# 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
#### 3.3.2 Analysis of the Combined Lattice Shell with Defects (Model B\({}_{2}\))  
In model B\({}_{2}\), the authors artificially set the geometric deviation of the node coordinates, i.e., we reduced the Z coordinate of the top of the model by 5.6 mm (1/250 of the combined lattice shell's span).  
As for model A\({}_{1}\), we conducted a finite element analysis of 200 samples using stochastic defects to obtain curves for the critical load samples and graphed the probability distributions of the critical load samples using the Gaussian method.  
The critical load sample were statistically analyzed and compared with the experimental results. The results are listed in Table 2. The critical load values P\({}_{\text{cr}}\) in the table were determined according to the \"3o\" principle (i.e., 99.87% guarantee rate).  
Figure 10 shows that, according to the random defect mode analysis of the combined lattice shell, the predicted theoretical failure pattern (Figure 10b) is very close to the experimental failure pattern (Figure 10a).  
Table 3 shows that the results of the finite element analysis of the aluminum alloy lattice shell model obtained using the random defect mode method are very close to the experimental values. In the finite element analysis, the mean critical load and three times the mean square deviation of the standard values are accounted for. The average error of the six models is 5.7%. This can be attributed to the small discrete coefficient and defect amplitude and to the use of a truncated normal distribution for the random defects (i.e., a truncated Gaussian distribution) in this paper. It is apparent that the testing load P\({}_{\text{e}}\) of the critical load is between P\({}_{\text{max}}\) and P\({}_{\text{min}}\).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**P\({}_{\text{e}}\)/N** & **D\({}_{\text{max}}\)/mm** & **C\({}_{\text{d}}\)** & **P\({}_{\text{max}}\)/N** & **P\({}_{\text{min}}\)/N** & **P\({}_{\text{n}}\)/N** & **P\({}_{\text{o}}\)/N** & **P\({}_{\text{cr}}\)** \\ \hline
5058 & 1.4 & 0.423 & 6210 & 3787 & 5256 & 220 & 4596 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of the results obtained from the random defect mode analysis and the measured values for B\({}_{2}\).  
Figure 10: Comparison of the failure modes of the combined lattice shell, model B\({}_{2}\): (**a**) Measured failure pattern; (**b**) Theoretical failure pattern.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model Configuration**} & \multicolumn{4}{c}{**Lattice Shell with No Plate**} & \multicolumn{4}{c}{**Combined Lattice Shell**} \\ \cline{2-7}  & **Experimental** & **Simulated** & **Error (\%)** & **Experimental** & **Simulated** & **Error (\%)** \\  & **Value (N)** & **Value (N)** & **Value (N)** & **Value (N)** & **Error (\%)** \\ \hline \hline \multirow{2}{*}{Without defects} & 4879 & \multirow{2}{*}{4506} & 7.6 & 5761 & \multirow{2}{*}{5947} & 3.2 \\  & 4601 & & 2.1 & 5556 & 5947 & 6.6 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of the critical load of the lattice shell with no plate and the combined lattice shell.