Best Introduction/Fundamentals of Finite Element Methods Texts

In summary: I find it more difficult to find an intro FE book that is good. 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'.
  • #1
karakoos23
6
0
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
 
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  • #2
...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.
 
  • #4
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.
 
  • #5
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 ... :tongue2: .
 
  • #6
Vanechka said:
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 [tex]\frac{d^2 u}{dx^2}[/tex] he uses [tex]u_{,xx}[/tex]. Perhaps the benefit of such notation will be seen later on in the book (?) ...
 
  • #7
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.
 
  • #8
radou said:
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.
 
  • #9
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).
 
  • #10
hotvette said:
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.
 
  • #11
Brenner and Scott book is the best ever. It is a must if you are serious about finite elements.
 

What is Finite Element Method?

Finite Element Method (FEM) is a numerical method used to solve engineering problems by dividing the problem into smaller, simpler parts called elements. The solution is then obtained by assembling the solutions of these elements.

Why is it important?

FEM is important because it allows engineers and scientists to solve complex problems that cannot be solved analytically. It is also a versatile method that can be applied to different types of problems in various engineering disciplines such as structural analysis, heat transfer, fluid mechanics, and electromagnetics.

What are the key components of FEM?

The key components of FEM are the discretization of the problem into smaller elements, the formulation of element equations, the assembly of element equations into a global system, and the solution of the system to obtain the final solution.

What are some popular texts for learning FEM?

Some popular texts for learning FEM include "The Finite Element Method: Its Basis and Fundamentals" by O.C. Zienkiewicz and R.L. Taylor, "A First Course in the Finite Element Method" by Daryl L. Logan, and "Introduction to Finite Element Analysis Using SOLIDWORKS Simulation" by Randy Shih.

What are the prerequisites for learning FEM?

A strong foundation in mathematics, specifically calculus and linear algebra, is essential for learning FEM. Familiarity with programming languages such as MATLAB or FORTRAN is also helpful. Additionally, a basic understanding of mechanics and engineering concepts is recommended.

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