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Linear Buckling Analysis

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Chapter Seven Linear Buckling Analysis Chapter Overview In this chapter, performing linear buckling analyses in Simulation will be covered. In Simulation, performing ... – PowerPoint PPT presentation

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Title: Linear Buckling Analysis


1
Linear Buckling Analysis
  • Chapter Seven

2
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.

3
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).

4
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.

5
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.

6
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

7
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
    yi Assumptions
  • 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.

8
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

9
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

10
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.

11
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.

12
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.

13
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.

14
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.

15
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 the initial static
    analysis.
  • Large Deflection is not supported for a
    buckling analysis.

16
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 branch was requested,
    detailed solution output is available in the
    Worksheet tab of that branch
  • If stress or strain results or more buckling
    modes are requested after a solution is
    performed, a new solution is required.

17
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.
18
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)

19
Reviewing Results
  • Interpreting the Load Multiplier (?)

Using the actual load
Using a unit load
20
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.

21
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.

22
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