## 5 Simulation Experimental Results and Discussions
### Range and Variance Analyses  
The results of the FEA reflect the range of indicator test values when varying the factor levels, as indicated by the R range. This range represents the difference between the maximum and minimum values of the average indicator test values for each level, as presented in the following formula:  
\[R=\max\{k_{m}\}-\min\{k_{m}\}\quad m=1,2,\ldots,l \tag{11}\]  
where \(m\) represents the factor level number and \(k_{\rm m}\) denotes the average test value related to level \(m\), which is evaluated by  
\[k_{m}=\frac{K_{m}}{s} \tag{12}\]  
in which \(K_{\rm m}\) is the sum of the test values corresponding to level \(m\) on any column and \(s\) denotes the number of times each level appears on any column. The R-value can help determine the primary and secondary factors affecting the test indicators, where a larger \(R\) indicates a greater influence of that factor on the test indicators. A trend chart, in which the factor level is plotted on the horizontal axis and the \(k_{\rm m}\) values on the vertical axis, can provide a more intuitive understanding of the primary and secondary factors. Variance analysis is an effective statistical test for experimental data. It determines the extent to which each factor affects the test indicators by calculating the sum of the squared deviations (\(SS_{T}\)) and the F-test value. More specifically, \(SS_{T}\) represents the total variance of the indicator test values from the overall mean, reflecting the total discrepancy between the test results. Mathematically, it is formulated as  
\[SS_{T}=\sum_{m=1}^{l}\sum_{g=1}^{t_{m}}\left(y_{mg}-\overline{y}\right)^{2} \tag{13}\]  
where \(t_{m}\) denotes the number of experiments at factor level \(m,y_{mg}\) represents the test result for the \(g\)-th experiment at factor level \(m\), \(\overline{y}=\frac{1}{l}\sum\limits_{m=1}^{l}t_{m}\overline{y}_{m}\) signifies the arithmetic average \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Mesh**} & \multirow{2}{*}{**No.**} & \multicolumn{2}{c}{**Factor Level**} & \multirow{2}{*}{**Compliance**} & \multirow{2}{*}{**Maximum**} & \multirow{2}{*}{**Number of**} & \multirow{2}{*}{**Computation**} & \multirow{2}{*}{**Weight Reduction**} \\
**Type** & & **C** & **D** & **E** & **(m) \(\times\) 10\({}^{4}\))** & & & & \\ \hline \multirow{8}{*}{Hexahedral} & 1 & 1.75 & 4.80 & 4.00 & 6.94 & 896.2 & 36 & 1166 & 20.95 \\  & 2 & 1.75 & 5.00 & 3.50 & 6.95 & 1095.7 & 37 & 1195 & 22.38 \\  & 3 & 1.75 & 4.60 & 3.00 & 6.94 & 1055.3 & 37 & 1189 & 22.38 \\  & 4 & 2.00 & 5.00 & 4.00 & 7.02 & 975.2 & 35 & 931 & 22.35 \\  & 5 & 2.00 & 4.80 & 3.00 & 6.94 & 959.6 & 38 & 900 & 21.31 \\  & 6 & 2.00 & 4.60 & 3.50 & 7.00 & 915.7 & 36 & 862 & 20.94 \\  & 7 & 2.50 & 5.00 & 3.00 & 7.00 & 957.7 & 38 & 460 & 20.64 \\  & 8 & 2.50 & 4.60 & 4.00 & 7.03 & 986.7 & 35 & 447 & 21.77 \\  & 9 & 2.50 & 4.80 & 3.50 & 7.04 & 948.8 & 36 & 442 & 23.46 \\ \hline \multirow{8}{*}{ Tetrahedral} & 1 & 3.5 & 6.0 & 3.0 & 6.88 & 1108.4 & 40 & 1232 & 21.03 \\  & 2 & 3.5 & 5.2 & 2.5 & 6.87 & 1080.9 & 49 & 1490 & 21.18 \\  & 3 & 3.5 & 5.6 & 3.5 & 6.87 & 998.5 & 38 & 1164 & 22.22 \\  & 4 & 4.0 & 5.2 & 3.0 & 6.86 & 928.0 & 40 & 1070 & 20.29 \\  & 5 & 4.0 & 6.0 & 3.5 & 6.91 & 969.8 & 37 & 837 & 20.36 \\  & 6 & 4.0 & 5.6 & 2.5 & 6.86 & 975.1 & 46 & 1017 & 21.24 \\  & 7 & 4.5 & 5.2 & 3.5 & 6.90 & 963.1 & 38 & 580 & 19.98 \\  & 8 & 4.5 & 6.0 & 2.5 & 6.90 & 972.7 & 46 & 699 & 20.18 \\  & 9 & 4.5 & 5.6 & 3.0 & 6.89 & 924.5 & 39 & 595 & 20.79 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: FEA results of the geometric reconstruction obtained from orthogonal experiments. of all test results, and \(\overline{y}_{m}=\frac{1}{I_{m}}\sum\limits_{g=1}^{I_{m}}y_{mg}\) denotes the arithmetic average of all test results at factor level \(m\). In addition, we need to define a statistical quantity for factors, that is, the so-called F\({}_{fac}\).