(u)-e^{th}\right):e^{th}dx+\int_{\Omega}f*udx+\int_{\Gamma_{N}}g* uds+\int_{\Gamma_{x}}\lambda_{u}*u_{0}ds\right]\\ &\quad=\left[-\frac{1}{2}\int_{\Omega}A\left(e(u)-e^{th}\right): \left(e(u)-e^{th}\right)dx+\int_{\Omega}f*udx+\int_{\Gamma_{N}}g*uds\right] \end{split}  \tag{3}\]  
where \(e(u)=\frac{1}{2}\left(\
abla u+(\
abla u)^{t}\right)\) is the total strain vector, \(e^{th}\) is the thermal strain vector, \(\left(e(u)-e^{th}\right)\) is the elastic strain vector, \(\sigma(u)=A\left(e(u)-e^{th}\right)\) is the stress vector, \((f,g)\) are the external loads, and \((\lambda_{u},u_{0})\) are the reaction force and the prescribed displacement, respectively. These formulas are equivalent and based on the potential energy. Compliance is a self-adjoint response, meaning that no adjoint problem needs to be solved, as compliance is always computed over the whole model [26]. Topological optimization is usually done by creating geometry that only considers the constraints of the part ranging from the supports to the vacant area that the body can move around in within the assembly. However, since that part has almost no space within the assembly, the original geometry has been considered in this study with a slight modification to simplify the calculations and some fitment issues, where the radius at the tip of the thumb does not perfectly match when attaching it to the main assembly. Results of topology optimization by SIMP and level-set methods are presented in Figure 5.  
For comparison, ANSYS Discovery Live software was also used to get a topologically optimized design. The geometry obtained for the final volume reduction of 63% is very similar as that from the level-set method applied in ANSYS Workbench. The main benefit of ANSYS Discovery Live is its speed and the smoother resulting shape, as visible in Figure 6a. Verification of the design was performed in ANSYS Workbench, leading to 214.2 MPa von Mises stress (232.3 MPa in ANSYS Discovery Live, as shown in Figure 6a), which is comparable with the 221.5 MPa von Mises stress obtained for the original design  
Figure 5: Resulting mesh and von Mises stress contours from the solid isotropic material with penalization (SIMP) method (**a**) and resulting mesh and von Mises stress contours from level-set method (**b**). (see Figure 4b). It is important to mention that a total force of 5000 N had to be applied on two facets in contrast to ANSYS Workbench analysis because there is no appropriate symmetry condition. The only one weak part is that between both used facets, which had to be stiffened in the validation analysis using ANSYS Workbench (see Figure 6b).