Good source that teaches how to do FEA by hand?

[ngrstdnt]

I'm a beginner (started studying FEA a day ago), and I'm looking to be able to do the finite element method by hand, to find displacements/stresses for different modes, in order to verify the results given by PATRAN (sorry I'm pretty sure all of my terminology here is correct). I've found a lot of good explanations/examples for doing this with, say, a rod, or a simple truss (something that has only 2 or 3 degrees of freedom), and I have a decent understanding of it. I get completely stumped when I try to apply these methods to shells, with four nodes and 6 DOFs (or anything that is 2D or 3D basically), and can not find any good resources (I have PATRAN/NASTRAN manuels and the internet at my disposal). If anyone might know of a good online source (or a textbook, if not an online source) that does a good job explaining how to do these hand calculations? Thank you so much for your time I really appreciate it!

 

[GregLocock]

Roark has the formulae, and a bit of discussion about how they are derived, but it is more of a refresher than a tutorial. It's an essential reference, so get it anyway.

http://www.amazon.com/gp/product/007072542X/002-0475928-0925603?v=glance&n=283155

If after looking at Roark you need a more in-depth derivation then I never found a really good structures textbook,

http://www.amazon.com/gp/product/03...002-0475928-0925603?s=books&v=glance&n=283155

was OK (now unavailable), and foolishly I sold my copy. If you really want to dazzle your friends and never have to buy a beer again then

http://www.amazon.com/gp/product/09...002-0475928-0925603?s=books&v=glance&n=283155

is another terrific resource. Again, rather light on derivations but it is a bit more explanatory than Roark, although it doesn't have quite as many wild and whacky loadcases as Roark.

Cheers

Greg Locock

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

 

[corus]

I don't know why you'd want to do finite elements by hand as the method largely came about because computers were able to handle the large number of arithmetic operations needed. However, An introduction to finite element computatiosn by Hinton, and Owen has the basics plus fortran code for most of the element types.

corus

 

[rb1957]

i think this is an excellent way to LEARN FEA; and i encourage your approach.

Bruhn has a nice section on matrix methods.

"Understanding Finite Element Stress Analysis" by Robinson is another excellent primer.

make some simple models, beams and trusses for example, that you can analyze by hand as a start. then more complicated structures (redundant beams). start modelling shells by modelling single elements.

you will learn alot about how the elements work, when they work well, and more importantly when not !

good luck

 

[jbaylor]

I have written a few custom FEA applications and have found that Cook is a great reference to start with (ISBN 0471356050). If your purpose for this exercise is to understand FEA theory better, then I recommend picking this book up and writing an application with a few simple elements. You will learn a lot from the process.

If you are looking for ways to validate your models with hand calculations, I agree with GregLocock that Roark is _the_ place to start. I also agree that Bruhn is a good book to have, especially if you are doing aerospace work. You will want to find a copy of the index though, it does not come with one.

I also have to add the various Timoshenko books to the list. They are great references especially if you are looking at plates and shells or elastic instability.

Regards,
Jeff

 

[ngrstdnt]

Thank you very much for the replies. I've managed to get my hands on the Roark book, and I am looking into the others. These responses have been very helpful thank you for taking the time to post them!

 

[GregLocock]

<corus>. sorry I got the impression he was also trying to validate the models by doing a hand analysis, rather than manually calculate an FE calculation. Either way, he'll need Roark sooner rather than later.

Cheers

Greg Locock

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