A very basic nonlinear FEA

[BeFEA]

Hello! I am trying to break though the nonlinear domain in Finite Element Analysis. However, everything I find on the Internet is either too long or too complicated. I was wondering if someone could explain me a very simple nonlinear model (for example, a nonlinear spring fixed at one end and axially loaded in the other end). Any brief explanation and/or links would be highly appreciated.
Regards!

 

[rb1957]

there are two types of non-linearity ...
1) material non-linearity, where fty is exceeded. a simple model is an open hole (a high Kt)
2) geometry non-linearity, where for example deformations increase the area of contact (ie close gaps).

another day in paradise, or is paradise one day closer ?

 

[IDS]

Further to what rb1957 said, the procedures to implement these two types of non-linearity are:

1: Calculate stresses with initial tangent elastic modulus (E) for all elements
- Recalculate E values based on calculated stresses.
- Repeat until change in E value and/or forces and deflections are acceptably small

2: Calculate deflections with initial undeformed shape
- Reform model with calculated deflected shape.
- Repeat until change in forces and deflections are acceptably small

You can (and usually do) do both of those at the same time of course.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[rapt]

I would have thought "non linear FEA" and "very basic" would be called an oxymoron!

 

[GregLocock]

Well, here's a non linear FEA that is hand coded.

Of course, it isn't a traditional FEA, but it is an analysis that uses discrete elements.

http://smath.info/wiki/GetFile.aspx?File=Examples/finger4.pdf

Cheers

Greg Locock

Cheers

Greg Locock


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[BeFEA]

Thank you rb1957 and IDS for your explanations. I already knew the types of nonlinearity. Since I am looking at the problem from a structural engineering point of view, I thought that an axially loaded nonlinear spring would be a good first example. The explanation of IDS is very helpful, thank you.

Thank you Greg Locock for the link, I will definitely check it carefully (it seems interesting and helpful for me).

@rapt: It may be indeed considered an oxymoron, but since I am not a beginner in linear FEA, I thought a soft transition into nonlinear could be possible