Post on 03-Jun-2018
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
1/34
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
2/34
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
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
3/34
2014 ANSYS, Inc. February 12, 20143 Release 15.0
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
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
4/34
2014 ANSYS, Inc. February 12, 20144 Release 15.0
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.
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
5/34
2014 ANSYS, Inc. February 12, 20145 Release 15.0
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
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
6/34
2014 ANSYS, Inc. February 12, 20146 Release 15.0
B. Buckling Analysis Procedure
A Static Structural analysis will need to be performed prior to (or in conjunction
with) a buckling analysis.
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
7/34 2014 ANSYS, Inc. February 12, 20147 Release 15.0
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
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
8/34
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
9/34 2014 ANSYS, Inc. February 12, 20149 Release 15.0
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
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
10/34 2014 ANSYS, Inc. February 12, 201410 Release 15.0
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 .
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
11/34
2014 ANSYS, Inc. February 12, 201411 Release 15.0
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.
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
12/34
2014 ANSYS, Inc. February 12, 201412 Release 15.0
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.
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
13/34
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
14/34
2014 ANSYS, Inc. February 12, 201414 Release 15.0
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)
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
15/34
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
16/34
2014 ANSYS, Inc. February 12, 201416 Release 15.0
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.
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
17/34
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
18/34
2014 ANSYS, Inc. February 12, 201418 Release 15.0
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.
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
19/34
2014 ANSYS, Inc. February 12, 201419 Release 15.0
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
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
20/34
2014 ANSYS, Inc. February 12, 201420 Release 15.0
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
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
21/34
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
22/34
2014 ANSYS, Inc. February 12, 201422 Release 15.0
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
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
23/34
2014 ANSYS, Inc. February 12, 201423 Release 15.0
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.
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
24/34
2014 ANSYS, Inc. February 12, 201424 Release 15.0
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.
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
25/34
2014 ANSYS, Inc. February 12, 201425 Release 15.0
. . . 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.
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
26/34
2014 ANSYS, Inc. February 12, 201426 Release 15.0
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.
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
27/34
2014 ANSYS, Inc. February 12, 201427 Release 15.0
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.
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
28/34
2014 ANSYS, Inc. February 12, 201428 Release 15.0
. . . 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.
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
29/34
2014 ANSYS, Inc. February 12, 201429 Release 15.0
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
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
30/34
2014 ANSYS, Inc. February 12, 201430 Release 15.0
. . . 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.
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
31/34
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
32/34
2014 ANSYS, Inc. February 12, 201432 Release 15.0
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.
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
33/34
2014 ANSYS, Inc. February 12, 201433 Release 15.0
. . . 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.
8/11/2019 Mechanical Intro 15.0 AppendixA Buckling
34/34
. . . 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.