# The Stability of New Single-Layer Combined Lattice Shell Based on Aluminum Alloy Honeycomb Panels
## 3 Analysis of the Nonlinear Stability of NSCLS to Defects
### Experimental Verification of Random Defect Mode Method
#### 3.3.1 Results for Model A\({}_{1}\), the Defect-Free Lattice Shell Model with No Aluminum Plate  
During the analysis, the authors measured the cross-sectional dimensions at the middle and at both ends of all the aluminum alloy bars. The average of the three measured cross-sectional dimensions was used for finite element modeling. In analyzing the ultimate bearing capacity of the random defect mode, as per the relevant literature, the mean was \(\mu=0\) and the discrete coefficient was \(\mathrm{C_{d}}=0.423\) (the average of the statistical results of the three coordinate components). The cutoff limit of the maximum amplitude of the deviation was \(\mathrm{X_{t}}=1.4\) mm (\(1/1000\) of the model's span), the maximum correlation coefficient was \(\rho_{\mathrm{max}}=0.65\), and the number of random samples was N = 200. Figure 7a,b show the history and mean square deviation of the critical load samples for model A\({}_{1}\), respectively. The blue curve in the middle of Figure 7b plateaus after the number of samples N exceeds 100. This indicates that the mean and mean square deviation of the critical load samples stabilize after the number of samples N exceeds 100. The red curves on the upper and lower sides are the boundaries at the 95% confidence level. The area between the curves in the graph decreases in size, which indicates that the accuracy of the history curve increases. Therefore, selecting 100 samples in practical engineering makes it possible to meet the accuracy requirements under normal conditions. The calculated results are reliable. After using finite element analysis to analyze 200 samples with defects, we obtain a curve for the critical load samples (Figure 8a). Using the Gaussian method (if the random variable follows a Gaussian distribution, the probability distribution function is a straight line), we plot the probability distribution of the critical load samples (Figure 8b). The middle section of the blue curve is somewhat close to a straight line. We check that the critical load samples are normally distributed by evaluating the fit. The normal distribution assumption is acceptable at the 5% significance level. Figure 7: The mean and mean square deviation of the critical load samples for model A\({}_{1}\): (**a**) Mean; (**b**) Mean square deviation. The critical load samples are statistically analyzed and compared with the experimental results. The results are listed in Table 1. The critical loads \(\mathrm{P_{cr}}\) in the table are determined by following the \"3\(\sigma\)\" principle (i.e., a 99.87% guarantee rate). Figure 9 shows that, according to the random defect mode analysis of the lattice shell with no aluminum plate, the predicted theoretical failure pattern (Figure 9b) is very close to the experimental failure pattern (Figure 9a). \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \(\mathbf{P_{e}/N}\) & \(\mathbf{D_{max}/mm}\) & \(\mathbf{C_{d}}\) & \(\mathbf{P_{max}/N}\) & \(\mathbf{P_{min}/N}\) & \(\mathbf{P_{\mu}/N}\) & \(\mathbf{P_{\sigma}/N}\) & \(\mathbf{P_{cr}}\) \\ \hline
4879 & 1.4 & 0.423 & 5376 & 4617 & 4962 & 152 & 4506 \\ \hline \hline \end{tabular} In the table: \(\mathrm{P_{e}}\)—The test value of the critical load; \(\mathrm{D_{max}}\)—The maximum defect size; \(\mathrm{C_{d}}\)—The discrete coefficient; \(\mathrm{P_{max}}\)—The maximum of the critical load samples; \(\mathrm{P_{min}}\)—The minimum of the critical load samples; \(\mathrm{P_{\mu}}\)—The mean of the critical load samples; \(\mathrm{P_{\sigma}}\)—The mean square deviation of the critical load samples; \(\mathrm{P_{cr}}\)—The standard value of the critical load (3 times the mean square deviation is accounted for).  
\end{table} 
Table 1: Comparison of the results obtained using the random defect mode analysis and the measured values for \(\mathrm{A_{1}}\). Figure 8: History and probability distribution for the critical load of model \(\mathrm{A_{1}}\): (**a**) History; (**b**) Probability distribution according to the Gaussian method.