Buckling analysis is crucial to successful structure design and simulation, especially when thin structures such as shells and beams are involved. While linear buckling analysis is comparatively straightforward, it is limited by approximations and cannot simulate post-buckling phenomena. Nonlinear buckling analysis does not have these limitations and is therefore preferred, even if it is a little more complicated and requires some trial-and-error experimentation.
By analogy, it is also difficult in the physical world to determine the initiation of buckling. "From a scientific and engineering point of view, the interesting phases of buckling phenomena generally occur before the deformations are very large when, to the unaided eye, the structure appears to be undeformed or only slightly deformed."[1] To perform a nonlinear buckling analysis, special nonlinear analysis techniques are necessary to overcome the convergence difficulties, and a few trials are usually needed.
The following techniques are available for solving instability or buckling problems:
This capability deals with both local and global instabilities of buckling and can be used with any other nonlinear technique except the arc-length method.
This method deals only with global instability or buckling when forces are applied, and can simulate the negative slope region of a load-displacement curve.
Running a static problem as a "slow dynamic" analysis
This technique uses the dynamic effect to prevent divergence, but can be difficult to use.
For more information, see Unstable Structures in the Structural Analysis Guide.
This example uses a ring-stiffened cylinder under external hydrostatic pressure to demonstrate how to predict buckling loads and simulate post-buckling phenomena with the aid of nonlinear stabilization. The numerical simulation results are compared to the reference experimental results.[2]