# Static Strength and Buckling Analysis of an Aircraft Support
## 5 Buckling Analysis
### Nonlinear Buckling Analysis  
The load-bearing components of aircraft are mostly composed of alloy metals with light weight and high strength. Under the load of more than a certain level, the components will undergo nonlinear deformation, which will produce plastic deformation. Due to the use and design factors of different component structures, structural instability may occur under loads less than this level, namely buckling. Nonlinear buckling analysis of the research object is considered. Nonlinear buckling analysis has created a step in Abaqus, and the procedure type of Buckle is used. By means of the first-order buckling mode and critical load obtained in the eigenvalue buckling calculation, the nonlinear buckling load is set to 464.9 KN. The Riks arc length method is used for nonlinear buckling analysis. The initial arc length is 0.01 mm, the maximum arc length is 0.1 mm, the minimum arc length is 0.001 mm, and the maximum number of iterations, with a total arc length of 1 mm, is 1000. Influence of geometric defects on the stability of the bearing assembly is considered. The 1% and 10% of the average thickness are taken as the initial imperfection values, respectively. The measured thickness of the bearing assembly is shown in Table 4. The nonlinear buckling of the bearing assembly, under no imperfection and initial imperfection, is calculated. After solving, the load-displacement curve on the main bearing surface is obtained as Figure 13. The critical load of nonlinear buckling without imperfection is 110.6 KN, the critical load of 1% initial imperfection is 108.4 KN, and the critical load of 10% initial imperfection is 106.2 KN. The critical load of nonlinear buckling under three conditions is only about 1/4 of the critical load of eigenvalue buckling, which shows that nonlinear buckling is more realistic than linear eigenvalue buckling. The three load values are not much different, indicating that the geometric defects of the bearing assembly are not obvious for nonlinear buckling and have certain structural stability. \begin{table}
\begin{tabular}{c c c c c} \hline  & \(\mathbf{D_{min}}\) (mm) & \(\mathbf{D_{max}}\) (mm) & \(\mathbf{D_{mid}}\) (mm) & \(\mathbf{D_{m}}\) (mm) \\ \hline
1 & 3.411 & 17.723 & 5.002 & 4.979 \\
2 & 3.396 & 17.704 & 5.037 & 5.011 \\
3 & 3.421 & 17.733 & 4.994 & 4.882 \\ mean value & 3.409 & 17.720 & 5.011 & 4.957 \\ \hline \end{tabular}
\end{table} 
Table 4: The measured thickness of the bearing assembly. Figure 12: Eigenvalue buckling modes. In the absence of disturbance, when the load in the load-bearing area of the load-bearing assembly reaches the critical load of nonlinear buckling, the displacement and deformation in the load-bearing area is 21.4 mm, and the corresponding stress situation is shown in Figure 14. The stress range on the load-bearing surface is 292.4-467.8 Mpa, which is less than the yield strength of the material; the stress in some areas reaches 701.7 Mpa, which exceeds the tensile strength of the material. At this time, the structure gradually loses stability. Since then, under the continuous load, the bearing capacity of the bearing area has decreased significantly, and the structure has entered the unstable state, which shows that it is necessary to consider the nonlinear buckling analysis. The stress curves of five nodes are extracted from the bearing surface area, and the node position is shown in Figure 15. The stress curves of nodes A to E are shown in Figure 16. Before reaching the critical load, the stress amplitude of nodes A, B, and C rises rapidly, and then, the stress level of the three points remains roughly unchanged. The stress of node E and node D increases with the load, and the stress at node D rises faster.