Finite element method introduction references [closed]

Question

Could you recommend some good articles/notes/tutorials on finite element method (FEM)? I don't deal with advanced math every day, so a tutorial that introduces me to math needed to understand FEM will be great.

My goal is to write my own simulation of deformable bodies (+plasticity). I must use FEM, but it will be good if I will know BEM (Boundary element method) and FDM (Finite difference method) too.

Answer 1

Really understanding Finite Element Methods requires quite a bit of fairly advanced mathematics; unless you have a few years to devote to the cause, let's leave that aside for now.

That said, the basic ideas underlying FEM are fairly simple if you have some experience with ODE solvers. Can you tell us some more about your background and what you really want to learn so that we can suggest some appropriate resources? Do you want to learn the underlying mathematics, or do you just want to learn some cookbook recipes for applying FEM to a certain class of problem?

Answer 2

Your question is unclear. I don't know what you want to know, because it's impossible to tell what you're ignorant of here.

You don't deal with advanced math every day. What do you know about the finite element method? Here are topics you'll need to know:

1. Statics and dynamics; how to draw free body diagrams
2. Solid mechanics - strength of materials, elasticity,
3. Continuum mechanics for large strain models: Lagrangian and Eulerian formulations
4. Material models - elasticity and plasticity
5. Partial differential equations
6. Method of weighted residuals and integral equations
7. Linear algebra
8. Numerical methods
9. Geometric modeling - CAD for geometry and meshing for FEA models
10. Commercial or open source packages

You don't say whether you want to use a commercial package (ANSYS, NASTRAN, ABAQUS) or something that you'll write.

As far as references go, there are lots of books available now, but they aren't easy to read or absorb. I'd recommend T.J.R. Hughes' Dover book on the subject. It's cheap and good.

But it's not easy.

I just skimmed through the paper. It looks like a survey article, with nothing new to contribute to the state of the art. It covers a lot more than just small strain plasticity of metals. I see fabric models, large strain problems, etc.

It also mentions boundary element methods and finite difference methods. Do you want to know about those, too? Boundary element methods are completely different from finite elements. The former are based on Green's function formulations; the latter use method of weighted residuals.

The paper doesn't have a great deal of depth to it, but it's very broad. What do you want to know?

I don't think it's possible for someone with so little background to write their own. A better place to start would be FENICS.