## 3 Results
### Structure 1
#### 3.1.3 Advanced Case of Structure 1 with 12 Members-14 Nodes  
The applied loads on nodes for this meshing option can be seen in Table 5.  
The results of the analyses are shown in Table 6. From the table, optimization results of the linear analysis are closely compared with the first meshing option in Figure 4. The displacement results show a great match with the FEM results for the linear case. However, nonlinear analysis results are very different from this structure, especially for nonlinear cases as 1 and 3. Besides that, in this model, energies can be provided less than the first model. Similar behavior with the other meshing option is observed as expected for the comparison of linear and nonlinear cases. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**TPOMA**} & \multicolumn{3}{c}{**TPOMA**} & \multicolumn{3}{c}{**TPOMA**} & \multicolumn{3}{c}{**TPOMA**} \\ \multirow{2}{*}{\(\mathbf{v}\)} & \multicolumn{3}{c}{**(Linear)**} & \multicolumn{3}{c}{**(Nonlinear 1)**} & \multicolumn{3}{c}{**(Nonlinear 2)**} & \multicolumn{3}{c}{**(Nonlinear 3)**} \\ \cline{2-10}  & **Node** & \begin{tabular}{c} **\(\Delta\mathbf{x}\)** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **\(\Delta\mathbf{y}\)** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **\(\Delta\mathbf{x}\)** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **\(\Delta\mathbf{y}\)** \\ **(mm)** \\ \end{tabular} & \
\begin{tabular}{c} **\(\Delta\mathbf{x}\)** \\ **(mm)** \\ \end{tabular} &
\begin{tabular}{c} **\(\Delta\mathbf{y}\)** \\ **(mm)** \\ \end{tabular} \\ \hline \multirow{6}{*}{0.28} & 1 & 0.4681 & 0.0000 & 26.2344 & 0.0000 & 0.9362 & 0.0000 & 19.5071 & 0.0000 \\  & 2 & 0.4136 & 0.0000 & \(-15.5831\) & 0.0000 & 0.8273 & 0.0000 & 9.0151 & 0.0000 \\  & 3 & 0.3696 & 0.3696 & 88.4359 & 88.4359 & 0.7391 & 0.7391 & 29.2697 & 29.2697 \\  & 4 & 0.2895 & 0.2895 & 82.5355 & 82.5355 & 0.5791 & 0.5791 & 27.1497 & 27.1497 \\  & 5 & 0.0000 & 0.4681 & 0.0000 & 26.2344 & 0.0000 & 0.9362 & 0.0000 & 19.5071 \\  & 6 & 0.0000 & 0.4136 & 0.0000 & \(-15.5831\) & 0.0000 & 0.8273 & 0.0000 & 9.0151 \\ \cline{2-10}  & \(\Pi\)p (Nmm) & \(-7583.2397\) & \(-118167986.0712\) & \(-15.166.4795\) & \(-699.183.7821\) \\ \hline \multirow{6}{*}{0.29} & 1 & 0.4667 & 0.0000 & 26.8047 & 0.0000 & 0.9334 & 0.0000 & 19.0866 & 0.0000 \\  & 2 & 0.4101 & 0.0000 & \(-16.1982\) & 0.0000 & 0.8202 & 0.0000 & 8.1306 & 0.0000 \\  & 3 & 0.3695 & 0.3695 & 91.4805 & 91.4805 & 0.7390 & 0.7390 & 0.2294 & 30.2294 \\  & 4 & 0.2869 & 0.2869 & 85.2366 & 85.2366 & 0.5739 & 0.5739 & 27.9006 & 27.9006 \\  & 5 & 0.0000 & 0.4667 & 0.0000 & 26.8047 & 0.0000 & 0.9334 & 0.0000 & 19.0866 \\  & 6 & 0.0000 & 0.4101 & 0.0000 & \(-16.1982\) & 0.0000 & 0.8202 & 0.0000 & 8.1306 \\ \cline{2-10}  & \(\Pi\)p (Nmm) & \(-7571.4371\) & \(-137.625581.0665\) & \(-15.142.8743\) & \(-709.938.7099\) \\ \hline \multirow{6}{*}{0.30} & 1 & 0.4652 & 0.0000 & 27.3819 & 0.0000 & 0.9304 & 0.0000 & 18.7847 & 0.0000 \\  & 2 & 0.4064 & 0.0000 & \(-16.8072\) & 0.0000 & 0.8128 & 0.0000 & 7.3561 & 0.0000 \\  & 3 & 0.3694 & 0.3694 & 94.5115 & 94.5115 & 0.7387 & 0.7387 & 31.1627 & 31.1627 \\ \cline{1-1}  & 4 & 0.2843 & 0.2843 & 87.9316 & 87.9316 & 0.5686 & 0.5686 & 28.6625 & 28.6625 \\ \cline{1-1}  & 5 & 0.0000 & 0.4652 & 0.0000 & 27.3819 & 0.0000 & 0.9304 & 0.0000 & 18.7847 \\ \cline{1-1}  & 6 & 0.0000 & 0.4064 & 0.0000 & \(-16.8072\) & 0.0000 & 0.8128 & 0.0000 & 7.3561 \\ \cline{1-1} \cline{2-10}  & \(\Pi\)p (Nmm) & \(-7558.4473\) & \(-159.977948.1027\) & \(-15.116.8946\) & \(-721.624.5843\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{3}{c}{**Concentrated Loads (N)**} \\ \hline
**Node** & \ \begin{tabular}{c} **x Direction** \\ \end{tabular}  & \begin{tabular}{c} **y Direction** \\ \end{tabular}