44774944-ansys-workbench-buckling.ppt 4g4w6p

Chapter Seven

Linear Buckling Analysis


Chapter Overview

Training Manual

– In Design Simulation, performing a linear buckling analysis is similar to a stress analysis. – It is assumed that the 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.

ANSYS Workbench - Simulation

• In this chapter, performing linear buckling analyses in Design Simulation will be covered.

– Harmonic and nonlinear static structural analyses are not discussed here but in their respective chapters. February 2, 2004 Inventory #002010 7-2


Background on Buckling

Training Manual

• 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). F

F Stable

Unstable


• Many structures require an evaluation of their structural stability. Thin columns, compression , and vacuum tanks are all examples of structures where stability considerations are important.

February 2, 2004 Inventory #002010 7-3


… Background on Buckling

Training Manual

• The eigenvalue formulation determines the bifurcation points of a 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.


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




Training Manual

– Consider the buckling of a soda can: • Material response is inelastic. Geometrically nonlinear effects need to be considered. is also required. Hence, these type of nonlinear behavior are not considered. • There may be slight imperfects 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.


• However, 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.




Training Manual

– 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


• Although unconservative, linear buckling has various advantages:



A. Basics of Linear Buckling

Training Manual

– A linear static analysis can include the stress stiffness matrix [S], which is a function of the stress state:

K   S x  F

– If we consider the analysis to be linear, we can multiply the load and the stress state by a constant l:

K  lS x  lF – In a buckling mode, displacements can be large (x+y) without an increase in load, so the following is also true:

K  lS x y   lF


• The idea behind performing linear buckling is that a bifurcation point is sought. The bifurcation point is where two configurations – the initial geometry and a buckled mode – are both possible, signifying the onset of buckling.



… Basics of Linear Buckling

Training Manual

K  lS y   0

– The above equation is what is solved for during a linear buckling analysis. • The buckling load multiplier l is multiplied to the applied loads to get the critical load for buckling • The buckling mode shape y expresses the shape of buckling. However, the magnitude is not known since y is indeterminate. • There are actually many buckling load multipliers and modes, although the is usually interested in the first few modes since these would occur before any higher buckling modes.

• Note the similarity of linear buckling equation with the free vibration equation (Chapter 5). Both are known as eigenvalue problems which are solved for with similar matrix methods.


– If the last two equations are subtracted from each other, the following is the result:




Training Manual

– A linear static analysis is performed first:

K xo   F 

– Based on the stress state from the static analysis, a stress stiffness matrix [S] is calculated:

 o   S 

– The aforementioned eigenvalue problem is then solved to get the buckling load multiplier li and buckling modes yi:

K   li S y i   0


• For a linear buckling analysis, two solutions are automatically performed internally:




Training Manual

K   li S y i   0

This results in certain assumptions related to the analysis: – [K] and [S] are constant: • Linear elastic material behavior is assumed • Small deflection theory is used, and no nonlinearities included • The response based on loading {F} is a linear function of li

– Some additional restrictions: • Nonzero displacement s or thermal loads are not allowed


• For a linear buckling analysis, the eigenvalue problem below is solved to get the buckling load multiplier li and buckling modes yi:

• It is important to these assumptions related to performing linear buckling analyses in Design Simulation. February 2, 2004 Inventory #002010 7-10


B. Buckling Analysis Procedure

Training Manual

– Attach Geometry – Assign Material Properties – Define Regions (if applicable)

– Define Mesh Controls (optional) – Include Loads and s – Request Buckling Results – Solve the Model

– Review Results


• 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.



… Geometry and Material Properties

Training Manual

– 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.

• For material properties, Young’s Modulus and Poisson’s Ratio are required as a minimum

ANSYS License DesignSpace Entra DesignSpace Professional Structural Mechanical/Multiphysics

Availability x x x x x


• Similar to linear static analyses, any type of geometry ed by Design Simulation may be used:



… Regions

Training Manual

Type Bonded No Separation Rough Frictionless

Initially Touching Bonded No Separation Bonded No Separation

Linear Buckling Analysis Inside Pinball Region Outside Pinball Region Bonded Free No Separation Free Free Free Free Free

• It is important to note the following: – The pinball region will influence some types of – All nonlinear types are reduced to either “Bonded” or “No Separation” . • No Separation should be used with caution in buckling analyses, as it provides no stiffness in the tangential direction. This may produce some superfluous buckling modes. Consider using bonded instead, if appropriate. ANSYS License DesignSpace Entra DesignSpace Professional Structural Mechanical/Multiphysics


• regions are available in buckling analyses. However, since this is a purely linear analysis, behavior will differ for the nonlinear types:

Availability x x x x



… Loads and s

Training Manual

– All structural loads will be multiplied by the load factor to determine the buckling load. Hence, non-proportional or constant loading is not directly ed (see next slide) – No Given Displacement s are allowed – No Thermal loading is allowed

– Compression-only s are nonlinear, so they are not recommended for use in buckling analyses

• The structure should also be fully constrained – No rigid-body motion should be present in the model. Be sure to constrain the model appropriately.




