Linear Buckling Analysis

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Linear Buckling Analysis

• Chapter Seven

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Chapter Overview

• In this chapter, performing linear buckling
  analyses in Simulation will be covered.
• In Simulation, performing a linear buckling
  analysis is similar to a stress analysis.
• It is assumed that the user has already covered
  Chapter 4 Linear Static Structural Analysis prior
  to this section.
• The capabilities described in this section are
  generally applicable to ANSYS DesignSpace Entra
  licenses and above.
• Some options discussed in this chapter may
  require more advanced licenses, but these are
  noted accordingly.
• Harmonic and nonlinear static structural analyses
  are not discussed here but in their respective
  chapters.

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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
  structures where 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 small load perturbation).

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Background on Buckling

• Eigenvalue or linear buckling analysis predicts
  the theoretical buckling strength of an ideal
  linear elastic structure.
• 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.

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Background on Buckling

• Imperfections and nonlinear behavior prevent most
  real world structures from achieving their
  theoretical elastic buckling strength. Linear
  buckling generally yields unconservative results,
  and should be used with caution.
• Consider the buckling of a soda can
• Material response is inelastic. Geometrically
  nonlinear effects need to be considered. Contact
  is also required. Hence, these type of nonlinear
  behavior are not considered.
• There may be slight imperfections in the soda
  can, such as a small dent, which would influence
  the response and not make the model symmetric.
  However, these small imperfections are also not
  usually considered in a linear buckling analysis.

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Background on Buckling

• Although unconservative, linear buckling has
  various advantages
• It is computationally cheaper than a nonlinear
  buckling analysis, and should be run as a first
  step to estimate the critical load (load at the
  onset of buckling).
• Relative comparisons can be made of the effect of
  differences in design to buckling
• Linear buckling can be used as a design tool to
  determine what the possible buckling mode shapes
  may be.
• The way in which a structure may buckle can be
  used as a possible guide in design

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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 li and buckling modes
  yiAssumptions
• K and S are constant
• Linear elastic material behavior is assumed
• Small deflection theory is used, and no
  nonlinearities included
• Some additional restrictions
• Nonzero displacement supports or thermal loads
  are not allowed
• It is important to remember these assumptions
  related to performing linear buckling analyses in
  Simulation.

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B. Buckling Analysis Procedure

• The linear buckling analysis procedure is very
  similar to performing a linear static analysis,
  so not all steps will be covered in detail. The
  steps in yellow italics are specific to buckling
  analyses.
• Attach Geometry
• Assign Material Properties
• Define Contact Regions (if applicable)
• Define Mesh Controls (optional)
• Include Loads and Supports
• Request Buckling Results
• Solve the Model
• Review Results

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Geometry and Material Properties

• Similar to linear static analyses, any type of
  geometry supported by Simulation 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 buckling
  analyses. However, since this is a purely linear
  analysis, contact behavior will differ for the
  nonlinear contact types
• It is important to note the following
• All nonlinear contact types are reduced to either
  Bonded or No Separation contact.
• No Separation contact should be used with caution
  in buckling analyses, as it provides no stiffness
  in the tangential direction.

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Loads and Supports

• At least one structural load, which causes
  buckling, should be applied to the model
• All structural loads will be multiplied by the
  load factor to determine the buckling load.
  Hence, non-proportional or constant loading is
  not directly supported (see next slide)
• No Given Displacement supports are allowed
• No Thermal loading is allowed
• Compression-only supports are not recommended
• The structure should be fully constrained, no
  rigid-body motion should be present in the model.

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Loads and Supports

• Special considerations must be given if constant
  and proportional 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 pole with self weight
  WO and an externally applied force A. You can
  iterate, adjusting the value of A until l 1.0.
  

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Requesting Results

• Most of the options for buckling analyses are
  similar to that of static analysis.
• Simulation triggers a buckling analysis when the
  Buckling tool is inserted
• The Details view of the Buckling branch allows
  the user to specify the number of buckling modes
  to find. The default is to find the first
  buckling mode. Increasing the number of modes to
  calculate will increase the solution time.
  However, usually only a few buckling modes are
  usually desired.

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Requesting Results

• Requested results are located under the Buckling
  branch
• Select the number of modes to find under the
  Details view of the Buckling branch
• Stress, strain, or directional displacement
  results can be requested under the Buckling
  branch
• The buckling mode is specified for each stress,
  strain, or displacement result requested
• If stresses or strains are requested for a model
  already solved, another solution is required.
• No additional results may be requested directly
  under the Solution branch.

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Solution Options

• The solution branch provides details on the type
  of analysis being performed
• For a buckling analysis, none of the options in
  the Details view of the Solution branch usually
  need to be changed.
• Solver Type should be left on the default
  option of Program Controlled. It only controls
  the solver used in the initial static analysis
  but not the buckling solution method.
• Weak springs is meant for theinitial static
  analysis.
• Large Deflection is not supported fora
  buckling analysis.

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Solving the Model

• After setting up the model, solve the buckling
  analysis via the Solve button.
• A linear buckling analysis is more
  computationally expensive than a static analysis
  on the same model.
• If a Solution Information branchwas requested,
  detailed solutionoutput is available in the
  Worksheettab of that branch
• If stress or strain results or morebuckling
  modes are requested after a solution is
  performed, a newsolution is required.

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Reviewing Results

• After the solution, the buckling modes can be
  reviewed
• The Load Multiplier for each buckling mode is
  shown in the Details view. The load multiplier
  times the applied loads represent the critical
  load
• The buckling modes can be used to determine what
  the failure modes may look like

Model shown is from a sample Inventor part.
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Reviewing Results

• Interpreting the Load Multiplier (?)
• 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 (?)

Using the actual load
Using a unit load
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Reviewing Results

• The buckling load multipliers can be reviewed in
  the Worksheet tab of the Bucking 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 7 Linear Buckling

• Workshop 7 Linear Buckling
• Goal
• Verify linear buckling results in Simulation for
  the pipe model shown below. Results will be
  compared to closed form calculations from a
  handbook.

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