!function(f,b,e,v,n,t,s) {if(f.fbq)return;n=f.fbq=function(){n.callMethod? n.callMethod.apply(n,arguments):n.queue.push(arguments)}; if(!f._fbq)f._fbq=n;n.push=n;n.loaded=!0;n.version='2.0'; n.queue=[];t=b.createElement(e);t.async=!0; t.src=v;s=b.getElementsByTagName(e)[0]; s.parentNode.insertBefore(t,s)}(window, document,'script', 'https://connect.facebook.net/en_US/fbevents.js'); fbq('init', '366319058984917'); fbq('track', 'PageView');
24 January 2017

# Linear vs nonlinear buckling explained!

Choosing between linear buckling and nonlinear buckling in a given case can be difficult. Both approaches have positive and negative aspects. I explain here what are the differences, and when to use each analysis. I promise not to use complicated mathematics, nor highly theoretical approaches. Instead, I will use a simple example to easily describe differences.

## My first encounter with this problem

The Linear vs nonlinear buckling dilemma got to me when I started my Ph.D. in shell stability. As a civil engineer, I wasn’t really trained in FEA during my studies (apart from obvious programs for structural design). Modeling a shell for Abaqus or NX Nastran was definitely a challenge, but one I could quickly overcome. Problems started when I had to actually define an analysis type for my problem.

I quickly realized that there are far too many possibilities I have never heard about to choose from. The analysis called “buckling” obviously looked promising, and was my first bet 🙂 Later I realized that such an approach was frown upon by some of the “scientific” crowd, so I have searched for an alternative. That way (and thanks to Cornelia Doerich Ph.D. thesis!) I managed to learn about nonlinear buckling! It was then when something “clicked” for me, and I simply never looked at any engineering problem in the same way as before. If you have no experience with nonlinear analysis, I would greatly advise you to take a look – you will be surprised how incredible it may be!

## Linear vs nonlinear buckling: all you need to know

Below, you will see a short video, where I describe what are the differences in linear and nonlinear buckling on a simple shell example. If you have missed it, you can read on my blog about both linear buckling, and nonlinear buckling.

Happy watching 🙂

It is true! You can enroll for a free essential FEA course below.

#### Author:Łukasz Skotny Ph.D.

I have over 10 years of practical FEA experience (I'm running my own Engineering Consultancy), and I've been an academic teacher for a decade. Here, I gladly share my engineering knowledge through courses, and on the blog!

### Join the discussion

Negar - 2019-09-13 07:30:00

Hi Łukasz!
I have a 3D modeling of a cell buckling in Abaqus and I want to apply displacement to the top sheet of the cell. so first I defined The Eigenvalues by using a "linear perturbation buckling" step and apply a 1N force at top of the cell. then I use this Eigenvalues and and imperfections in the first model by editing the "keyboard" and apply the displacement at the top of cell. finally I got the results and Reaction Force- Displacement diagram. Now I want to now this modeling is a mixture of LNA and GNA? and my results including critical Force is True?
Thank,

Łukasz Skotny Ph.D. - 2019-09-13 19:58:30

Hey Negar!

I haven't used Abaqus in a decade or so, so the names escape me. Could you make some schematics of what you did so it is easier for me to understand and sent them to my email ([email protected]). I'm not sure if I follow the entire procedure you described and I don't want to misinform you by not fully understanding the situation :)

All the best
Ł

Harish - 2019-04-02 17:12:34

Hello Łukasz,
Great video but I have certain doubts regarding imperfection sensitivity factor that is given during non-linear buckling analysis. I usually take it as a certain percentage of the shell thickness ( 0.1 % to 100 %) i.e if the thickness of my structure is 10 mm then i will take 5 ( 50 % of thickness of the pressure vessel). Is this a correct way to do it ? can you please explain about imperfection sensitivity factors. Thanks in advance.

Łukasz Skotny Ph.D. - 2019-04-03 06:27:32

Hey!

This is a really tricky question. I mostly do shell design according to EN and in EN 1993-1-6 they actually introduced the methods to calculate how big imperfections should be. I don't use a "fixed percentage" imperfections in my work, but of course, this is very industry-specific. I can see a rationale behind doing so, ut 10% of thickness seems quite low... even though in relatively thick shells this actually may be reasonable I guess...

I hope this helps a bit? If you have any follow up questions shoot!

Andrew - 2018-05-05 03:06:49

Hi Łukasz,

Great tutorial! I'm wondering what constraints you used on the uniformly loaded shell on 4 columns example?

Thanks
Andrew

Łukasz Skotny Ph.D. - 2018-05-05 18:57:51

Hey Andrew!

Ha! That is a tough question after all this time :P I don't think this model "survived" to any of my archives as it was to simple to store.

Knowing me it was:

radial support on the top and bottom part, plus additional vertical support where the support actually is at the bottom. And then symmetry boundary conditions on the vertical edges.

If you have any more questions feel free to write - I will try to help out :)
Are you asking as you try to reproduce the outcomes? Any specific issues/

All the best
Ł

Joetox Goaline - 2017-01-31 08:13:25

My guess is the observed shape of the peak in the graph you show coordinating force with deflection will be less cornice-like and more like a bell if nonlinear material yielding is an influence to buckling.

Łukasz Skotny Ph.D. - 2017-01-31 10:44:22

Hey Joetox :)

I would say it depends. I completely agree that this might happen in some cases, however many buckling phenomenons appear in a strictly elastic regime with stresses far smaller that yield. And in those cases I would say we are still looking at the chart as I have shown.

My experience is that imperfections greatly reduce such "peaks" and "smooth things out"

Have a great day!
Łukasz