# Topology Optimization and Testing of Connecting Rod Based on Static and Dynamic Analyses
## 3 Computational Analysis
### Topology Optimization  
ANSYS Discovery software uses the Solid Isotropic Material with Penalization (SIMP) method. During the iteration process, the ANSYS Discovery solver adjusts the material density, (\(\rho\)) from 0 (\(\rho\)) to 1 within the permissible area outside the protected depth. Herein, if the material density (\(\rho\)) is equal to 1, it represents full material density, and if the (\(\rho\)) is equal to 0, it represents zero material density [20]. There are several options for the TO process in ANSYS Discovery, i.e., optimizing for the strength or response to free vibration,  
Figure 4: (**a**) Boundary conditions applied during the static structural analysis in the initial design. (**b**) Mesh properties used during the static structural analysis in the initial design.  
optimizing for a specified frequency, optimizing to minimize stress, and optimizing to minimize volume [21].  
\[(\rho)=\rho^{p}\times K \tag{6}\]  
where \(K\) denotes the real stiffness matrix of an element, and \(p\) denotes the factor of penalization [14; 22].  
The following targets were outlined for the TO process:  
* To reduce the mass at least by 3%;
* To reduce the maximum von Mises stress and von Mises strain;
* To define the protected depths at both ends of the connecting rod;
* To maintain major dimensions;
* To obtain a different cross-section than the I-Section;
* To keep the FOS above 2.5;
* To manufacture the component in both additive manufacturing and conventional forging.  
In this research, minimizing stress was set as the objective of the TO process. While setting the boundary conditions, the same conditions were used as in the static structural analysis, and by defining the protected depths of 0.012 m on both ends of the connecting rod, the TO process could be carried out as shown in Figure 5[23]. The TO process was carried out at various target percentages from 3% to 5% to reduce the mass of the existing design [24].  
Two of the important factors influencing the optimization process were the quality of the mesh and the number of elements. Once the topology was achieved, facets were created for that percentage of reduced mass, and we were required to clean up the facet design using the repair facet tool and subD hybrid option as shown in Figure 6, before exporting it as an STL or STEP file [25].  
The goal of the TO in this study was to minimize mass while ensuring structural integrity by controlling the von Mises stress.  
\[\min_{\rho}M(\rho)=\int\rho\;d\Omega \tag{7}\]  
where \(\rho\) is the material density function, \(M(\rho)\) is the total mass of the connecting rod, and \(\Omega\) denotes the design domain.  
\[\min_{\rho}\sigma_{max}(\rho) \tag{8}\]  
where \(\sigma_{max}\) is the maximum von Mises stress in the structure [26; 27].  
The connecting rod was subject to the following constraints.  
The optimized design had to ensure that von Mises stress did not exceed an allowable limit:  
\[\sigma_{max}(\rho)\leq\;\sigma_{allow} \tag{9}\]  
Figure 5: Protected depth of 0.012 m on both ends of the connecting rod.  
To ensure structural safety, the minimum FOS had to be maintained as the following:  
\[\text{FOS}=\frac{\sigma_{yield}}{\sigma_{max}}\ \geq\ 2.5 \tag{10}\]  
As a boundary condition, the big end of the connecting rod was fixed, and force was applied to the small end of the connecting rod [28].  
After solving the topology at various percentages on a trial-and-error basis, the results targeted at 4% mass reduction had a mass reduction of 5.66% with minimum von Mises stress compared to the targeted values of 3% and 5%. Figure 7a shows the original shape of the connecting rod, and Figure 7b shows the final optimized topology of the connecting rod with a 5.66% mass reduction and initial design.  
The obtained topology had a 5.66% reduction in mass from 654 g to 618 g.