mechanical intro 15.0 appendixa buckling

8/11/2019 Mechanical Intro 15.0 AppendixA Buckling

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2014 ANSYS, Inc. February 12, 20142 Release 15.0

Chapter OverviewIn this Appendix, performing linear buckling analyses in Mechanical will be

covered.

Contents:

A. Background On Buckling

B. Buckling Analysis Procedure

C. Workshop AppA-1


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A. Background on Buckling

Many structures require an evaluation of their structural stability. Thin columns,

compression members, and vacuum tanks are all examples of structureswhere stability considerations are important.

At the onset of instability (buckling) a structure will have a very large change in

displacement {x} under essentially no change in the load (beyond a smallload perturbation).

F F

Stable Unstable


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Background on Buckling

Eigenvalue or linear buckling analysispredicts the theoretical buckling strength of

an ideal linear elasticstructure.

This method corresponds to the textbook approach of linear elastic buckling

analysis.

The eigenvalue buckling solution of a Euler column will match the classical Euler solution.

Imperfections and nonlinear behaviors prevent most real world structures fromachieving their theoretical elastic buckling strength.

Linear buckling generally yields unconservativeresults by not accounting for these

effects.

Although unconservative, linear buckling has the advantage of beingcomputationally cheap compared to nonlinear buckling solutions.


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Basics of Linear Buckling

For a linear buckling analysis, the eigenvalue problem below is solved to get the

buckling load multiplier liand buckling modes yi:

Assumptions:

[K] and [S] are constant: Linear elastic material behavior is assumed

Small deflection theory is used, and nononlinearities included

It is important to remember these assumptions related to performing linear

bucklinganalysesin Mechanical.

0ii

SK yl


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B. Buckling Analysis Procedure

A Static Structural analysis will need to be performed prior to (or in conjunction

with) a buckling analysis.


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Geometry and Material Properties

Any type of geometry supported by Mechanical may be used in buckling analyses:

Solid bodies

Surface bodies (with appropriate thickness defined)

Line bodies (with appropriate cross-sections defined)

Only buckling modes and displacement results are available for line bodies.

Although Point Masses may be included in the model, only inertial loads affect point

masses, so the applicability of this feature may be limited in buckling analyses

For material properties, Youngs Modulus and Poissons Ratio are required as a

minimum


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Loads and Supports

At least one structural load, which causes buckling, should be applied to the

model: Allstructural loads will be multiplied by the load multiplier (l)to determine the buckling

load (see below).

Compression-only supports are not recommended.

The structure should be fully constrained to prevent rigid-body motion.

F x l = Buckling Load

In a buckling analysis all appliedloads (F) are scaled by a

multiplication factor (l) until the

critical (buckling) load is reached



Loads and Supports

Special considerations must be given if constant andproportional loads are

present.

The user may iterate on the buckling solution, adjusting the variable loads until the load

multiplier becomes 1.0 or nearly 1.0.

Consider the example of a column with self weight WOand an externally applied forceA.

A solution can be reached by iterating while adjusting the value ofAuntil l= 1.0. This

insures the self weight = actual weight or WO* l WO .


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Buckling SetupBuckling analyses are always coupled to a structural analysis within the project

schematic.

The Pre-Stress object in the tree contains the results from a structural analysis.

The Details view of the Analysis Settings under the Linear Buckling branch allows the

user to specify the number of buckling modes to find.


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Solving the Model

After setting up the model the buckling analysis can be solved along with the static

structural analysis.

A linear buckling analysis is more computationally expensivethan a static analysis on the

same model.

The Solution Information branch provides detailed solution output.


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Reviewing Results

Interpreting the Load Multiplier (l):

The tower model below has been solved twice. In the first case a unit load is applied. In

the second an expected load applied (see next page)


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Reviewing Results

The buckling load multipliers can be reviewed in the Timeline section of the

results under the Linear Buckling analysis branch

It is good practice to request more than one buckling mode to see if the structure may be

able to buckle in more than one way under a given applied load.


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GoalsThe goal in this workshop is to verify linear buckling results in ANSYS Mechanical.

Results will be compared to closed form calculations from a handbook.

Next we will apply an expected load of 10,000 lbf to the model and determine its

factor of safety.

Finally we will verify that the structures material will not fail before buckling

occurs.


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Assumptions

The model is a steel pipe that is assumed to be fixed at one end and

free at the other with a purely compressive load applied to the

free end. Dimensions and properties of the pipe are:

OD = 4.5 in ID = 3.5 in. E = 30e6 psi, I = 12.7 in^4, L = 120 in.

