Buckling Analysis

Chapter 7: Buckling Analysis

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7.1 Definition of Buckling Analysis

Buckling analysis is a technique used to determine buckling loads-critical loads at which a structure becomes

unstable-and buckled mode shapes-the characteristic shape associated with a structure's buckled response.

7.2 Types of Buckling Analyses

Two techniques are available in the ANSYS/Multiphysics, ANSYS/Mechanical, ANSYS/Structural, andANSYS/LinearPlus programs for predicting the buckling load and buckling mode shape of a structure:

nonlinear buckling analysis, and eigenvalue (or linear) buckling analysis. Since these two methods frequently

yield quite different results, let's examine the differences between them before discussing the details of theirimplementation.

7.2.1 Nonlinear Buckling Analysis

Nonlinear buckling analysis is usually the more accurate approach and is therefore recommended for design

or evaluation of actual structures. This technique employs a nonlinear static analysis with gradually increasingloads to seek the load level at which your structure becomes unstable, as depicted in Figure 7-1(a).

Using the nonlinear technique, your model can include features such as initial imperfections, plastic behavior,

gaps, and large-deflection response. In addition, using deflection-controlled loading, you can even track thepost-buckled performance of your structure (which can be useful in cases where the structure buckles into a

stable configuration, such as "snap-through" buckling of a shallow dome).

7.2.2 Eigenvalue Buckling Analysis

Eigenvalue buckling analysis predicts the theoretical buckling strength (the bifurcation point) of an ideal

linear elastic structure. (See Figure 7-1(b).) This method corresponds to the textbook approach to elasticbuckling analysis: for instance, an eigenvalue buckling analysis of a column will match the classical Euler

solution. However, imperfections and nonlinearities prevent most real-world structures from achieving their

theoretical elastic buckling strength. Thus, eigenvalue buckling analysis often yields unconservative results,and should generally not be used in actual day-to-day engineering analyses.

Figure 7-1 (a) Nonlinear load-deflection curve (b) Linear (Eigenvalue) buckling curve

STRUCTURAL: Chapter 7: Buckling Analysis (UP19980818) http://mechanika2.fs.cvut.cz/old/pme/examples/ansys55/html/guide_55/g-s...

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7.3 Commands Used in a Buckling Analysis

You use the same set of commands to build a model and perform a buckling analysis that you use to do any

other type of finite element analysis. Likewise, you choose similar options from the graphical user interface(GUI) to build and solve models no matter what type of analysis you are doing.

Section 7.7, "Sample Buckling Analysis (Command or Batch Method)," shows you the sequence of

commands you would issue (either manually or while running ANSYS as a batch job) to perform an exampleeigenvalue buckling analysis. Section 7.6, "Sample Buckling Analysis (GUI Method)," shows you how to

execute the same sample analysis using menu choices from the ANSYS GUI. (To learn how to use the

commands and GUI selections for building models, read the ANSYS Modeling and Meshing Guide.)

For detailed, alphabetized descriptions of the ANSYS commands, see the ANSYS Commands Reference.

7.4 Procedure for Nonlinear Buckling Analysis

A nonlinear buckling analysis is a static analysis with large deflections turned on [NLGEOM,ON], extended

to a point where the structure reaches its limit load or maximum load. Other nonlinearities such as plasticity

may be included in the analysis. The procedure for a static analysis is described in Chapter 2, andnonlinearities are described in Chapter 8.

7.4.1 Applying Load Increments

The basic approach in a nonlinear buckling analysis is to constantly increment the applied loads until the

solution begins to diverge. Be sure to use a sufficiently fine load increment as your loads approach the

expected critical buckling load. If the load increment is too coarse, the buckling load predicted may not beaccurate. Turn on bisection and automatic time stepping [AUTOTS,ON] to help avoid this problem.

