Eigenvalue
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analysis
Please note that Buckling is the load case used for Eigenvalue analysis.
Eigenvalue 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.
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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
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is the load case for Nonlinear buckling analysis.
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 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
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considerations
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The primary output
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of linear buckling analysis is a set of buckling factors.
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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
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(Linear Buckling Analysis
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, page 315) for additional information.
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- Since the deflections, forces, and reactions
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- of linear buckling analysis correspond to the normalized buckled shape of
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- a structure,
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- users must run Nonlinear buckling analysis to obtain the actual displacements, forces, and reactions
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- . Figure 1 illustrates the Nonlinear-buckling-analysis output of a column
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- subjected to an initial imperfection where lateral load induces displacement equal to 0.6% of
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- column height
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- . Softening behavior indicates the onset of buckling.
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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 page.
See
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Also
- post-Nonlinear buckling
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- article