Simple 1D Stress FE Model
 

Hello, I am reading a book about finite elements with regards to stress analysis. I'm pretty sure the book is full of mistakes, which makes following and doing the examples fairly difficult.
I have posted a 1D analysis from the book, I'm not even sure how he comes up with some of the numbers in the calculations.

I do understand the method but what hasn't exactly "clicked" is the sign convention or the displacement of each node equating to the change in element length. The author has (u1-u2), then on the last element he switches to (u4-u3), is there a reason for this or is it because u4 is the last node?

Would someone mind having a really quick look at the images I posted to give their oppinion. But definetely his answers do not satisfy the simulataneous equations.

Thanks a lot for your time.

http://img2.imageshack.us/img2/3816/scan0001xo.jpg
http://img203.imageshack.us/img203/8407/scan0002r.jpg
http://img242.imageshack.us/img242/3311/scan0003e.jpg
http://img43.imageshack.us/img43/5510/scan0004al.jpg

FEM beams
 

Hi Jonny,
just a quick glance to the rod in compression (I'm sorry but I haven't time to go in the details of formulas, especially for debug an error!).
If you are interested in beams I have developed a solver. First for FSI of cantilever beams in 2D and then a general one valid for 3d space frame.
You can take a look to this paper (in Italian) http://www.pcm.unifi.it/Aias/XXXI_CO...TI/PDF/149.pdf.
I have also a MathCAD worksheet implementation for 3d space frame (but I still haven't published a pdf version on the web); the version valid for plane stress is here: http://www.uniroma2.it/didattica/TCM..._piano_TCM.pdf.
We have also used 3d beam in FSI in the past: in this case you have to create an interface between the FEM nodes at the centre of the cross section and the CFD nodes on the actual skin.

MEB