• You can apply a nonzero constraint in the prestressing pass as the static load. The eigenvalues found in the buckling solution will be the load factors applied to these nonzero constraint values. However, the mode shapes will have a zero value at these degrees of freedom (and not the nonzero value specified).
• At the end of the solution, leave SOLUTION [FINISH].
7.5.3. Obtain the Eigenvalue Buckling Solution
This step requires files Jobname.EMAT and Jobname.ESAV from the static analysis. Also, the database must contain the model data (issue RESUME if necessary). Follow the steps below to obtain the eigenvalue buckling solution.
1. Enter the ANSYS solution processor.
Command(s): /SOLU GUI: Main Menu> Solution 2. Specify the analysis type.
Command(s): ANTYPE,BUCKLE
GUI: Main Menu> Solution> Analysis Type> New Analysis Note — Restarts are not valid in an eigenvalue buckling analysis.
Note — When you specify an eigenvalue buckling analysis, a Solution menu that is appropriate for buckling analyses appears. The Solution menu will be either "abridged" or "unabridged", depending on the actions you took prior to this step in your ANSYS session. The abridged menu contains only those solution options that are valid and/or recommended for buckling analyses.
If you are on the abridged Solution menu and you want to access other solution options (that is, solution options that are valid for you to use, but their use may not be encouraged for this type of analysis), select the Unabridged Menu option from the Solution menu. For details, see Section 3.11.1: Using Abridged Solution Menus in the ANSYS Basic Analysis Guide.
3. Specify analysis options.
Command(s): BUCOPT, Method, NMODE, SHIFT
GUI: Main Menu> Solution> Analysis Type> Analysis Options
Regardless of whether you use the command or GUI method, you can specify values for these options:
• For Method, specify the eigenvalue extraction method. You can choose subspace iteration or Block Lanczos. The Block Lanczos and subspace iteration methods use the full system matrices. See Sec-tion 3.5.2.3: OpSec-tion: Mode-ExtracSec-tion Method [MODOPT] in this manual for more informaSec-tion about these solution methods.
• For NMODE, specify the number of eigenvalues to be extracted. This argument defaults to one, which is usually sufficient for eigenvalue buckling.
• For SHIFT, specify the point (load factor) about which eigenvalues are calculated. The shift point is helpful when numerical problems are encountered (due to negative eigenvalues, for example). Defaults to 0.0.
4. Specify load step options.
The only load step options valid for eigenvalue buckling are output controls and expansion pass options.
Command(s): OUTPR,NSOL,ALL
GUI: Main Menu> Solution> Load Step Opts> Output Ctrls> Solu Printout
You can make the expansion pass a part of the eigenvalue buckling solution or perform it as a separate step. In this document, we treat the expansion pass as a separate step. See Section 7.5.4: Expand the Solution for details.
5. Save a backup copy of the database to a named file.
Command(s): SAVE
Section 7.5: Procedure for Eigenvalue Buckling Analysis
GUI: Utility Menu> File> Save As 6. Start solution calculations.
Command(s): SOLVE
GUI: Main Menu> Solution> Solve> Current LS
The output from the solution mainly consists of the eigenvalues, which are printed as part of the printed output (Jobname.OUT). The eigenvalues represent the buckling load factors; if unit loads were applied in the static analysis, they are the buckling loads. No buckling mode shapes are written to the database or the results file, so you cannot postprocess the results yet. To do this, you need to expand the solution (explained next).
Sometimes you may see both positive and negative eigenvalues calculated. Negative eigenvalues indicate that buckling occurs when the loads are applied in an opposite sense.
7. Exit the SOLUTION processor.
Command(s): FINISH
GUI: Close the Solution menu.
7.5.4. Expand the Solution
If you want to review the buckled mode shape(s), you must expand the solution regardless of which eigenvalue extraction method is used. In the case of the subspace iteration method, which uses full system matrices, you may think of "expansion" to simply mean writing buckled mode shapes to the results file.
7.5.4.1. Points to Remember
• The mode shape file (Jobname.MODE) from the eigenvalue buckling solution must be available.
• The database must contain the same model for which the solution was calculated.
7.5.4.2. Expanding the Solution
The procedure to expand the mode shapes is explained below.
