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Linear Buckling Analysis
with Femap V10.1.1 and Nastran 7.0
Adrian JensenMechanical Engineer
2010 – All Rights Reserved
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Introduction
Calculating the buckling force for a ideal column is quite simple. As long as you know the length, second moment of inertia and elastic modulus of the beam, you can calculate the force by hand. What if you don’t have an ideal column. What if you don’t havecolumn or beam geometry at all but buckling is still a concern for your design?
This white paper will walk you through the NX Nastran Linear Buckling Analysis Additionally the paper will show you how to
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This white paper will walk you through the NX Nastran Linear Buckling Analysis. Additionally, the paper will show you how to validate your linear buckling analysis with a non‐liner static analysis.
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Shown above are the cross sectional properties for the beam we will be analyzing. Given a length of 300”, the critical load is 57,562 lbf.
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Boundary ConditionsyThe beam is pinned at both ends. The vertical degree of freedom is released at the upper constraint. Rotation about the vertical axis is prevented at the lower constraint. An arbitrary load is applied to the upper most node.
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The title of the Output Set will include a load factor value. This factor multiplied by the applied load is equal to the critical load. 5.75*10,000lbf = 57,500 lbf, correlating with the hand calculation.
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A similar example can be found in the NX Nastran 7 User’s Guide.
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ValidationMore common than not, the solution cannot be validated with a hand calculation (this is why we are doing FEA, right?). You can validate your solution with the slightly trickier Non Linear Static analysis For this validation the
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trickier Non‐Linear Static analysis. For this validation, the load has been increased to 100,000 lbf such that the critical load will be evaluated in the intermediate steps of the non‐linear analysis. Additionally, a small bending moment (Mx = 100 in‐lbf) has been added to direct the analysis to the first buckling load.
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The non‐linear solution diverges at time = 0.575. With the load increasing from 0 to 100,000 lbf as time increases from 0 to 1, this correlates to a load of 57,500 lbf.
“The arc‐length method should be used if the problem involves snap‐through or postbuckling deformation”
– NX Nastran 7 Basic Nonlinear Analysis User’s Guide
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Once you are confident analyzing simple members for buckling with both the linear and non‐linear approach, move on to more complicated geometry Above is an exampleon to more complicated geometry. Above is an example from the NX Nastran Handbook of Non Linear Analysis for an Imperfect Spherical Shell.
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Adrian JensenAdrian JensenMechanical Engineer
Adrian.Jensen@PredictiveEngineering.comwww.PredictiveEngineering.comwww.PredictiveEngineering.com
2010 – All Rights Reserved