nafems4/nafems4.md

We will dig into some math. If you do not like equations, just ignore them for now. Read the text skipping them. It is fine (for now).

We will need your imagination. Equations, numbers, plot, schematics, 3d views, interactive rotable 3d models... but still, when the theory says "thermal expansion produces linear stresses" you have to picture in your head three little arrows pulling away from the same point in three directions.

If you do not know what a Gauss point is, pause here, grab a classical FEM book and resume when you do.

FEM is like magic to me. I can follow the whole derivation, from the strong, the weak and varitionals formulations down to the algebraic multigrid preconditioner for the inversion of the stiffness matrix passing through Sobolev spaces and the grid generatoin. Then I can sit down and code all these steps, including shape funcions, matrix assembly and computation of derivatives^{This is a task that if you can, you definitely have to do. Your time and effort will be highly rewarded in the not-so-far-away future.}. Yet, the fact that all these a-priori unconnected steps once gets a pretty picture that resembles reality is astonishing.


tomen este cpitulo como una charla - imginacion! ecuaciones numeros plot 3d drawing intrctive 3d model, but still you have to imagine dericatives nd stress tensors... "thermal expansion gives normal stresses" and then picture out three arrows pulling away