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About basics of FEM

I am mahantesh, i am doing Mtech in design engg.  please tell me which books or articles i have to reffer so that i get good and depth knowledg of Finite element method.


Zhigang Suo's picture

The text by Zienkiewicz and Taylor has been a classic.  I looked at the text with great interest when I was a student.  Since I have never taught a full course on the method itself, I don't know if this text is suitable for learning the subject for the first time.  I'd be curious about recommendations by teachers and learners of FEM.

For nonlinear FEM, I like the text by Belytchko, Liu, and Moran.

In my course on solid mechanics, I have inserted several lectures on the basics of FEM, assigned homework using ABAQUS, and required a final project using FEM to study a phenomenon chosen by each individual student.  So in this course FEM is treated as a tool, like a calculator.  Here are the notes of my lectures on FEM.

It really depends on the reader's background.  In the introductory graduate course I teach on the FEM at Duke University, we use Tom Hughes' text The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. For undergraduates, I use Mike Gosz's text Finite Element Method: Applications in Solids, Structures, and Heat Transfer. 


The text by Zienkiewicz is my favorite . . . I have found the older, used editions available on Amazon or ABEbooks to be very useful.  Since you are new to FEM, you might consider a copy of Schaum's Outline of Finite Element Analysis as a good reference. 

For the undergraduate FEA course I am planning to teach next year, I will be using Logan's book A First Course in the Finite Element Method.

I was resisting the temptation to jump in, but here's what I think.

I learned FE theory from Oden's series of books - but I'm not sure that's the best place to start.  Students at Utah liked Logan's book for a beginning course.  Cook, Malkas, Plesha, Witt (CMPW) is also a failrly popular starting point.

Some of the things most introductory books don't cover very well are modal analysis and plates/shells.  In my experience, finite elements are most widely used in linear simulations of vibrations in structures consisting (at least partly) of shells.  I would recommend CMPW for students who would like to have an introductory book that can also be used as a reference later on.  

-- Biswajit 

WaiChing Sun's picture

Zienkiewicz and Morgan's book Finite Elements and Approximation (ISBN-13: 978-0486453019) is also a very good introduction for undergraduate students.

Alejandro Ortiz-Bernardin's picture

From the engineering point of view, the book that Professor Dolbow mentioned Finite Element Method: Applications in Solids, Structures, and Heat Transfer is notable and simple to read. Of course it is not a book in which you are going to find a lot of details or advanced things but it presents the basic of FEM so clearly. I find interesting how simple the author explains the nonlinear part which for many students (like me) would be a difficult task to start. This book will give you a broad knowledge of the method in several applications and in a simple manner. I would also suggest An Introduction to the Finite Element Method by J.N. Reddy which has more details on the mathematical formulation of the method but always maintaining an equilibrium between mathematics and engineering. 

There is also another book that might be interesting but (at least for me) sometimes the notation is not good:  Finite Element Procedures by K.J. Bathe. The good thing about this book is if you buy it you can get from the author a PDF file with the solution to almost all exercises in the book.

From the mathematics point of view, these books are the most famous (maybe not a complete list):

The Finite Element Method for Elliptic Problems by Philippe G. Ciarlet. If you are a SIAM student member you can buy it now for a great price since they are having a student book sale throughout October.

An Analysis of the Finite Element Method by Gilbert Strang and George Fix.

The Mathematical Theory of Finite Element Method by Susanne C. Brenner and L. Ridgway Scott.

I cannot say how good are they because I haven't read them deeply (too much complicated for me). For now, I prefer the engineering point of view.

If you are starting to learn the topic I would suggest trying first those books from engineering point of view.


Good luck,

Alejandro A. Ortiz

Dear Mahantesh,

You can also go through the "textbook of FEA" by Dr. P Seshu before going through Zinchewitch and Taylor.

You find the book by P.Seshu is more simpler than Zinchewitch and Taylor. After reading Seshu's book then you jump on Z & T..


Abhijit Nalawade.


Dear Mahantesh

If you are doing an MTEch in Design Engg I conclude you may be looking for a text less mathematical than most of those cited above (apologies if I am wrong!) If I am right then the Cook, Malkus & Plesha book is good, containing a mix of maths (although not too difficult maths), and practical advice. Bathe's book is similar.

Other books we use to teach UK undergraduate engineers are the books by RJ Astley and Ottosen and Petersson. A list of FE texts is available here.

Always try to flick through a copy before spending any money. Understanding from reading textbooks is not just a matter of choosing a highly-cited author, it depends on you connecting with the style. Irons's book on FE is written in an eclectic style that you wither love or hate. Also some texts (including one of those suggested in other posts) contain errors that are baffling to a new reader.

Of course you may just learn all you need form the lecture notes aorund on the web, but the same warnings apply.



Dear Mahantesh,

There are a lot of text books available on finite element analysis for purchase. But for a beginner at post-graduate level you could do perfectly fine with "Concepts and applications of Finite Element Analysis" by Cook, MAlkus Plesha and Witt. As I write this note to you, I have it in front of me lying on my worktable. It is One such book which you will probably read like a novel. The language is simply lucid. It filters easily.

Another one to go for, if you can't procure the above one is the one by David Hutton. Practical finite element analysis BY Liu is also an interesting and compact book with an insight shared over ABAQUS. The one by S S RAo is a recent one and is a good book to follow.

 These, my dear friend, are some of the options amongst other books.

Shubhankar Bhowmick

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