Best Introduction/Fundamentals of Finite Element Methods Texts

[karakoos23]

Hi! Anyone know what would the best INTRODUCTION / FUNDAMENTALS of Finite Element Methods oriented text be? I had read O. C. Zienkiewicz’s The Finite Element Method: Its Basis and Fundamentals, 6E, Butterworth-Heinemann … No practice problems at all, un-systematic, etc. Any advice would be highly appreciated

 

[PerennialII]

...as a first book I might recommend Reddy's Introduction to the FEM ... Zienkiewicz is an excellent book but I wouldn't "learn" FEM from it, but rather read it when a bit more seasoned.

 

[radou]

I have the same question.

What about "The Finite Element Method: Linear Static and Dynamic Finite Element Analysis" by Thomas J. R. Hughes ? Just found it on Amazon. Anyone read that book? It's pretty cheap and seems to be rather comprehensive.

 

[radou]

An update related to the upper book; I ordered it, and it arrived a few days ago. I've started reading it, and, for now, I'm more than satisfied.

 

[Vanechka]

I've always enjoyed stuff by Hughes the book included ... it's "intense" and complete. He flips every stone and the notation & math in particular are way above average I'd say. Perhaps the book is slightly light in terms of treatment of nonlinear aspects, but excellent in any case. Best book to start ... not perhaps the easiest but if one doesn't mind it's a great read and worth every spent hour ... .

 

[radou]

He flips every stone and the notation & math in particular are way above average I'd say.

Right, I found some pretty interesting notation I've never seen before, for example, instead of writing $$\frac{d^2 u}{dx^2}$$ he uses $$u_{,xx}$$. Perhaps the benefit of such notation will be seen later on in the book (?) ...

 

[Vanechka]

Don't know about the benefits but he seems to take elements from tensor analysis and FE as presented by "mathematically-oriented-FE-people" quite extensively (I personally appreciate the notation of his long-time co-worker Ted Belytschko probably most). Reminds of Zienkiewicz in terms of general continuum mechanical expressions, douped with how "math people" present their variational formulations for general solution of PDEs using FEM -- when working with notation heavily influenced by expressions of various spaces (Hilbert spaces and so on, when defining function spaces added with suitable scalar products++). At least the resulting notation doesn't lead to a book which would look too elementary.

 

[hotvette]

An update related to the upper book; I ordered it, and it arrived a few days ago. I've started reading it, and, for now, I'm more than satisfied.

I'm curious, are there any example problems? For me, understanding is far easier with detailed example problems. I've been looking for a good intro FE book for a long time and never found one I thought lived up to the word 'intro'. I also have Zienkiewicz but need a preliminary introduction before tackling it.

 

[uiulic]

You have overcome Zienkiewicz, then why need another better introduction of FEM.
Oden, Owen, Belytschko, etc could be a further reading, depending on your interest.I used Kikuchi (finite element methods in mechancis) in my class, which is ok for a beginner.
Fung and Tong (2001, classical and computational mechanics) give a good introduction to FEM (its introduction is very easy for anybody to understand) as well as a good introduction to solid mechanics. I now find any FEM book (so long as it can be published) gives good introduction actually, as grasping the basic computational aspect of FEM is not a big business.
If you have mastered the theory of FEM, you do not need another better introduction.What you need might be a FEM code by yourself (at least for solving a simple question even though there is a ready-made one).

 

[radou]

I'm curious, are there any example problems? For me, understanding is far easier with detailed example problems. I've been looking for a good intro FE book for a long time and never found one I thought lived up to the word 'intro'. I also have Zienkiewicz but need a preliminary introduction before tackling it.

Well, so far, there are various solved example problems, often about linear elastostatics and heat conduction.

 

[timur]

Brenner and Scott book is the best ever. It is a must if you are serious about finite elements.