# A Comparative Study of the Application of Different Commercial Software for Topology Optimization
## 4 Case Studies and Methodology  
Three well-known structures found in the literature were used in this paper as case studies--a bell crank lever, a pillow bracket, and a small bridge. A bell crank lever is a crank that is used in aircraft, automotive, and bicycles for transmitting motion between two parts meeting at an angle [174]. The arms of the used bell crank lever were 150 mm in length and 15 mm thick. A pair of 500 N bearing forces  
Figure 3: (**a**) Commercial vs. open source software, and (**b**) the availability of the different TO methods in software. were applied at the end of each arm while the crank lever was fixed on its 60 mm/80 mm fulcrum, as shown in Figure 4a. This case study is an ordinary TO with limited design space. In other words, the main design of the product was known from the beginning, but a material reduction was needed. A pillow bracket, 130 \(\times\) 52 \(\times\) 52 mm, was used as the second case study. The pillow bracket is a mechanical part designed to resist high bending forces [8]. The four holes of the bracket are fixed while a pair of 1000 N forces is applied to the hole on its top, as is depicted in Figure 4b. In this optimization case, the main design of the structure was also known; however, the number of the components in the final solution can be differentiated, as is presented in the results section. Finally, the last case study was a small bridge (2500 \(\times\) 500 \(\times\) 600 mm). The authors intended to use a bigger structure here for comparison reasons. The initial CAD of the bridge was a hollow box, which was fixed at two sections to the left and right, as presented in Figure 4c. Furthermore, a vertical force of 800 KN was applied at the inner bottom surface of the box. This example was an optimization problem where the structure's design space was increased significantly to let the optimization algorithm decide the final design. The expanded design space increased the flexibility of the algorithm, leading to new and better-optimized solutions, but also dramatically increased the optimization time [11]. The CAD models were first designed in SolidWorks. ANSYS Mechanical was used for both FEA at the pre-processing and post-processing steps with the validation of the optimized designs. It was crucial to use the same FEA software for comparison reasons. The TO was conducted in three different software platforms--SolidWorks, ANSYS Mechanical, and ABAQUS, with the same settings. The assigned material in all cases was a structural steel with the following properties: elastic modulus (E) = 210,000 MPa, Poisson's ratio (v) = 0.28, mass density (\(\rho\)) = 7700 Kg/m\({}^{3}\), and yield strength (\(\sigma_{y}\)) = 724 MPa. Both the bell crank lever and the pillow bracket were discretized to 3 mm tetrahedral elements, while 30 mm tetrahedral elements were used for the bridge. The element sizes were identified using mesh convergence studies in each CAD model. Figure 5 shows the results of the conducted studies by presenting No. of Elements-Max Von Mises Stress diagrams of five FEA with different element sizes for each model. The tested element sizes are written near the data points inside the diagrams. Figure 4: The three case studies: (**a**) bell crank lever, (**b**) pillow bracket, and (**c**) small bridge. Figure 5: The conducted mesh convergence studies: (**a**) bell crank lever, (**b**) pillow bracket, and (**c**) small bridge. The used TO method was the traditional compliance optimization with SIMP. A 50% weight reduction was used as a constraint for the first optimization case, while the lightest designs were identified for the second one for a factor of safety (FOS) \(\geq\) 1.2. Specific manufacturing constraints were used in each case study. An XY planar symmetry was used for the bell crank lever. Both XY and YX planar symmetries were used for the pillow bracket. The same planar symmetries were also used for the bridge together with a minimum size member of 100 mm.