Linear Buckling Analysis

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ar Buckling Analysis

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inear Buckling Analysis

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ntroduction

inear buckling (also called as Eigenvalue buckling) analysis predicts the theoretical buckling strength of an ideal elasticructure. This method corresponds to the textbook approach to elastic buckling analysis: for instance, an eigenvalue bucklingnalysis of a column will match the classical Euler solution. However, imperfections and nonlinearities prevent most real-worructures from achieving their theoretical elastic buckling strength. Thus, linear buckling analysis often yields quick but non-onservative results.

a) Nonlinear load-deflection curve, (b) Linear (Eigenvalue) buckling curve

A more accurate approach to predicting instability is to perform a nonlinear buckling analysis. This involves a static structuralnalysis with large deflection effects turned on. A gradually increasing load is applied in this analysis to seek the load level at

which your structure becomes unstable. Using the nonlinear technique, your model can include features such as initial

mperfections, plastic behavior, gaps, and large-deflection response. In addition, using deflection-controlled loading, you can eack the post-buckled performance of your structure (which can be useful in cases where the structure buckles into a stableonfiguration, such as "snap-through" buckling of a shallow dome).

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oints to Remember

Linear buckling analysis must be preceded by a static structural analysis.

The results calculated by the linear buckling analysis are buckling load factors that scale the loads applied in the staticstructural analysis. Thus for example if you applied a 10 N compressive load on a structure in the static analysis and if th

linear buckling analysis calculates a load factor of 1500, then the predicted buckling load is 1500x10 = 15000 N. Becausof this it is typical to apply unit loads in the static analysis that precedes the buckling analysis.

The buckling load factor is to be applied to all the loads used in the static analysis.

A structure can have infinitely many buckling load factors. Each load factor is associated with a different instability pattTypically the lowest load factor is of interest.

Only linear behavior is valid. If your model includes contact connections, for example, their effects are calculated basedtheir status at the end of the static analysis.

Note that the load factors represent scaling factors for all loads. If certain loads are constant (for example, self-weightgravity loads) while other loads are variable (for example, externally applied loads), you need to take special steps to en

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Remember that a linear buckling analysis uses the model and connections from a linear static analysis. Only linearbehavior is valid in a linear buckling analysis. If your model includes contact regions, for example, the effect of thesecontact regions are calculated based on their status at the end of the static analysis.

Joints and springs are taken into account if they are present in the static analysis.

pply Mesh Controls/Preview Mesh

Basic general information about this topic

... for this analysis type:

There are no considerations specifically for a linear buckling analysis.

efine Analysis Type



Choose Linear Buckling as the New Analysis type.

stablish Analysis Settings



For linear buckling analysis the basic controls are:

Options for Modal, Harmonic, Linear Buckling, and Random Vibration Analyses: Number of Modes: You need tospecify the number of buckling load factors and corresponding buckling mode shapes of interest. Typically the first(lowest) buckling load factor is of interest.

Output Controls: By default only buckling load factors and corresponding buckling mode shapes are calculated. Youcan request Stress and Strain results to be calculated but note that stress results only show the relative distributionof stress in the structure and are not real stress values.

In Analysis Data Management, users can set the save ANSYS database and delete unneeded file settings.

efine Initial Condition



You must point to a static structural analysis of the same model in the initial condition environment.

Linear buckling analysis must be preceded by a static structural analysis.

If the static structural analysis has multiple result sets, the values from the last solve point are used as the basisfor the linear buckling analysis.

The results calculated by the linear buckling analysis are buckling load factors that scale the loads applied in thestatic structural analysis. Thus for example if you applied a 10 N compressive load on a structure in the staticanalysis and if the linear buckling analysis calculates a load factor of 1500, then the predicted buckling load is1500x10 = 15000 N. Because of this it is typical to apply unit loads in the static analysis that precedes thebuckling analysis.
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The buckling load factor is to be applied to all the loads used in the static analysis.

pply Loads and Supports



No loads are allowed in the linear buckling analysis. The supports as well as the stress state from the static structural

analysis are used in the linear buckling analysis.

Note

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If the static analysis has a pressure load applied normal to faces (3-D) or edges (2-D), this couldresult in an additional stiffness contribution called the pressure load stiffness effect. This effect playsa significant role in linear buckling analyses. This additional effect is computed during a buckling

analysis using the pressure value in the static analysis at time = 0. Because of this if the static analysisis to be used for a subsequent buckling analysis you should step apply any pressure loads in the staticanalysis.

