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28 March 2016

# Issues in result interpretation of nonlinear analysis

I think that one of the most difficult things about FEA (or really any other form of analysis) is an interpretation of results. Unfortunately in my engineering work, I have found many examples where people completely misunderstood what is the outcome of the analysis they have performed.

I will use an example to illustrate what I mean: we are designing a silo and the question is how much material load is allowed. To make things a bit simpler let’s assume that our silo is not very slender and we are more afraid of plastic collapse rather than stability failure (as it is easier to show plasticity on pictures to show my point, for steel silo that is usually not the case!).

If we would adopt the simplest of approaches to this problem, we would perform a series of calculations for different loads in silo (assuming nonlinear material and linear geometry since for now we forgo stability issues). The outcome of some of those calculations could look like this (von Misses stress, yield marked in red):

At the first glance, it is obvious that on the left are outcomes from models that have smaller loads, while on the right the loads were bigger. This is however exactly how many answers we can obtain from results presented this way, as unfortunately such drawings rarely are a proper result of calculations. None of the shown figures gives a definite answer to our question, since we do not know how much yielding (red zones) we can allow (and “none” would be a very conservative answer). However, I have received such contour plots as an outcome for the design I had to verify more often than I care to remember.

There is no simple solution to this problem. In my engineering carrier I have found that in most cases where you have to verify the load-capacity of the model, stability path (force – deformation plot) is a tool that can give a satisfying result. I will describe this more and give a few examples in the following posts.

Have a nice day!

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#### 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!

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### Join the discussion

Jakub - 2020-12-14 07:58:52

Hi Łukasz,

thanks for your post. I have a question, because when you are designing a silo you allow to yield steel but it means that occured deformations will be "forever" so what now? Does it mean that silo can't be use longer and require some repair?

Łukasz Skotny Ph.D. - 2020-12-16 23:40:11

Jakub,

This is a very long topic, concerning low cycle fatigue (that may or may not be a problem) as well as a general approach to design, etc. Let me tell you this: when you use a plastic section modulus of a beam, this means that you actually allow it to yield on the entire cross section. This will also cause permanent deformation etc. This is not the end of the world... but it can be in the "right circumstances"!

But to answer your questions, no plastic deformations do not mean that the silos need repairs :)

All the best!
Ł

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