mechanical intro 14.5 appa buckling
TRANSCRIPT
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Introduction to ANSYS
Mechanical
14.5 Release
Appendix A
Linear Buckling Analysis
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Chapter OverviewIn this chapter, performing linear buckling analyses in Mechanical will be covered.
Contents:
A. Background On Buckling
B. Buckling Analysis Procedure
C. Workshop 7-1
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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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Contact Regions
Contact regions are available in free vibration analyses, however,
contact behavior will differ for the nonlinearcontact types
exactly as with modal analyses.
Discussed earlier (see chapter 5).
Initially Touching Inside Pinball Region Outside Pinball Region
Bonded Bonded Bonded Free
No Separation No Separation No Separation Free
Rough Bonded Free Free
Frictionless No Separation Free Free
Contact TypeLinear Buckling Analysis
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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 thecritical (buckling) load is reached
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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. Thisinsures 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 theuser 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 ResultsAfter the solution is complete, the buckling modes can be reviewed:
The Load Multiplier for each buckling mode is shown in the Details view as well as the
graph and chart areas. The load multiplier times the applied loads represent thepredicted buckling load.
Fbuckle= (Fappliedx l)
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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
Interpreting the Load Multiplier (l):
LoadUnitadBucklingLo _*l
l adBucklingLo
LoadActualadBucklingLo _*l
FactorSafetyLoadActual
adBucklingLo_
_
l
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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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C. Workshop AA.1Linear Buckling
Workshop WSAA.1Linear Buckling
Goal:
Verify linear buckling results in Mechanical for the pipe model
shown below. Results will be compared to closed form
calculations from a handbook.
http://localhost/var/www/apps/conversion/tmp/ANSYS_Mechanical-Intro_12.1_1st-edition/Workshops/WB-Mech_120_WS_07.1.ppthttp://localhost/var/www/apps/conversion/tmp/ANSYS_Mechanical-Intro_12.1_1st-edition/Workshops/WB-Mech_120_WS_07.1.ppthttp://localhost/var/www/apps/conversion/tmp/ANSYS_Mechanical-Intro_12.1_1st-edition/Workshops/WB-Mech_120_WS_07.1.ppthttp://localhost/var/www/apps/conversion/tmp/ANSYS_Mechanical-Intro_12.1_1st-edition/Workshops/WB-Mech_120_WS_07.1.ppthttp://localhost/var/www/apps/conversion/tmp/ANSYS_Mechanical-Intro_12.1_1st-edition/Workshops/WB-Mech_120_WS_07.1.ppthttp://localhost/var/www/apps/conversion/tmp/ANSYS_Mechanical-Intro_12.1_1st-edition/Workshops/WB-Mech_120_WS_07.1.ppthttp://localhost/var/www/apps/conversion/tmp/ANSYS_Mechanical-Intro_12.1_1st-edition/Workshops/WB-Mech_120_WS_07.1.ppt -
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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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Project Schematic1. Double click Static Structural in the
Toolbox to create a new system.
2. Drag/drop a Linear Buckling systemonto the Solution cell of the staticstructural system.
2.
1.
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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
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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. . . ResultsWhen the solution completes note the Load Multiplier field now shows a value
of 6.56. Since we now have a real world load applied, the load multiplier is
interpreted as the buckling factor of safety for the applied load.
Given that we have already calculated a buckling load of 65600 lbf, the result is
obviously trivial (65600 / 10000). It is shown here only for completeness.
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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.