Eigenvalue analysis

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

Eigenvalue analysis predicts the theoretical buckling strength of a structure which is idealized as elastic. For a basic structural configuration, structural eigenvalues are computed from constraints and loading conditions. Buckling loads are then derived, each associated with a buckled mode shape which represents the shape a structure assumes under buckling. 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. Therefore, we recommend Nonlinear buckling analysis.

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 than elastic formulation. Applied loading incrementally increases until a small change in load level causes a large change in displacement. This condition indicates that a structure has become unstable. 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 CSI 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.

Figure 1 - Nonlinear buckling analysis of a column

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

See Also

Nonlinear buckling article

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