Finite Element Stress Analysis: Best Way to Get Accurate Results?

[OffTheRecord]

What's the best way to do Finite Element stress analysis?

By that, I mean I'm looking for the best set of general fundamental assumptions to start with. In your opinion.

I ask because I'm trying to write a computer code in Matlab that I can use as a general tool for who-knows-what sort of problem might come up. I want it to be versatile. Precision is second to versatility, because I can always find ways to simplify problems when they arise. I want to start from a fairly general set of underlying assumptions.

Here's what I've tried so far: the Hooke's law normal and shear stress equations, in terms of strain. Namely, σ = Eε (plus some function of Poisson's ratio), and τ = Gγ.
σ is normal stress caused by 2 teeny weeny pieces of material moving towards each other.
τ is shear stress caused by 2 teeny weeny pieces of material sliding past each other.
ε is essentially the amount of stretching caused by σ.
γ is the angle by which one side of said teeny weeny piece gets dragged forward compared to the other side, by τ.
E and G are natural constants.

The problem I'm having: when I plug those equations into a big matrix full of many tiny little pieces, I don't quite get the right answers. I'm plugging these equations into a classic cantilever-bending model (i.e. guy standing on end of diving board), and plotting the results to see if the big picture looks right. Sometimes it does look almost right, but it's very finicky. If I change the size of the system or the natural constants E and G even slightly, I tend to come out with a wildly different-looking beam each time.

Anyone know a better way to model a solids problem? Ignore shear? Add some more assumptions? Let me know your thoughts.

 

[AlephZero]

If you want to write your own software, get a good book on the FE method, or go to
http://www.colorado.edu/engineering/CAS/courses.d/IFEM.d/

(The UC website seems to be off line right now - maybe they are recovering from wildfire damage or something.)

But if you just want to create FE models and run them, getting an open source FE program and will save you months (or even years) of programming work.

 

[OffTheRecord]

yeah... i read a book and found some open source stuff. I kinda want to write my own anyway to get some understanding of the internals.

I actually found a site where the guy wrote a bunch of FEA's in Matlab... got the code... read through it. It was extremely complicated: more so than I deem necessary. So I went to the library and found a book on it. Turns out the book I picked up used the exact same methods he did (down to the variable names)... I'm pretty sure he read the same book. That was equally overcomplicated.

I don't really want (or need) to talk about the programming. I'd prefer to discuss the engineering aspect. What are the basic assumptions that work best?

 

[OffTheRecord]

on a side-note, that link was very helpful!