7.4.2 Automatic Time Stepping

With automatic time stepping on, the program automatically seeks out the buckling load. If automatic time

stepping is ON in a static analysis having ramped loading and the solution does not converge at a given load,the program bisects the load step increment and attempts a new solution at a smaller load. In a buckling

analysis, each such convergence failure is typically accompanied by a "negative pivot" message indicating

that the attempted load equals or exceeds the buckling load. You can usually ignore these messages if theprogram successfully obtains a converged solution at the next, reduced load. If stress stiffness is active

[SSTIF,ON], you should run without adaptive descent active [NROPT,FULL,,OFF] to ensure that a lower


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bound to the buckling load is attained. The program normally converges to the limiting load as the process ofbisection and re-solution continues to the point at which the minimum time step increment (specified by

DELTIM or NSUBST) is achieved. The minimum time step will directly affect the precision of your results.

7.4.3 Important

Remember that an unconverged solution does not necessarily mean that the structure has reached its

maximum load. It could also be caused by numerical instability, which might be corrected by refining your

modeling technique. Track the load-deflection history of your structure's response to decide whether an

unconverged load step represents actual structural buckling, or whether it reflects some other problem.Perform a preliminary analysis using the arc-length method [ARCLEN] to predict an approximate value of

buckling load. Compare this approximate value to the more precise value calculated using bisection to help

determine if the structure has indeed reached its maximum load. You can also use the arc-length method itselfto obtain a precise buckling load, but this method requires you to adjust the arc-length radius by trial-

and-error in a series of manually directed re-analyses.

7.4.4 Points to Remember

If the loading on the structure is perfectly in-plane (that is, membrane or axial stresses only), theout-of-plane deflections necessary to initiate buckling will not develop, and the analysis will fail to

predict buckling behavior. To overcome this problem, apply a small out-of-plane perturbation, such as a

modest temporary force or specified displacement, to begin the buckling response. (A preliminaryeigenvalue buckling analysis of your structure may be useful as a predictor of the buckling mode shape,

allowing you to choose appropriate locations for applying perturbations to stimulate the desired

buckling response.) The imperfection (perturbation) induced should match the location and size of thatin the real structure. The failure load is very sensitive to these parameters.

In a large-deflection analysis, forces (and displacements) will maintain their original orientation, but

surface loads will "follow" the changing geometry of the structure as it deflects. Therefore, be sure toapply the proper type of loads.

You should carry your stability analysis through to the point of identifying the critical load in order to

calculate the structure's factor of safety with respect to nonlinear buckling. (Merely establishing thefact that a structure is stable at a given load level is generally insufficient for most design practice; you

will usually be required to provide a specified safety factor, which can only be determined by

establishing the actual limit load.)You can extend your analysis into the post-buckled range by activating the arc-length method

[ARCLEN]. Use this feature to trace the load-deflection curve through regions of "snap-through" and

"snap-back" response.For most solid elements, you do not need to use stress stiffening in a nonlinear buckling analysis. Do

not use stress stiffening on "discontinuous" elements (nonlinear elements that experience sudden

discontinuous changes in stiffness due to status changes, such as various contact elements, SOLID65,etc.) or on elements adjacent to discontinuous elements.

For those elements that support the consistent tangent stiffness matrix (BEAM4, SHELL63, and

SHELL181), activate the consistent tangent stiffness matrix (KEYOPT(2)=1 and NLGEOM,ON) toenhance the convergence behavior of your nonlinear buckling analyses and improve the accuracy of

your results. This element KEYOPT must be defined before the first load step of the solution and

cannot be changed once the solution has started.

7.5 Procedure for Eigenvalue Buckling Analysis


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Again, remember that eigenvalue buckling analysis generally yields unconservative results, and should usuallynot be used for design of actual structures. If you decide that eigenvalue buckling analysis is appropriate for

your application, follow this five-step procedure:

1. Build the model.

2. Obtain the static solution.

3. Obtain the eigenvalue buckling solution.

4. Expand the solution.

5. Review the results.

7.5.1 Build the Model

In this step, you specify the jobname and analysis title and then use PREP7 to define the element types,

element real constants, material properties, and the model geometry. These tasks are common to mostanalyses. The ANSYS Modeling and Meshing Guide explains them in detail.

