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This is my first question in this medium, which has helped me at many times. Perhaps, for that reason, it is not well posed or formulated.

I would be interested in starting, on my own, in the finite element method. I have consulted on the Internet several manuals and web pages on the fundamentals and some applications of this method.

Most of the time, I am confronted with long mathematical developments that I do not understand.

Also, I cannot find any freely available software that would allow me to carry out a simple simulation.

So, I ask you to recommend me some book or web that, from a simple point of view, can introduce me to this method. Also, although this concerns me less, I hope you can recommend me some freeware to be able to perform, as I said before, some simple simulation.

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  • $\begingroup$ Are you looking for material from the perspective of a user, or from the perspective of somebody who needs to develop/implement/really deeply understand the method? I think most textbooks on FEM are going to be geared towards developing/implementing the method and will all be very math heavy, but there might be some books/materials out there on structural mechanics and analysis that have chapter(s) on FEM from a "Here's what you can do and why it's useful" perspective. $\endgroup$
    – tpg2114
    Commented Mar 17, 2021 at 20:44
  • $\begingroup$ What I am looking for is a book or web resource where the fundamentals, in a simple way, and its historical development and examples of this method are exposed. @tpg2114 $\endgroup$
    – Programar
    Commented Mar 18, 2021 at 7:43

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There is a book: "Programming Finite Elements in Java" from G. Nikishkov that was very helpful for me.

One of the dificulties of FEM is that even simple exemples requires a lot of calculations. The book builds chapter by chapter a complete software for a 3D elastic isotropic material. And also how to deal with plastic deformation, when the loads are above the elastic limit.

It alternates chapters where the maths are explained and others were the code is presented and commented.

It is important to learn and exercise some basic of java programming, before read the book.

As the purpose is to present a code, the math explanations are not so detailed. For each math chapter, additional research in the web about the topic may be necessary.

The advantage of learning FEM by building a software is to be sure about what that condensed notations of integrals or sums really are.

There is also "introduction to Finite Elements in Enginnering" by Chandrupatla and Belegundu, that presents the method also from the perspective of elastic deformation in solids.

Finally, as a reference for elasticity that is behind the FEM for solid bodies, there is "Theory of elasticity" from Atanackovic and Guran.

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  • $\begingroup$ Thank you very much. The first book, the one on Java programming, will certainly be of great help to me to be able to perform some simple simulation (such as a steel bar subjected to unixial traction). On the other hand, I see that the books provided, although they make an excellent historical review, are dedicated to explain the mechanical properties of the solids instead of commenting on the fundamentals of the technique (calculations on which it is based, why the model works, alternatives...) $\endgroup$
    – Programar
    Commented Mar 18, 2021 at 7:53

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