Buckling loads are critical loads under which the structure becomes unstable. There are two primary means to perform a buckling analysis, eigenvalue analysis and nonlinear buckling analysis.

Eigenvalue Analysis (load case type "Buckling")

Eigenvalue buckling analysis predicts the theoretical buckling strength of an ideal elastic structure. It computes the structural eigenvalues for the given system, its loading and constraints. This is known as classical Euler buckling analysis. Buckling loads for basic structural configurations are readily available from tabulated solutions. Each load has an associated buckled mode shape; this is the shape that the structure assumes in a buckled condition. However, in real-life, structural imperfections and non-linearities prevent most real-world structures from reaching their eigenvalue predicted buckling strength; in other words, the eigenvalue analysis over-predicts the expected buckling loads. A more realistic, nonlinear buckling analysis is therefore recommended to analyze real-world structures for buckling.

Nonlinear Buckling Analysis (load case type "Static", Nonlinear with P-Delta and Large Displacements)

Nonlinear buckling analysis is more accurate than eigenvalue analysis because it employs non-linear, large-deflection, static analysis to predict buckling loads. Its mode of operation is very simple: it gradually increases the applied load until a load level is found whereby the structure becomes unstable (ie. suddenly a very small increase in the load will cause very large deflections). The true non-linear nature of this analysis thus permits the modeling of geometric imperfections, load perturbations, material nonlinearities and gaps. For this type of analysis, that small destabilizing loads or initial imperfections are necessary to initiate the desired buckling mode.

Important Considerations

(1) The primary output from linear buckling analysis is a set of buckling factors. These buckling factors are scale factors that must multiply the applied loads to cause buckling in a given model. Please refer to CSI Analysis Reference Manual, chapter "Load Cases", section "Linear Buckling Analysis" for additional information.

(2) Since the deflections, forces and reactions for linear buckling analysis correspond to normalized buckled shape of the structure, you would need to run nonlinear buckling analysis to obtain the actual displacements, forces and reactions for your structure. The screenshot below illustrates output from nonlinear buckling analysis of a column with initial imperfections. You will notice a softening of the structure that would indicate an onset of buckling.

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See also

• post-buckling

...

Buckling occurs physically when a structure becomes unstable under a given loading configuration, and mathematically when a bifurcation occurs in the solution to equations of static equilibrium. The two primary means for performing buckling analysis include Eigenvalue and Nonlinear buckling analyses. Buckling must be explicitly evaluated for each set of loads considered because, unlike natural frequencies, buckling modes are dependent upon a given load pattern. When evaluating buckling, any number of load cases may be defined, each of which should specify loading, convergence tolerance, and the number of modes to be found. Since the first few buckling modes may have similar factors, we recommend finding a minimum of six modes.

Additional information is available in the CSI Analysis Reference Manual (Chapter XVII Load Cases, Linear Buckling Analysis).

Attribution

• [1] – Photo by SSMG, Univeristy of Trento, Italy, December 12, 2011 - Retrieved from Wikimedia Commons under Creative Commons CC BY 3.0 licensing.

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