Imperfections in buckling design

Using deformations from linear buckling as imperfections in nonlinear buckling case is the most common approach. I will use a simple example to prove that this is not always the best idea. Proper selection of imperfections is a very complicated process - I hope to shed some light on this matter.

Model

As you may know, I like to show complex problems on simple models. Today we will deal with small shell with some stiffening. Such solution can be often observed in silos structures in their support zones. Below you can see a model I will use (simplified for the task), and one of the silos I have designed with similar support (marked in red).

Such shell is usually loaded with friction (from the material inside), but at the bottom part we can almost assume that the load is vertical from the top. I used such approach in my simplified model as you can see above. Model is made from 1mm thick steel plate with stiffeners and rings 10mm thick. Total height and diameter is equal to 1000mm. Support is 10 degrees wide (around 87mm).

Outcomes from ideal model

I want to measure how imperfections influence the capacity of the model. This means I need a reference to compare to. The easiest is to calculate the capacity of the model without any imperfections, and use this value. Below are the outcomes from linear (LBA) and nonlinear (GNA) bucling without any imperfections (follow the links to read more about the methods, you can also join my free FEA course to learn more).

As you can see above, the linear buckling gave the multiplier of 0.6813 while nonlinear buckling is 0.4725. This means that the critical load is 200 x 0.6813 = 136.3 kN/m for linear buckling (200 kN/m is the load I have applied in my model). Note that the capacity drops in nonlinear buckling (without any imperfections) by 44% which is a big difference to start with!

To distinguish somehow the outcomes I will compare imperfection influence on linear buckling and nonlinear buckling separately on the same charts.

Imperfections from linear and nonlinear buckling shapes

Read the full text here!

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