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



… Loads and s

Training Manual

– The 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.




• Special considerations must be given if constant and proportional loads are present.



… Requesting Results

Training Manual

– The Buckling tool adds another branch to the Solutions branch – The Details view of the Buckling branch allows the 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. ANSYS License DesignSpace Entra DesignSpace Professional Structural Mechanical/Multiphysics


Although most s are only concerned with the first buckling mode, it is generally a good idea to request the first 2 or 3 buckling modes. There may be closely-space buckling modes, so this would tell the if the model may be susceptible to more than one failure mode.


• Most of the options for buckling analyses are similar to that of static analysis. However, Design Simulation knows to perform a buckling analysis when the Buckling tool is selected under the Solutions Branch:




– The buckling modes are controlled by the number of modes to find under the Details view of the Buckling branch – Stress, strain, or directional displacement results can be requested additionally 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 result may be requested directly under the “Solution” branch. ANSYS License DesignSpace Entra DesignSpace Professional Structural Mechanical/Multiphysics



• Requested results are located under the Buckling branch:

Training Manual




Training Manual

– A static analysis with PSTRES,ON is performed first – A buckling analysis (ANTYPE,1) is then run with PSTRES,ON – The buckling modes is set with BUCOPT,LANB,nmodes • The eigenvalue extraction method is always set to Block Lanczos, regardless of the “Solver Type” setting in the Solutions branch

– Output requests are limited to what is requested • If any stress or strain results are requested for any modes, the stress results are expanded with MXPAND,,,,YES. Otherwise, MXPAND is not used.

Advanced ANSYS Details


• The corresponding ANSYS commands for the Buckling tool are as follows:



… Solution Options

Training Manual

– For a buckling analysis, none of the options in the Details view of the Solution branch usually need to be changed. • In the majority of cases, “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 also meant for the initial static analysis. • “Large Deflection” is not ed for a buckling analysis.

– The “Analysis Type” will display “Buckling” for the case of a linear buckling analysis.




• The solution branch provides details on the type of analysis being performed



… Solution Options

Training Manual

– “Solver Type” can be set to “Direct” or “Iterative,” but it only sets the equation solver for the static analysis (EQSLV), not the buckling eigenvalue extraction method (BUCOPT) – “Weak Springs” are meant for the initial static analysis • One can use „weak spring‟ option to automatically add COMBIN14 elements for the initial static analysis, but keep in mind that these elements will also be present for the buckling analysis.

– “Large Deflection” is not ed for a linear buckling analysis

Advanced ANSYS Details


• For a linear buckling analysis, none of the solution options have effect. These affect the initial static analysis only.



… Solving the Model

Training Manual

– A linear buckling analysis is more computationally expensive than a static analysis on the same model. This is because a static analysis and a buckling analysis are both performed. – The Worksheet tab of the Solution branch provides detailed solution output, including the amount of memory being used and how many modes have been extracted already. – If stress or strain results or more buckling modes are requested after a solution is performed, a new solution is required. ANSYS License DesignSpace Entra DesignSpace Professional Structural Mechanical/Multiphysics



• After setting up the model, one can solve the buckling analysis just like any other analysis by selecting the Solve button.



… Reviewing Results

Training Manual

– The Load Multiplier for each buckling mode is shown in the Details view. The load multiplier times the actual loads represent the critical load. – The buckling modes represent relative values, not absolute magnitudes. However, these can be used to determine what the failure modes may look like.



Model shown is from a sample Inventor assembly.


• After the solution, the buckling modes can be reviewed



… Reviewing Results

Training Manual

– All requested modes will be summarized in the table below – As mentioned earlier, it may be advisable to request more than just the first buckling mode. This allows the to see if the structure may be able to buckle in more than one way under a given applied load.




• The buckling load multipliers can be reviewed in the Worksheet tab of the Bucking branch.



C. Workshop 7

Training Manual

• Goal: – linear buckling results in ANSYS Workbench for the pipe model shown below. Results will be compared to closed form calculations from a handbook.


• Workshop 7 – Linear Buckling


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