7.5.1.1 Points to Remember

Only linear behavior is valid. Nonlinear elements, if any, are treated as linear. If you include contact

elements, for example, their stiffnesses are calculated based on their status after the static prestress run

and are never changed.Young's modulus (EX) (or stiffness in some form) must be defined. Material properties may be linear,

isotropic or orthotropic, and constant or temperature-dependent. Nonlinear properties, if any, are

ignored.

7.5.2 Obtain the Static Solution

The procedure to obtain a static solution is the same as described in Chapter 2, with the following exceptions:

Prestress effects [PSTRES] must be activated. Eigenvalue buckling analysis requires the stress stiffness

matrix to be calculated.

Unit loads are usually sufficient (that is, actual load values need not be specified). The eigenvaluescalculated by the buckling analysis represent buckling load factors. Therefore, if a unit load is specified,

the load factors represent the buckling loads. All loads are scaled. (Also, the maximum permissible

eigenvalue is 1,000,000-you must use larger applied loads if your eigenvalue exceeds this limit.)Note that eigenvalues represent scaling factors for all loads. If certain loads are constant (e.g.,

self-weight gravity loads) while other loads are variable (e.g., externally applied loads), you need to

ensure that the stress stiffness matrix from the constant loads is not factored by the eigenvalue solution.

One strategy that you can use to achieve this end is to iterate on the eigensolution, adjusting the

variable loads until the eigenvalue becomes 1.0 (or nearly 1.0, within some convergence tolerance).

Design optimization could be useful in driving this iterative procedure to a final answer.

Consider, for example, a pole having a self-weight W0, which supports an externally-applied load, A.

To determine the limiting value of A in an eigenvalue buckling solution, you could solve repetitively,

using different values of A, until by iteration you find an eigenvalue acceptably close to1.0.


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Figure 7-2 Adjusting variable loads to find an eigenvalue of 1.0

You can apply a non-zero constraint in the prestressing pass as the static load. The eigenvalues found in

the buckling solution will be the load factors applied to these non-zero constraint values. However, themode shapes will have a zero value at these degrees of freedom (and not the non-zero 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 geometry data (issue RESUME if necessary). The following tasks are involved in obtainingthe eigenvalue buckling solution:

1. Enter the ANSYS solution processor.

Command(s):

/SOLU

GUI:

Main Menu>Solution

2. Define the analysis type and analysis options. ANSYS offers these options for a buckling analysis:

Table 7-1 Analysis types and analysis options

Option Command GUI Path

New Analysis ANTYPE Main Menu>Solution>-Analysis Type-New Analysis

Analysis Type: Eigen Buckling ANTYPEMain Menu>Solution>-Analysis Type-

New Analysis>Eigen Buckling

Eigenvalue Extraction Method BUCOPT Main Menu>Solution>Analysis Options

No. of Eigenvalues to be Extracted BUCOPT Main Menu>Solution>Analysis Options

Shift Point for Eigenvalue Calculation BUCOPT Main Menu>Solution>Analysis Options

No. of Reduced Eigenvectors to Print BUCOPT Main Menu>Solution>Analysis Options

Each of these options is explained in detail below.

7.5.3.1 Option: New Analysis [ANTYPE]

Choose New Analysis. Restarts are not valid in an eigenvalue buckling analysis.


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7.5.3.2 Option: Analysis Type: Eigen Buckling [ANTYPE]

Choose Eigen Buckling analysis type.

7.5.3.3 Option: Eigenvalue Extraction Method [BUCOPT]

Choose one of the following solution methods. The Block Lanczos or subspace iteration methods are

generally recommended for eigenvalue buckling because they use the full system matrices. (If you choose the

reduced method, you will need to define master degrees of freedom before initiating the solution.) See Section3.4.2.3, "Option: Mode Extraction Method," in this manual for more information about these solution

methods.

