What is Geometrical Nonlinearity?

[suryamadduri]

I heard 3 reasons to use Geometrical nonlinear behaviour.
1)FE elements completely distoretd then will use Geometrical nonlinear behaviour.
2)If plastic strain is 6-10%
3)In metal forming process.

Can any body discuss with topic?

 

[Walterke]

If you look at this image you can see the table that shows the relation between the stress and the strain in steel. As you can see, in the first part of the table, there is a linear correlation between the two.
As long as your stresses stay inside this linear part, you can perform a linear analysis. Once the strains become too big however, the object will no react in a linear matter to the applied stresses. Hence, non-linear behaviour.

Another reason to use nonlinear is when the deformation of a structure in itself causes the applied loads to change, even if the material is still in the elastic deformation part.

NX 7.5
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[izax1]

My understanding of Geometrical Non-linearity is not what is shown in the image.
Geometrical non-linearity is typical: contact between surfaces, centrifugal stiffening and such phenomena.

 

[btrueblood]

Deflection of a rectangular beam to the point where its radius of curvature is more than 10% of its span is entering the realm of geometric nonlinearites - here the load path to the part becomes dependent on the deflection, which creates a geometric non-linearity (in the sense that the standard linear simple beam theory becomes increasingly inaccurate). Similar problems result from buckling, or more so post-buckling responses. Walter's post is about material nonlinearities.

 

[btrueblood]

As an aside...knowing where and when geometric nonlinearities come into play with FEA can be something of a grey area. Partly you gain knowledge of the boundaries of the grey areas when you study the element formulations (and limitations of the theory behind those formulations) in taking a BS or MS degree with some emphasis in FEM. Partly, you have a "gut feel" based on your experience when the model results just don't look right. And finally, in the end, you compare your model to experimental results, with the presumption that nature is not being capricious but is telling you honestly when you've loaded the part beyond its limits.

 

[suryamadduri]

btruebood,
thanks for your suggstions,

ya, i understand the your beam example. If suppose i have closed vessel. Is there any chance to vessel come into geometrical nonlinearity? my question is to what are the other parameters to components get in to the geometrical nonlinearity except radious of curvature.

 

[TGS4]

If you are doing pressure vessel analysis, then the code is very clear on when you activate geometric non-linearities, and when you do not.

My rule of thumb is that if the deflected shape will be stronger or weaker than the undeformed shape, then I will turn geometric non-linearities on. Of course, with this type of evaluation, you are automatically into the load-factor type of evaluation rather than the allowable stress type.