## 4 Optimal Design of Element Section Based on Structural Robustness
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \begin{tabular}{c} **Elements** \\ \end{tabular} & \begin{tabular}{c} _Section Area_ \\ \end{tabular} & \begin{tabular}{c} _0.4 A_ \\ \end{tabular} & \begin{tabular}{c} _0.6 A_ \\ \end{tabular} & \begin{tabular}{c} _0.8 A_ \\ \end{tabular} & \begin{tabular}{c} _1.0 A_ \\ \end{tabular} & \begin{tabular}{c} _1.2 A_ \\ \end{tabular} & \
\begin{tabular}{c} _1.4 A_ \\ \end{tabular} &
\begin{tabular}{c} _1.6 A_ \\ \end{tabular} \\ \hline \multirow{2}{*}{DC1} & \(I_{R}\) & 4.470 & 4.060 & 3.837 & 3.697 & 3.601 & 3.530 & 3.477 \\  & \((I_{R}-I_{R0})/I_{R0}\) & 20.9\% & 9.8\% & 3.8\% & 0\% & \(-2.6\%\) & \(-4.5\%\) & \(-6.0\%\) \\  & \(I_{R}\) & 4.058 & 3.860 & 3.759 & 3.697 & 3.655 & 3.625 & 3.603 \\  & \((I_{R}-I_{R0})/I_{R0}\) & 9.8\% & 4.4\% & 1.7\% & 0\% & \(-1.1\%\) & \(-1.9\%\) & \(-2.5\%\) \\  & \(I_{R}\) & 3.660 & 3.679 & 3.690 & 3.697 & 3.702 & 3.706 & 3.708 \\  & \((I_{R}-I_{R0})/I_{R0}\) & \(-1.0\%\) & \(-0.5\%\) & \(-0.2\%\) & 0\% & 0.1\% & 0.2\% & 0.3\% \\  & \(I_{R}\) & 3.864 & 3.783 & 3.732 & 3.697 & 3.672 & 3.652 & 3.636 \\  & \((I_{R}-I_{R0})/I_{R0}\) & 4.5\% & 2.3\% & 0.9\% & 0\% & \(-0.7\%\) & \(-1.2\%\) & \(-1.6\%\) \\  & \(I_{R}\) & 4.338 & 4.013 & 3.823 & 3.697 & 3.608 & 3.542 & 3.491 \\  & \((I_{R}-I_{R0})/I_{R0}\) & 17.3\% & 8.5\% & 3.4\% & 0\% & \(-2.4\%\) & \(-4.2\%\) & \(-5.6\%\) \\  & \(I_{R}\) & 4.735 & 4.209 & 3.901 & 3.697 & 3.553 & 3.445 & 3.361 \\  & \((I_{R}-I_{R0})/I_{R0}\) & 28.1\% & 13.8\% & 5.5\% & 0\% & \(-3.9\%\) & \(-6.8\%\) & \(-9.1\%\) \\  & \(I_{R}\) & 3.712 & 3.704 & 3.700 & 3.697 & 3.696 & 3.694 & 3.693 \\  & \((I_{R}-I_{R0})/I_{R0}\) & 0.4\% & 0.2\% & 0.1\% & 0\% & 0\% & \(-0.1\%\) & \(-0.1\%\) \\  & \(I_{R}\) & 3.699 & 3.698 & 3.697 & 3.697 & 3.697 & 3.697 & 3.697 \\  & \((I_{R}-I_{R0})/I_{R0}\) & 0.1\% & 0\% & 0\% & 0\% & 0\% & 0\% & 0\% \\  & \(I_{R}\) & 3.697 & 3.697 & 3.697 & 3.697 & 3.697 & 3.698 & 3.698 \\  & \((I_{R}-I_{R0})/I_{R0}\) & 0\% & 0\% & 0\% & 0\% & 0\% & 0\% & 0\% \\  & \(I_{R}\) & 5.045 & 4.356 & 3.958 & 3.697 & 3.512 & 3.373 & 3.265 \\  & \((I_{R}-I_{R0})/I_{R0}\) & 36.5\% & 17.8\% & 7.1\% & 0\% & \(-5.3\%\) & \(-8.8\%\) & \(-11.7\%\) \\  & \(I_{R}\) & 3.975 & 3.823 & 3.745 & 3.697 & 3.665 & 3.642 & 3.625 \\  & \((I_{R}-I_{R0})/I_{R0}\) & 7.5\% & 3.4\% & 1.3\% & 0\% & \(-0.9\%\) & \(-1.5\%\) & \(-1.9\%\) \\  & \(I_{R}\) & 3.861 & 3.771 & 3.725 & 3.697 & 3.678 & 3.665 & 3.655 \\  & \((I_{R}-I_{R0})/I_{R0}\) & 4.4\% & 2.0\% & 0.8\% & 0\% & \(-0.5\%\) & \(-0.9\%\) & \(-1.1\%\) \\  & \(I_{R}\) & 3.696 & 3.696 & 3.697 & 3.697 & 3.697 & 3.698 & 3.698 \\  & \((I_{R}-I_{R0})/I_{R0}\) & 0\% & 0\% & 0\% & 0\% & 0\% & 0\% & 0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Structural robustness indicator under various section-area of each kind of elements. 4. Steps (2)-(3) were repeated for cyclic iterative calculation, the best individual of the offspring was extracted until the optimal value of robustness was obtained. The most optimal algorithm for structural robustness was explored and the optimal section layout within a controlled sectional scope of all kinds of elements was searched with the goal of minimizing structural quality. Meanwhile, the structural robustness indicator being less than that of the initial structure was ensured, that is, the structural robustness should remain more superior than that of the initial structure, the mathematical optimization model could be expressed as Equation (21). \[\left\{ \begin{array}{c}\underset{A}{minM}\ =\ \underset{i=1}{\overset{13}{\sum}} \rho L_{i}A_{i}\\ s.t.\ I_{R}\ \leq\ I_{R0}\\ A_{imin}\ \leq\ A_{i}\ \leq A_{imax}\end{array} \right. \tag{21}\]  
In this formula, the change range of the element section area was to ensure that the stress of all kinds of elements under the combined action of conventional load and interference load did not exceed the material yield strength of the lower limit, and the upper limit was 2.5 times the area of each element of the initial structure model.