Different buckling loads may be predicted from seemingly equivalent pressure and force loads in abuckling analysis because in Simulation a force and a pressure are not treated the same. As with anynumerical analysis, we recommend that you use the type of loading which best models the in-servicecomponent. For more information, see the Theory Reference for ANSYS and ANSYS Workbench, underStructures with Geometric Nonlinearities> Stress Stiffening> Pressure Load Stiffness.

olve



Solution Information continuously updates any listing output from the solver and provides valuable information onthe behavior of the structure during the analysis.

Review Results



You can view the buckling mode shape associated with a particular load factor by displaying a contour plot or byanimatingthe deformed mode shape. The contours represent relative displacement of the part.

Buckling mode shape displays are helpful in understanding how a part or an assembly deforms when buckling, but donot represent actual displacements.

Stresses from a modal analysis do not represent actual stresses in the structure, but give you an idea of the relativestress distributions for each mode. Stress andStrain results are available only if requested before solution usingOutput Controls.

reate Report (optional)
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There are no specific considerations for a linear buckling analysis.

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xample: Linear Buckling Analysis

he following example illustrates performing a linear buckling analysis in Simulation.

he model is a sheet body created in DesignModeler. Plate dimensions are 20 in by 10 in.

he objective of the analysis is to compute the critical buckling load of a simply supported plate subjected to a uniformlyistributed end load.

he model geometry was attached to Simulation and saved under the name Pl atebuckl e. dsdb.

1. Open the model in Simulation, establish units, and define a thickness of 0.125 in.

Open the file Pl atebuckl e. dsdb from one of the following locations:

Windows platform:

. . . \ Program Fi l es\ ANSYS I nc\ v110\ AI SOL\ Sampl es\ Si mul at i on

Unix platform: . . . / ansys _i nc/ v110/ ai sol / Sampl es/ Si mul at i on

From the main menu, choose Units> U.S. Customary (in, lbm, lbf, oF, s, V, A).

Highlight the Surface Body object in the tree and in the Details View, enter a Thickness of 0.125.
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2. Add a mapped face meshing control.

Click the right mouse button on the Mesh folder and choose Insert> Mapped Face Meshing.

Select the surface body and click the Apply button.

3. Set up a static structural analysis.

Choose New Analysis> Static Structural from the toolbar.


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4. Apply a zero displacement support in the z direction to all edges.

Highlight the Static Structural folder choose Supports> Displacement from the toolbar.

Select all four edges of the surface body and click the Apply button.

In the Details View, enter 0.0 for the Z Component.

5. Apply a zero displacement support in the y direction to one of the long edges.


Select one of the long edges of the surface body and click the Apply button.

In the Details View, enter 0.0 for the Y Component.


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6. Apply a zero displacement support in the x direction to one of the short edges.


Select one of the short edges of the surface body and click the Apply button.

In the Details View, enter 0.0 for the X Component.

7. Apply a force of 10000 lb. to the other short edge of the surface body.


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Highlight the Static Structural folder choose Loads> Force from the toolbar.

Select the other short edge of the surface body and click the Apply button.

In the Details View, set Define By to Components and enter -10000 for the X Component.

8. Add total deformation and normal stress as result objects.

Highlight the Solution folder choose Deformation> Total from the toolbar.

Highlight the Solution folder choose Stress> Normal from the toolbar.


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9. Solve the static structural analysis.

Choose Solve from the toolbar.

10. Review the displacement solution.

Highlight the Total Deformation object.

11. Review the axial stress state.

Highlight the Normal Stress object.


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12. Set up a linear buckling analysis.

Choose New Analysis> Linear Buckling from the toolbar.

13. Link the static structural solution to the linear buckling analysis.


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Highlight the Initial Condition object.

In the Details View, set Initial Condition Environment to Static Structural. This operation links the staticstructural solution to the buckling analysis.

14. Add a total deformation result object to the linear buckling analysis.

Highlight the Solution folder underLinear Buckling and choose Deformation> Total from the toolbar.


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15. Solve the linear buckling analysis.

Choose Solve from the toolbar.

16. Obtain the value of the critical load multiplier from the total deformation result.

Highlight the Total Deformation object. The critical Load Multiplier is visible in the Tabular Data window.

Documents

Linear Buckling Analysis