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Buckling Under Dynamic Loading

April 24, 2014 By: Eric Stamper

Buckling may sometimes be thought of in terms of a gradual application of load until a structural collapse occurs. If that were the case, this scenario would represent the maximum amount of load that the structure could support before inducing buckling. The collapsed shape, or buckling mode, would be a unique response to the applied loading.

This case study explains a similar type of buckling analysis that was performed as an FEA consulting service by CAE Associates.

However; it’s possible for a single structure to exhibit many different types of buckling responses depending upon its physical characteristics.

A simple illustrative example is a tube subjected to an external pressure. An implicit buckling analysis performed with FEA software would predict that the lowest pressure that would cause buckling would deform the cylinder into two lobes (similar to what would happen if the air was slowly removed from an empty plastic soda bottle). There are, however, other possible shapes which the same cylinder could buckle into, i.e. three, four, etc. lobes as shown below.

What would cause a cylinder to buckle into a shape that would have more than two lobes? One possible situation that would drive a cylinder to buckle into one of these shapes is the rate of the applied load. If the external pressure is applied as a pulse load, it will drive different buckling modes depending upon the magnitude and time duration of the pressure pulse. Some examples are shown below. 

If the same cylinder is exposed to a range of pressure pulses, its buckling response will include rate dependencies. The dynamics of this system due to these varying pressures pulses were evaluated using an explicit FEA software and the chart below illustrates the cylinder’s response.

The area under the curve in the “No Buckling” region shows that when the pressure pulse is applied very slowly, the magnitude that will cause buckling is relatively low. However; if the pressure pulse is applied over a very short time duration, a significantly higher pressure can be withstood without causing buckling.

Once the right combination of magnitude and period of the pressure pulse has been reached to cause buckling, a range of possible buckling modes can be initiated (as shown previously). This chart demonstrates the rate dependency of a cylinder buckling, along with its resulting mode shape.

This type of information, derived as part of the FEA consulting process, is critically important if the structure will be subjected to a range of pressure pulses in service, so that the necessary strength can be designed into the structure and supports. An example design scenario could be the exhaust nozzle on a jet engine, which can experience a negative internal pressure pulse under a stall event.

More information related to performing implicit buckling analyses can also be found here.