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• 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).
•
•
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.
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May 5, 2009 Inventory #002593
Linear Buckling
B. Buckling Analysis Procedure
Training Manual
• A Static Structural analysis will need to be performed prior to (or in conjunction with) a buckling analysis. The steps in italics are specific to buckling analyses.
– – – – – – – – – – – Attach Geometry Assign Material Properties Define Contact Regions (if applicable) Define Mesh Controls (optional) Include Loads and Supports Solve Static Structural Analysis Link a Linear Buckling Analysis Set Initial Conditions Request Results Solve the Model Review Results
– 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).
• For material properties, Young’s Modulus and Poisson’s Ratio are required as a minimum
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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May 5, 2009 Inventory #002593
Linear Buckling
… Geometry and Material Properties
Training Manual
Linear Buckling
Chapter Overview
•
Training Manual
In this chapter, performing linear buckling analyses in Mechanical will be covered. Contents:
A. Background On Buckling B. Buckling Analysis Procedure C. Workshop 7-1
• The way in which a structure may buckle can be used as a possible guide in design
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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May 5, 2009 Inventory #002593
([K] + λi [S]){ψi } = 0
Assumptions:
– [K] and [S] are constant:
• Linear elastic material behavior is assumed • Small deflection theory is used, and no nonlinearities included
Linear Buckling Analysis Inside Pinball Region Outside Pinball Region Bonded Free No Separation Free Free Free Free Free
Contact Type Bonded No Separation Rough Frictionless
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May 5, 2009 Inventory #002593
Linear Buckling
… Background on Buckling
Training Manual
• Although unconservative, linear buckling has various advantages:
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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May 5, 2009 Inventory #002593
Linear Buckling
A. Background on Buckling
Training Manual
F
Stable Unstable
F
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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May 5, 2009 Inventory #002593
Linear Buckling
… Background on Buckling
Linear Buckling
… Basics of Linear Buckling
Training Manual
• For a linear buckling analysis, the eigenvalue problem below is solved to get the buckling load multiplier λi and buckling modes ψi:
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May 5, 2009 Inventory #002593
Linear Buckling
… Contact Regions
Training Manual
• Contact regions are available in free vibration analyses, however, contact behavior will differ for the nonlinear contact types exactly as with modal analyses. • Discussed earlier (see chapter 5).
– Material response that is inelastic. – Nonlinear effects. – Imperfections in the structure which are not modeled (dents etc.).
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– The eigenvalue buckling solution of a Euler column will match the classical Euler solution.
• Imperfections and nonlinear behavior prevent most real world structures from achieving their theoretical elastic buckling strength. Linear buckling generally yields unconservative results. • Linear buckling will not account for:
• 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.
• It is important to remember these assumptions related to performing linear buckling analyses in Simulation.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
• 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
Workbench - Mechanical Introduction 12.0
Chapter 7 Linear Buckling Analysis
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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May 5, 2009 Inventory #002593
• 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)
Training Manual
• 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.