Buckling Factor without imperfection < Buckling Factor with imperfection (?!)

[EngineerMickeyMouse]

Hi gents,

As per figure below, I have performed simple test for beam in Critical Buckling Load linear analysis.

First model is beam without any imperfection introduced. Buckling Load Multiplier (BLM) is 65.

Second model is based on scaled unitless deformation from the first model, hence imperfection is introduced.

Similar Critical Buckling Load linear analysis is performed, now BLM is 165. Loading and supports the same.

What is going on, do you have any suggestions? One shall expect that with imperfection BLM should be less, but not higher than without imperfection modelled...

[John_Holtz · Accepted solution]

Hi E.M.M.

I never gave it much thought, so the following may not be entirely correct. But it probably depends on what the "mode shape" is when the model buckles and whether the "imperfect" shape makes that buckling mode stronger or weaker.

I did a test on a simply supported beam (modeled from plate elements) with a compression load. (If I had oriented to that the beam was vertical, it would look like a column. Oh well, it's late.) Notice that the buckling load multiplier is 52, and the shape is that the flanges will buckle locally. The beam is not buckling like a banana that we are used to seeing from textbook calculations. See the attached image "beam - no imperfections.png".

Then I exported the displaced shape to a new model (with the scale factor set to 1, not the highly exaggerated shape shown in the image). Just as you found in your model, the buckling load is now much higher (180. See "beam - with imperfections.png"). What I notice is that the areas that buckle are the flange and web that are closest to being flat in the "undeformed" shape. The wavy flange is not buckling.

So, the question is whether a flat plate is weaker, stronger, or the same stiffness as a wavy plate when it comes to localized bending. I do not know the answer from a theoretical view point.

In my mind, I am thinking of something like corrugated sheet metal used for a roof. The corrugations make it stronger in one direction of bending compared to a flat sheet. Maybe the wavy buckling mode of the flat sheet makes the flange in my example stronger.