Recommended books for FEA theory 8

[hobo_ist]

Can somebody recommend a good book that explains the full theory behind FEA and goes into detail about shape functions etc (including Gaus points and Jacobian matrixes..)?

Ideally want something that's simply explained with examples but doesn't not compromise on detail.

Thanks

 

[FE_struct1]

For basics on FEA, I can personally vouch for Daryl Logan's "A First Course in the Finite Element Method" (link:

https://www.amazon.com.au/First-Course-Finite-Element-Method/dp/0495668257).

 

[FEA way]

Check this FAQ in FEA forum:

https://www.eng-tips.com/faqs.cfm?fid=2021

There are many good books about FEM theory (much fewer about practice) but I can particularly recommend those written by Bathe, Cook, Huebner, Ottosen, Logan, Fish, Belytschko, Chandrupatla, Hutton, Seshu, Kwon and Bhavikatti.

 

[XR250]

What is your background? Do you have a solid understanding of linear algebra? What is your goal in learning the "full theory"?

 

[SWComposites]

Bathe, Finite Element Procedures is very good. Don't recall how deep it goes into shape functions.

Zienkiewicz, The Finite Element Method has shape function info if I recall correctly from long ago.

 

[dik]

Zienkiewicz is very good.

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[Celt83]

Matrix Analysis of Structures by Kassimali shows the derivation for truss and beam members via both statics/classic mechanics and virtual work/shape functions.

Concepts and Applications of Finite Element Analysis by Cook goes into the shape function formulation pretty well.

The Finite Element Method: Linear Static and Dynamic Finite Element Analysis by Hughes also has good coverage of the shape functions for 2D elements

This lecture series on youtube covers shape functions and the jacobian well also: Dr. Clayton Pettit - Intro to Finite Element Method

 

[KootK]

1) I always recommend Cook & Malkus for those seeking a moderately deep dive from a practitioner perspective.

2) Things get tougher if one wants a dive so deep that they can actually touch the bottom of the pool with a toe. In that case, I feel that it becomes difficult to escape the need for an understanding of:

a) Variational energy methods and, mostly likely, a bit of variational calculus.

b) Tensor notation and, mostly likely, a bit of tensor calculus.

Shape functions are, after all, primarily devices that allow us to approximate the strain energy of complex systems under deformation in a manner that is computationally tenable.

For a deep dive like this, I've found nothing remotely as good as the Wallerstein book shown below.

I know, this seems like a weird recommendation given that it doesn't have FEM in the title and only mentions it in one of the chapter subsection titles. This is how it should be. All that is FEM really amounts to little more than an application footnote the the grander picture of variational methods. I assure you that a PDF search for "finite elements" and "shape function" in the book turns up a ton of hits, as you would hope.

I've included some clips of the Wallerstein book below so that anyone is interested in it may get a flavor for it.

The Wallerstein book only gets as far into FEM as axially load member systems. However, it dives deeply enough into the development of that version of FEM that it's easy for a reader to imagine the extension of the method to more complicated systems. It's a brilliant presentation in my opinion.

 

[centondollar]

Gauss points are the weighting points of numerical integration.

I would say that as an application-focused engineer, all you need to know about Jacobians (shape function derivative w.r.t. global coordinates requires the Jacobian and derivative w.r.t. reference element; also needed to transform the domain of integration global --> reference) is that distorted elements (e.g., quads with extreme corner angles) can make the Jacobian ill-conditioned and cause ill-conditioning of the solution.

 

[hobo_ist]

Thanks for all your replies. This should be enough material to get me going

@XR250 I'm a temporary works design engineer. I learned the theory behind FE during my time as a student but that was a long time ago and I've come to find that my note taking skills back then were, lets say, insufficient!

 

[ALK2415]

@ KOOTK
Kindly, should spare some of your time teaching us some of your insights about FEM (ANSYS or ABAQUS parameters)
since most use it without any understanding of their actual effects/meaning ..
NOTE: see FEM as Rubber material that can fit any solution you desire, which is absurd to me ..

 

[KootK]

@ KOOTK. Kindly, should spare some of your time teaching us some of your insights about FEM (ANSYS or ABAQUS parameters). since most use it without any understanding of their actual effects/meaning ..

If you have a specific question I'll try to answer it but I wouldn't dare give a general purpose sermon on FEM use here. I myself am still very much a "tourist" when it comes to the finer points of FEM theory. I would only consider myself to be marginally qualified in the used of general purpose FEM software. I mostly stick to the dumbed down stuff like SAFE and RISA in practice.

The Cook & Malkus book is an excellent reference for avoiding the pitfalls of spurious modelling. As shown below, there are two entire chapters that are pretty much focused on that topic and, in my opinion, they are the chief strength of the book.

I don't feel that it is practical for all FEM users to be deep dive experts in the theory as Wallerstein wishes. I think that we'll wind up being a world of semi-black box FEM software operators who, at best, are well trained in avoiding mistakes even if their understanding of the underlying theory is limited. One goes to ware with the army they have, not the army they wish they had.

 

[ALK2415]

@ kootk, this website should but more efforts in FEM sector ! (only few operators are there when i asked a question !!!)
all the experts are here "Structural Form", and they only expel their knowledge when there is a competitive argument
science should be spread-out. try from some time to time to a give them a lecture on generosity as they did in Corona times !