## 4 Conclusions  
In this study, the aim was to enhance the structural performance of concrete-encased steel composite columns. To achieve this goal, the height of the steel profile used in the composite columns was increased. Topology optimization was employed to determine the optimal opening shapes within the steel profile, resulting in shapes resembling sinusoidal curves. These shapes were adapted for production purposes. Subsequently, a composite column experiment from existing literature was modeled to validate the accuracy of our nonlinear modeling. The load-displacement curves of the experimental and numerical models exhibited remarkable similarity, confirming the precision of our numerical model. Following this validation, a comparison was made between two composite columns: one utilizing a standard steel profile and the other incorporating the optimally designed steel profile. The study's findings are presented below:  
* To determine the optimal opening shape within the steel profile body, topology optimization was conducted, resulting in shapes resembling sinusoidal curves. The resulting shape was then adapted for production. \begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Composite Column with** & **Composite Column with** & \\  & **Standard HEB200** & **Optimally Designed Steel** & **Increase Amount (\%)** \\  & & **Profile** & \\ \hline Lateral load capacity (kN) & 491 & 586 & 19 \\ \hline Maximum lateral displacement (mm) & 67 & 71 & 6 \\ \hline Maximum stress in steel profile (MPa) & 272 & 288 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Analysis results of composite columns. Figure 15: Von [PERSON] stresses of the steel profile in the composite column before failure (unit: N/m\({}^{2}\)) (**a**) optimum designed steel profile (**b**) standard steel profile. * SOLID65 elements for modeling concrete, SOLID185 for steel profile, and LINK180 for reinforcement were employed in modeling the experiment. The behavior of confined concrete was considered using the Mander model. Additionally, the [PERSON] crack model was utilized to describe the nonlinear behavior of concrete, with coefficients of 0.15 for open crack shear load transmission and 0.90 for closed crack shear force transmission. The numerical analyses were validated with experimental results, demonstrating a very close match between the two. As a result, these design parameters can be confidently used for modeling concrete-encased steel composite columns. * As a result of the nonlinear analysis, it was observed that using the optimally designed steel profile in the composite column, instead of the standard steel profile, increased the load-carrying capacity of the composite column by approximately 19%. * It was observed that using the optimally designed steel profile in the composite column, instead of the standard steel profile, increased the ductility of the composite column and improved its energy absorption capacity by approximately 24%. Energy absorption capacity was obtained considering the area under load-displacement curves. * The failure of both composite columns was attributed to the rupture of longitudinal reinforcement. The standard steel profile reached a stress of 272 MPa before failure, while the optimally designed steel profile reached 288 MPa before failure. This indicates that the optimally designed steel profile performs more effectively. Manufacturing and welding operations of the optimally designed steel profile require additional cost and labor. However, the positive effect of increasing the height of the steel section on the composite column's performance is obvious. Improving the structural performance of the composite column was achieved with the same amount of material, highlighting the significance of optimal design. Future studies aim to further develop the sinusoidal-like opening shape using various metaheuristic algorithmic methods. Conceptualization, E.G.I. and F.M.O. ; methodology, E.G.I. and F.M.O. ; software, E.G.I. and F.M.O. ; validation, E.G.I. and F.M.O. ; formal analysis, E.G.I. and F.M.O.