Reduced (Householder) methodBlock Lanczos method

Subspace iteration method

7.5.3.4 Option: Number of Eigenvalues to be Extracted [BUCOPT]

Defaults to one, which is usually sufficient for eigenvalue buckling.

7.5.3.5 Option: Shift Point for Eigenvalue Calculation [BUCOPT]

This option represents 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.

7.5.3.6 Option: Number of Reduced Eigenvectors to Print [BUCOPT]

This option is valid only for the reduced method. This option allows you to get a listing of the reduced

eigenvectors (buckled mode shapes) on the printed output file (Jobname.OUT).

3. Specify load step options.

The only load step options valid for eigenvalue buckling are expansion pass options and output

controls. Expansion pass options are explained next in Section 7.5.4. You can request buckled modeshapes from the reduced method to be included in the printed output. No other output control is

applicable.

Command(s):

OUTPR,NSOL,ALL

GUI:

Main Menu>Solution>-Load Step Opts-Output Ctrls>Solu Printout

4. Save a back-up copy of the database to a named file.

Command(s):

SAVE

GUI:


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Utility Menu>File>Save As

5. 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 appliedin 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.

6. Leave 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 systemmatrices, 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. Re-enter SOLUTION.

Command(s):

/SOLU


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GUI:

Main Menu>Solution

Note-You must explicitly leave SOLUTION (using the FINISH command) and re-enter (/SOLUTION)before performing the expansion pass.

2. Activate the expansion pass and its options. The following options are required for the expansion pass:

Table 7-2 Expansion pass options

Option Command GUI Path

Expansion Pass On/Off EXPASS Main Menu>Solution>-Load Step Opts-ExpansionPass>ON

No. of Modes to Expand MXPANDMain Menu>Solution>-Load Step Opts-ExpansionPass>

Expand Modes

Stress Calculations On/Off MXPANDMain Menu>Solution>-Load Step Opts-ExpansionPass>

Expand Modes

7.5.4.3 Option: Expansion Pass ON/OFF [EXPASS]

Choose ON.

7.5.4.4 Option: Number of Modes to Expand [MXPAND]

Defaults to all modes that were extracted.

7.5.4.5 Option: Stress Calculations On/Off [MXPAND]

"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.

3. 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):


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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.

4. 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

5. 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) 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 expansion passmust be available.

1. List all buckling load factors.

Command(s):

SET,LIST

GUI:


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Main Menu>General Postproc>Results Summary

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 or

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 $B (B 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. A total of 10 masterdegrees of freedom in the X-direction are selected to characterize the buckling mode. The moment of inertia

of the bar is calculated as I = Ah2/12 = 0.0052083 in4.

7.6.2 Problem Specifications


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The following material properties are used for this problem:

E = 30 x 106 psi

The following geometric properties are used for this problem:

$B (B = 200 in

A = 0.25 in2

h = 0.5 in

Loading for this problem is:

F = 1 lb.

7.6.3 Problem Sketch

Figure 7-3 Diagram of Bar with Hinged Ends

7.6.3.1 Set the Analysis Title

After you enter the ANSYS program, follow these steps to set the title.

1. Choose menu path Utility Menu>File>Change Title.

2. Enter the text "Buckling of a Bar with Hinged Ends" and click on OK.

7.6.3.2 Define the Element Type

In this step, you define BEAM3 as the element type.

1. Choose menu path Main Menu>Preprocessor>Element Type> Add/Edit/Delete. The Element Types

dialog box appears.


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2. Click on Add. The Library of Element Types dialog box appears.

