Eigenvalue analysis

Please note that Buckling is the load case used for Eigenvalue analysis.

Eigenvalue analysis predicts the theoretical buckling strength of a structure idealized as elastic. In the classic Eigenvalue method, structural eigenvalues are computed from the loading conditions and constraints of a given system. For a basic structural configuration, tabulated solutions provide buckling loads. Each load has an associated buckled mode shape which represents the shape a structure assumes when buckled. In a real structure, imperfections and nonlinear behavior keep the system from achieving this theoretical buckling strength, leading Eigenvalue analysis to over-predict buckling load. Nonlinear buckling analysis is therefore recommended.

Nonlinear buckling analysis

Please note that Static, Nonlinear with P-Delta and Large Displacements is the load case for Nonlinear buckling analysis.

Nonlinear buckling analysis provides greater accuracy by incrementally increasing load application until a structure becomes unstable. This condition of instability is indicated when a small increase in load level causes a very large change in displacement. Nonlinear buckling analysis is a static method which accounts for material and geometric nonlinearities (P-Δ and P-δ), load perturbations, geometric imperfections, and gaps. Either a small destabilizing load or an initial imperfection is necessary to initiate the solution of a desired buckling mode.

Important considerations

• The primary output of linear buckling analysis is a set of buckling factors. The applied loading condition is multiplied by these factors such that loading is scaled to a point which induces buckling. Please refer to the
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  Analysis Reference Manual (Linear Buckling Analysis, page 315) for additional information.

• Since the deflections, forces, and reactions of linear buckling analysis correspond to the normalized buckled shape of a structure, users must run Nonlinear buckling analysis to obtain the actual displacements, forces, and reactions. Figure 1 illustrates the Nonlinear-buckling-analysis output of a column subjected to an initial imperfection where lateral load induces displacement equal to 0.6% of column height. Softening behavior indicates the onset of buckling.

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Users may download the analytical model for this system through the P-Delta effect for fixed cantilever column test problem.

See Also

• Nonlinear buckling