•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 {Dx} under essentially no
change in the load (beyond a small load perturbation).
•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.
•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:
–Material
response that is inelastic.
–Nonlinear
effects.
–Imperfections
in the structure which are not modeled (dents etc.).
•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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