1. Reenter SOLUTION.
Command(s): /SOLU GUI: Main Menu> Solution
Note — You must explicitly leave SOLUTION (using the FINISH command) and reenter (/SOLU) before performing the expansion pass.
2. Specify that this is an expansion pass.
Command(s): EXPASS,ON
GUI: Main Menu> Solution> Analysis Type> ExpansionPass 3. Specify expansion pass options.
Command(s): MXPAND, NMODE, , , Elcalc
GUI: Main Menu> Solution> Load Step Opts> ExpansionPass> Expand Modes
Regardless of whether you use the command or GUI method, the following options are required for the expansion pass:
• For NMODE, specify the number of modes to expand. This argument defaults to the total number of modes that were extracted.
• For Elcalc, indicate whether you want ANSYS to calculate stresses. "Stresses" in an eigenvalue analysis do not represent actual stresses, but give you an idea of the relative stress or force distribution for each mode. By default, no stresses are calculated.
4. Specify load step options.
The only options valid in a buckling expansion pass are the following output controls:
• Printed Output
Use this option to include any results data on the output file (Jobname.OUT).
Command(s): OUTPR
GUI: Main Menu> Solution> Load Step Opts> Output Ctrl> Solu Printout
• Database and Results File Output
This option controls the data on the results file (Jobname.RST).
Command(s): OUTRES
GUI: Main Menu> Solution> Load Step Opts> Output Ctrl> DB/Results File Note — The FREQ field on OUTPR and OUTRES can only be ALL or NONE, that is, the data can be requested for all modes or no modes - you cannot write information for every other mode, for instance.
5. Start expansion pass calculations.
The output consists of expanded mode shapes and, if requested, relative stress distributions for each mode.
Command(s): SOLVE
GUI: Main Menu> Solution> Solve> Current LS
6. Leave the SOLUTION processor. You can now review results in the postprocessor.
Command(s): FINISH
GUI: Close the Solution menu.
Note — The expansion pass has been presented here as a separate step. You can make it part of the eigenvalue buckling solution by including the MXPAND command (Main Menu> Solution>
Load Step Opts> ExpansionPass> Expand Modes) as one of the analysis options.
7.5.5. Review the Results
Results from a buckling expansion pass are written to the structural results file, Jobname.RST. They consist of buckling load factors, buckling mode shapes, and relative stress distributions. You can review them in POST1, the general postprocessor.
Note — To review results in POST1, the database must contain the same model for which the buckling solution was calculated (issue RESUME if necessary). Also, the results file (Jobname.RST) from the ex-pansion pass must be available.
1. List all buckling load factors.
Command(s): SET,LIST
GUI: Main Menu> General Postproc> Results Summary
Section 7.5: Procedure for Eigenvalue Buckling Analysis
2. Read in data for the desired mode to display buckling mode shapes. (Each mode is stored on the results file as a separate substep.)
Command(s): SET,SBSTEP
GUI: Main Menu> General Postproc> Read Results> load step 3. Display the mode shape.
Command(s): PLDISP
GUI: Main Menu> General Postproc> Plot Results> Deformed Shape 4. Contour the relative stress distributions.
Command(s): PLNSOL or PLESOL
GUI: Main Menu> General Postproc> Plot Results> Contour Plot> Nodal Solution Main Menu> General Postproc> Plot Results> Contour Plot> Element Solution
See the ANSYS Commands Reference for a discussion of the ANTYPE, PSTRES, D, F, SF, BUCOPT, EXPASS, MXPAND, OUTRES, SET, PLDISP, and PLNSOL commands.
7.6. Sample Buckling Analysis (GUI Method)
In this sample problem, you will analyze the buckling of a bar with hinged ends.
7.6.1. Problem Description
Determine the critical buckling load of an axially loaded long slender bar of length l with hinged ends. The bar has a cross-sectional height h, and area A. Only the upper half of the bar is modeled because of symmetry. The boundary conditions become free-fixed for the half-symmetry model. The moment of inertia of the bar is calculated as I = Ah2/12 = 0.0052083 in4.
7.6.2. Problem Specifications
The following material properties are used for this problem:
E = 30 x 106 psi
The following geometric properties are used for this problem:
l = 200 in A = 0.25 in2 h = 0.5 in
Loading for this problem is:
F = 1 lb.