Equations For Large Deflection Of Beams
when to use nonlinear finite element analysis | Product ...
Dig even a little bit into the different fea packages out there and you will notice a distinction between linear and nonlinear analysis. You might then wonder under what circumstances to use linear analysis and what circumstances to use nonlinear analysis?
First off, let me say that mechanically speaking, there is no such thing as a linear situation. That being said, there are circumstances under which a linear approximation is close enough. It’s just like when you neglected friction back in college, your answer isn’t going to be right, but maybe (just maybe) it’s right enough.
As an aside, one of my favorite ah-ha moments in college was when one of my professors, in explaining ‘accuracy’ vs. ‘precision’ said (i paraphrase)”even if you could measure things to an infinite precision, uncertainty prevents you from measuring with infinite accuracySo let’s get into it. The major circumstances that will dictate whether you should be using a nonlinear analysis are material stiffness, displacement, and contact.
material stiffnessSpecifically, I’m talking about the stiffness (Young’s modulus). If it’s been a while, Young’s modulus (or tensile modulus) is the slope of the elastic region (the far left) on a stress-strain diagram .
As you can see, the graph is linear up to the proportional limit. As you might imagine, the proportional limit marks the end of linearity. It is also around this point that the yield strength and elastic limit occur. Everything below this limit can be accurately approximated using a linear material model. This is often suitable for analyses because most designs typically try to stay well below the yield strength in order to maintain a healthy factor of safety.
But…
The stress-strain diagram I mentioned before ( this one ) is typical of metals. Plastics are a different story (and anisotropic materials are another story).
Just look at this set of stress-strain curves from Azom (one of the best materials sites ). Some plastics like ABS are linear for a stretch, others (like polypropylene and polyethylene) are not. To perform an accurate (not precise, FEA will give you precision regardless) analysis, you would need to crank the analysis up to nonlinear.
It’s worth noting that it can be difficult to get stress-strain curves for specific material.Equations For Large Deflection Of Beams - Bookshelf
Poroelastic structures
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