linear vs. non - linear analysis 2

[cgelsi]

Are there any general guidelines as to when to use a non-linear analysis vs. a linear analysis?
I don't mean code specific or structure specific...for example if your out of plane deflection exceeds x percent of your part thickness, things of that nature.


Thanks

 

[johnhors]

I wouldn't say that there are any such guidelines. It's probably down to what is considered to be reasonable and acceptable error in any particular model when run linearly, and whether a non-linear analysis would improve matters by raising the confidence in reported results, OR NOT. If you have accurate material plastic-strain curves, a clear understanding of what is actually happening in real life.... and many other factors which tend to make linear analysis seem like child's play in comparison.

Also standards and required levels of accuracy tend to vary depending on the industry in which you work.

You may find this link (and web site interesting):-

http://www.dermotmonaghan.com/feInformation/solutionTypes/nonLinear.php

 

[cgelsi]

Good link, thanks! What I had heard considered only material plasticity as the factor for when to switch to a non-linear analysis, so it is good to know about the other effects. A linear analysis seems to be possible anyway though by reducing the material properties by a factor (approximating the non-linear side of the stress strain curve)...this, like you say, depends on how much accuracy you need out of a model.
Are there cases when running a non-linear analysis would actually take you further from the real result?

 

[feadude]

All structural problems are nonlinear in nature. However most of the times a linear analysis is a good approximation. For example for a plate that is fixed on all 4 sides , if out of plane deflection is more than 1t, then stress stiffening makes the problem nonlinear, but the same plate in a cantilever mode (fixed in one side only) is linear for 1t. Another good example where (material) nonlinear analysis is a must is when you run linear fea on a steel part for example and you find out that stress in a location has exceeded the yield, in this case all the linear stress results that exceed yield are useless because after yield steel does not behave per Hook's law.

good57morning@netzero.com

 

[gwolf]

I find that in structural analysis, nonlinear analysis is rarely needed below the yield point of the material. Even above yield there are hand calcs such as Neuber which give a reasonably good correction from elastic to elastic-plastic stresses.

The one exception to this is thin plates as feadude suggests. These structures frequently require nonlinear analysis when the plate deformation allows a redistribution of load from bending to membrane. Given that the linear bending stresses are usually higher than the nonlinear bending/membrane stresses, one does not tend to underestimate the resulting stresses.

 

[mloew]

This topic has been covered before. Please see the FAQ Resources for Non-linear Analysis (faq727-833).

Best regards,

Matthew Ian Loew


Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[feadude]

gwolf:
Neuber correction can be used for fea nonlinear analysis of complicated structures?

good57morning@netzero.com

 

[gwolf]

feadude,

You use Neuber to estimate an elastic-plastic stress at a stress concentration feature starting from an elastic stress from a linear FE analysis.

 

[gio1]

Any reason causing a variation in stiffness of the assembly being analysed is potentially a source of non-linearity and therefore requires a non-linear analysis to be captured.
It is widely accepted that the three main sources of non-linearity are:

- Plasticity of material (variation of the material Young's modulus will cause the stiffness of the structure to change)

- Large displacements (Stiffness varies as a result of large geometric difference between the initial and deformed shape)

- Contact: if two parts or bodies of the assembly come into contact, or lose contact, or the extent of their contact patch changes, then the stiffness of the assembly also varies.

 

[GBor]

gio1,

Could you be a little clearer in "variation in stiffness"? One such variation is precisely what you are referring to when you talk about the variation in Young's modulus...varying the Young's modulus for plates or beams varies the stiffnes...I'm assuming you are referring to some other stiffness alteration?

I suspect the answer to your question is, "yes". If the material stiffness varies, you must input some type of curve properties. If you are simply referring to periodically stepping down to smaller beams under a plate, then you don't necessarily have to do this non-linearly.

Garland

Garland E. Borowski, PE
Borowski Engineering & Analytical Services, Inc.

http://www.borowskiengineering.com

 

[gio1]

One thing is the stiffness of the material (Young's modulus measured from axial tests). Another thing is the stiffness of the structure, which depends on a lot of factors: type of restraints, number/type of bolts or other fasterers, and of course also depends on the type of material (young's modulus).

The behaviour of the WHOLE STRUCTURE under the effect of loads can be non-linear (the stiffness of the structure varies) even if the stress in the material does not exceed the plastic limit anywhere (the stiffness of the material does not vary). Points 2 and 3 from my previous post are possible reasons of this effect

 

[GregLocock]

Also anything involving gas springs, and many types of rubber spring, and anything with non -proportional damping, such as friction and stiction and most real world damping systems, will have to either be linearised or analysed non-linearly.


Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[DRDearth]

My input would be that before you charge off into a non-linear analysis I would investigate your linear approach. For example, if you feel a non-linear model is necessary due to high localized stresses, then search around for the magnitude of stresse/strain components in the local region adjacent to regions of high stress/strain. If stress gradients are high (i.e. stress levels dissipate rapidly over short distances away from regions of high stress) then one can assume some local yielding. A non-linear material model will be the best way to estimate the extent of local yielding.

But if overall deflections are beyond "rules-of-thumb" for deflections as a ratio of overall geometry then non-linear large deflection models might be needed.


David R. Dearth, P.E.
Applied Analysis & Technology