How can you perform an aircraft structure buckling analysis?

1 FEM basics

FEM is a numerical technique that divides a complex structure into smaller and simpler elements, such as beams, plates, shells, or solids. Each element has a set of nodes that connect to other elements and define the geometry and displacement of the structure. By applying the material properties, boundary conditions, and load cases to the elements, you can solve a system of equations that gives you the stress, strain, and displacement of the structure. FEM is widely used for structural analysis because it can handle complex geometries, nonlinearities, and multiple load cases.

4 Nonlinear buckling analysis

Nonlinear buckling analysis is a more advanced and realistic type of buckling analysis. It accounts for the nonlinear behavior of the structure, such as material plasticity, geometric nonlinearity, contact, or large deformations. Nonlinear buckling analysis simulates the actual load-displacement response of the structure and determines the load at which the structure loses its equilibrium or stability. Nonlinear buckling analysis can also capture the post-buckling behavior of the structure, such as snap-through, snap-back, or progressive collapse. Nonlinear buckling analysis is more accurate and reliable than linear buckling analysis, but it is also more complex and computationally intensive.

5 Meshing and convergence

Meshing and convergence are two important aspects of any FEM analysis, especially for buckling analysis. Meshing is the process of creating the elements and nodes that represent the structure. The quality and size of the mesh affect the accuracy and efficiency of the analysis. A good mesh should have well-shaped elements, smooth transitions, and adequate refinement in regions of high stress or curvature. Convergence is the process of verifying that the results of the analysis are independent of the mesh size. A converged solution means that the results do not change significantly when the mesh is refined or coarsened. To achieve convergence, you should perform a mesh sensitivity study and compare the results for different mesh sizes.

6 Tips and tricks

To improve your buckling analysis and avoid common pitfalls, you should use appropriate material models and properties for your structure, such as a stress-strain curve that reflects the material behavior beyond the elastic limit. Additionally, you should apply realistic boundary conditions and load cases to your structure. For example, consider symmetry or anti-symmetry conditions to reduce the model size and complexity, or use load factors or ramp functions to control the load increment and convergence. Afterward, it is important to check the results for physical and numerical validity. This includes examining the stress distribution, deformation pattern, reaction forces, eigenvalues, eigenvectors, and load-displacement curves for any anomalies or errors. Finally, post-processing tools and techniques can help visualize and interpret the results. This includes contour plots, animations, mode shapes, graphs, tables, and reports to compare and summarize the results.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?