3. In the scroll box on the left, click on "Structural Beam" to select it.

4. In the scroll box on the right, click on "2D elastic 3" to select it.

5. Click on OK, and then click on Close in the Element Types dialog box.

7.6.3.3 Define the Real Constants and Material Properties

1. Choose menu path Main Menu>Preprocessor>Real Constants. The Real Constants dialog box appears.

2. Click on Add. The Element Type for Real Constants dialog box appears.

3. Click on OK. The Real Constants for BEAM3 dialog box appears.

4. Enter .25 for area, 52083e-7 for IZZ, and .5 for height.

5. Click on OK.

6. Click on Close in the Real Constants dialog box.

7. Choose menu path Main Menu>Preprocessor>Material Props> -Constant-Isotropic. The IsotropicMaterial Properties dialog box appears.

8. Click on OK to specify material number 1. The Isotropic Material Properties dialog box appears.

9. Enter 30e6 for Young's modulus, and click on OK.

7.6.3.4 Define Nodes and Elements

1. Choose menu path Main Menu>Preprocessor>-Modeling-Create> Nodes>In Active CS. The CreateNodes in Active Coordinate System dialog box appears.

2. Enter 1 for node number.

3. Click on Apply. Node location defaults to 0,0,0.

4. Enter 11 for node number.

5. Enter 0,100,0 for the X,Y,Z coordinates.

6. Click on OK. The two nodes appear in the ANSYS Graphics window.

7. Choose menu path Main Menu>Preprocessor>-Modeling-Create> Nodes>Fill between Nds. The Fill

between Nds menu appears.

8. Click on node 1, then 11, and click on OK. The Create Nodes Between 2 Nodes dialog box appears.

9. Click on OK to accept the settings (fill between nodes 1 and 11, and number of nodes to fill 9).

10. Choose menu path Main Menu>Preprocessor>-Modeling-Create> Elements>-Auto Numbered-Thru

Nodes. The Elements from Nodes picking menu appears.


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11. Click on nodes 1 and 2, then click on OK.

Note-The triad, by default, hides the node number for node 1. To turn the triad off, choose menu path

Utility Menu>PlotCtrls>Window Controls> Window Options and select the "Not Shown" option

for Location of triad.

12. Choose menu path Main Menu>Preprocessor>-Modeling-Copy> -Elements-Auto Numbered. The

Copy Elems Auto-Num picking menu appears.

13. Click on Pick All. The Copy Elems Auto-Num dialog box appears.

14. Enter 10 for total number of copies and enter 1 for node number increment.

15. Click on OK. The remaining elements appear in the ANSYS Graphics window.

7.6.3.5 Define the Boundary Conditions

1. Choose menu path Main Menu>Solution>-Analysis Type-New Analysis. The New Analysis dialog box

appears.

2. Click OK to accept the default of "Static."

3. Choose menu path Main Menu>Solution>Analysis Options. The Static or Steady-State Analysis dialog

box appears.

4. In the scroll box for stress stiffness or prestress, scroll to "Prestress ON" to select it.

5. Click on OK.

6. Choose menu path Main Menu>Solution>-Loads-Apply>-Structural- Displacement>On Nodes. TheApply U,ROT on Nodes picking menu appears.

7. Click on node 1, then click on OK. The Apply U,ROT on Nodes dialog box appears.

8. Click on "All DOF" to select it, and click on OK.

9. Choose menu path Main Menu>Solution>-Loads-Apply>-Structural- Force/Moment>On Nodes. The

Apply F/M on Nodes picking menu appears.

10. Click on node 11, then click OK. The Apply F/M on Nodes dialog box appears.

11. In the scroll box for Direction of force/mom, scroll to "FY" to select it.

12. Enter -1 for the force/moment value, and click on OK. The force symbol appears in the ANSYS Graphics

window.

7.6.3.6 Solve the Static Analysis

1. Choose menu path Main Menu>Solution>-Solve-Current LS.

2. Carefully review the information in the status window, and click on Close.

3. Click on OK in the Solve Current Load Step dialog box to begin the solution.


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4. Click on Close in the Information window when the solution is finished.

