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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 de café - 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
Background and introduction
Take this as a chat between you an me, i.e. an average engineer that have already taken the path from college to actual engineering.
Imagination! Try to picture how the results converge, and what they actually mean besides the pretty-colored figures. 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.
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).
Practice math! prsctise math! hace diferencia de cuadrados una vez por mes como si hicieras crucigramas, buscá los libros de analisis y de fisica y hacé los ejercicios
Solid mechanics, or what we are taught at college
An infinite pipe subject to uniform internal pressure
ecuación diferencial 1D -> appendix
Finite elements, or solving an actual engineering problem
The name of the game
FEM, FVM and FDM
Simulation
Why do you want to do FEA?
five whys
Computers, those little magic boxes
ENIAC
A brief review of history
FEM, Computers
graphics cards
Hardware
Software
FOSS
Avoid black boxes
Reflections on trusting trust
UNIX, scriptability, make programs to make programs (here a program is a calculation)
front and back
avoid monolithic
Nuclear-grade piping and ASME
The infinite pipe revisited
3D full
Quarter
2 grados
2D axysimmetric
1D collocation
struct vs unstruct
1st vs 2nd
complete vs incomplete (hexa)
Linearity of displacements and stresses
cantilever beam, principal stresses, linearity of von mises
ASME stress linearization
The relativity of wrong
citar a asimov y al report de convergencia
errors and uncertainties: model parameters (is E what we think? is the material linear?), geometry (does the CAD represent the reality?) equations (any effect we did not have take account), discretization (how well does the mesh describe the geometry?)
Two (or more) materials
Young and Poisson
two cubes