Mathematical Solution Theory on FEM 4

[nhcu0lt]

Hi,
For years I been working with FEM software. I also been doing my master degree working with the mathematical approach. My question is concerned with proccedures to solve the models ecuations to make the finite element approach. In fact, I been programing some small problems in solid mechanics. The point is that I would like to find some documentation about the programing methods in FEM. I know Modulef that is an open source software, but the mathematical model is not in the manuals.
I will appreciate any comments.
Agustin.

 

[pja]

Any book on FEM will go into the mathematical details...I'm not quite sure
on what you are looking for. Are you looking for theory on how the discretized equations are solved using linear algebra methods or are you looking for info on how the equations are developed starting with the theory of virtual work. If it's the latter than any decent book on FEM will go into this. For linear algebra techniques search for sparse equation solver techniques,

 

[JWB46]

Have a look at 'Techniques of Finite Elements' by Irons and Ahmad. It's not an easy book, but its the classic text for your question.

Hope this helps.

 

[manam]

There is a new book by Babuska and Strouboulis. It has very good mathematical foundations of FE theory.

 

[hombre]

Don't forget about Finite Element Procedures by Bathe and Finite Elements: Their Design and Performance by MacNeal (of MSC fame)!

Hombre

 

[nhcu0lt]

thanks,

 

[ThomasH]

I agree that both Finite Element Procedures by Bathe and MacNeals books are good. The others I'm not familiar with.

To me the "reference" is: The Finite Element Method by O.C. Zienkiewicz et al. I believe they now have three volumes that should cover quite a lot. (My version is a two volume set). But you can't call it "easy reading".

Good Luck

Thomas

 

[manam]

IMHO, Bathe's book is just a confusing bundle of notation and arachaic definition. It is definitely only for those who want to study the history of FEA !