7.6.3.7 Solve the Buckling Analysis

1. Choose menu path Main Menu>Solution>-Analysis Type-New Analysis.

Note-Click on Close in the Warning window if the following warning appears: Changing the analysis

type is only valid within the first load step. Pressing OK will cause you to exit and re-enter solution.

This will reset the load step count to 1.

2. Click the "Eigen Buckling" option on, then click on OK.

3. Choose menu path Main Menu>Solution>Analysis Options. The Eigenvalue Buckling Options dialog

box appears.

4. Click the "Reduced" option on, and enter 1 for number of modes to extract.

5. Click on OK.

6. Choose menu path Main Menu>Solution>-Load Step Opts- ExpansionPass>Expand Modes.

7. Enter 1 for number of modes to expand, and click on OK.

8. Choose menu path Main Menu>Solution>Master DOFs>-User Selected-Define. The Define Master

DOFs picking menu appears.

9. Click on nodes 2-11. Click on OK. The Define Master DOFs dialog box appears.

10. In the scroll box for 1st degree of freedom, scroll to UX to select it.

11. Click on OK.

12. Choose menu path Main Menu>Solution>-Solve-Current LS.

13. Carefully review the information in the status window, and click on Close.

14. Click on OK in the Solve Current Load Step dialog box to begin the solution.

15. Click on Close in the Information window when the solution is finished.

7.6.3.8 Review the Results

1. Choose menu path Main Menu>General PostProc>-Read Results-First Set.

2. Choose menu path Main Menu>General PostProc>Plot Results> Deformed Shape. The Plot Deformed

Shape dialog box appears.

3. Click the "Def + undeformed" option on. Click on OK. The deformed and undeformed shapes appear in the

ANSYS graphics window.

7.6.3.9 Exit ANSYS

1. In the ANSYS Toolbar, click on Quit.


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2. Choose the save option you want and click on OK.

7.7 Sample Buckling Analysis (Command or Batch

Method)

You can perform the example buckling analysis of a bar with hinged ends using the ANSYS commands shown

below instead of GUI choices. Items prefaced by an exclamation point (!) are comments.

/PREP7

/TITLE, BUCKLING OF A BAR WITH HINGED SOLVES

ET,1,BEAM3 ! Beam element

R,1,.25,52083E-7,.5 ! Area,IZZ, height

MP,EX,1,30E6 ! Define material properties

N,1

N,11,,100

FILL

E,1,2

EGEN,10,1,1

FINISH

/SOLU

ANTYPE,STATIC ! Static analysis

PSTRES,ON ! Calculate prestress effects

D,1,ALL ! Fix symmetry ends

F,11,FY,-1 ! Unit load at free end

SOLVE

FINISH

/SOLU

ANTYPE,BUCKLE ! Buckling analysis

BUCOPT,REDUC,1 ! Use Householder solution method, extract 1 mode

MXPAND,1 ! Expand 1 mode shape

M,2,UX,11,1 ! Select 10 UX DOF as masters

SOLVE

FINISH

/POST1

SET,FIRST

PLDISP,1

FINISH

7.8 Where to Find Other Examples

Several ANSYS publications, particularly the ANSYS Verification Manual, describe additional bucklinganalyses.

The ANSYS Verification Manual consists of test case analyses demonstrating the analysis capabilities of the

ANSYS program. While these test cases demonstrate solutions to realistic analysis problems, the ANSYS

Verification Manual does not present them as step-by-step examples with lengthy data input instructions and

printouts. However, most ANSYS users who have at least limited finite element experience should be able to

fill in the missing details by reviewing each test case's finite element model and input data with accompanyingcomments.

The following list shows you the variety of buckling analysis test cases that the ANSYS Verification Manual

includes:


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VM17 Snap-Through Buckling of a Hinged Shell

VM127 Buckling of a Bar with Hinged Ends (Line Elements)

VM128 Buckling of a Bar with Hinged Ends (Area Elements)

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