In this case we assume the pipe conforms to the following handbookformula where P is the critical load:

For the case of a fixed / free beam the parameter K = 0.25.

2

2

'L

IEKP


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Assumptions

Using the formula and data from the previous page we can

predict the buckling load will be:

lbfeP 3.65648)120( 771.1263025.0' 22


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When the schematic is correctly set up it should appear as shown

here.

The drop target from the previous page indicates the outcome ofthe drag and drop operation. Cells A2 thru A4 from system (A) are

shared by system (B). Similarly the solution cell A6 is transferred to

the system B setup. In fact, the structural solution drives the

buckling analysis.

Project Schematic

Drop Target


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Project SchematicVerify that the Project units are set to US Customary (lbm, in, s, F, A, lbf, V).

Verify units are set to Display Values in Project Units.


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3. From the static structural system (A),double click the Engineering Data cell.

4. To match the hand calculations referencedearlier, change the Youngs modulus of thestructural steel.

a. Highlight Structural Steel.b. Expand Isotropic Elasticity and modify

Youngs Modulus to 3.0E7 psi.

c. Return to Project.

Note : changing this property here does not affect thestored value for Structural Steel in the General Materiallibrary. To save a material for future use we wouldExport the properties as a new material to the materiallibrary.

. . . Project Schematic

3.

b.

a.

c.


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. . . Project Schematic5. From the static structural system (A),

RMB the Geometry cell and Import

Geometry. Browse to the filePipe.stp.

6. Double click the Model cell to start

Mechanical.

When the Mechanical application opens the tree

will reflect the setup from the project schematic.

5.

6.


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Preprocessing7. Set the working unit system to the U.S. customary

system:

a. U.S. Customary (in, lbm, psi, F, s, V, A).

8. Apply constraints to the pipe:

a. Highlight the Static Structural branch (A5).

b. Select the surface on one end of the pipe.

c.RMB > Insert > Fixed Support.

a.

b.

a.

c.


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Environment9. Add buckling loads:

a. Select the surface on the opposite end of the pipe from the

fixed support.

b. RMB > Insert > Force.

c. In the force detail change the Define by field toComponents.

d. In the force detail enter 1 in the Magnitude field for the

Z Component (or use -1 depending on which ends of thepipe are selected).

c.

d.

a.

b.


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. . . Environment10. Solve the model:

a. Highlight the Solution branch for the Linear Buckling analysis

(B6) and Solve.

Note, this will automatically trigger a solve for the

static structural analysis above it.

11. When the solution completes:

a. Highlight the buckling Solution branch (B6).

The Timeline graph and the Tabular Data will display

the 1stbuckling mode (more modes can be requested).

b. RMB in the Timeline and choose Select All.

c. RMB > Create Mode Shape Results (this will add a TotalDeformation branch to the tree).

c.

b.

a.

a.


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Click Solve to view the first mode

Recall that we applied a unit (1) force thus the result compares well with our closed formcalculation of 65648 lbf.

Results


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. . . Results12. Change the force value to the expected load (10000

lbf):

a. Highlight the Force under the Static Structural (A5)branch

b. In the details, change the Z Component of the forceto 10000 (or use -10000 depending on your selections).

13. Solve:

a. Highlight the Linear Buckling Solution branch (B6),RMB and Solve.

11b.

11a.

12a.


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VerificationA final step in the buckling analysis is added here as a best practices exercise.

We have already predicted the expected buckling load and calculated the factor of

safety for our expected load. The results so far ONLY indicate results as they

relate to buckling failure. To this point we can say nothing about how our

expected load will affect the stresses and deflections in the structure.

As a final check we will verify that the expected load (10000 lbf) will not cause

excessive stresses or deflections before it is reached.


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. . . Verification14. Review Stresses for 10,000lbf load:

a. Highlight the Solution branch under the Static

Structural environment (A6).b. RMB > Insert > Stress > Equivalent Von Mises Stress.

c. RMB > Insert > Deformation > Total.

d. Solve.

a.

b.

c.


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. . . VerificationA quick check of the stress results shows the model as loaded is well within the

mechanical limits of the material being used (Engineering Data shows

compressive yield = 36,259 psi).

As stated, this is not a required step in a buckling analysis but should be regarded

as good engineering practice.

mechanical intro 15.0 appendixa buckling

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