cosas

nafems4.md

@@ -2,9 +2,9 @@
 
 
 
-If you do not know what a Gauss point is, pause here, grab a classical FEM book and resume when you do.
+dnl 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.
+dnl 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
@@ -14,7 +14,7 @@ tomen este cpitulo como una charla de café - imginacion! ecuaciones numeros plo
 
 # 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.
+Take this as a chat between you an me, i.e. an average engineer that have already taken the journey 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.
@@ -24,7 +24,15 @@ We will dig into some math. If you do not like equations, just ignore them for n
 
  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
 
+## Nuclear reactors, pressurized pipes and fatigue
+ 
+Piping systems in sensitive industries like nuclear or oil & gas should be designed and analysed following the recommendations of an appropriate set of codes and norms, such as the ASME\ Boiler and Pressure Vessel Code.
+This code of practice (book) was born during the late XIX century, before finite-element methods for solving partial differential equations were even developed, and much longer before they were available for the general engineering community. Therefore, much of the code assumes design and verification is not necessarily performed numerically but with paper and pencil. However, it still provides genuine guidance in order to ensure pressurised systems behave safely and properly without needing to resort to computational tools. Combining finite-element analysis (even plain linear equations) with the ASME code gives the cognizant engineer a unique combination of tools to tackle the problem of designing and/or verifying pressurised piping systems.
 
+In the years following Enrico Fermi’s demonstration that a self-sustainable fission reaction chain was possible, people started to build plants in order to transform the energy stored within the atoms nuclei into usable electrical power. They quickly reached the conclusion that high-pressure heat exchangers and turbines were needed. So they started to follow the ASME\ Boiler and Pressure Vessel Code. They also realised that some requirements did not fit the needs of the nuclear industry, but instead of writing a new code from scratch they added a new section to the existing body of knowledge: the celebrated ASME Section\ III\ [1].
+
+After further years passed by, people (probably the same characters as before) noticed that fatigue in nuclear power plants was not exactly the same as in other piping systems. There were some environmental factors directly associated to the power plant that was not taken into account by the regular ASME code. Again, instead of writing a new code from scratch, people decided to add correction factors to the previous body of knowledge. This is how knowledge evolves, and it is this kind of complexities that engineers are faced with during their professional lives. And, yes, it would be a very hard work to re-write everything from scratch every time something changes.
+ 
 # Solid mechanics, or what we are taught at college
 
 An infinite pipe subject to uniform internal pressure
@@ -123,3 +131,5 @@ two cubes
 ## In water
 
 # Conclusions
+
+Back in College, we all learned how to solve engineering problems. But there is a real gap between the equations written in chalk on a blackboard (now probably in the form of beamer slide presentations) and actual real-life engineering problems. This chapter introduces a real case from the nuclear industry and starts by idealising the structure such that it has a known analytical solution that can be found in textbooks.  Additional realism is added in stages allowing the engineer to develop an understanding of the more complex physics and a faith in the veracity of the FE results where theoretical solutions are not available. Even more, a brief insight into the world of evaluation of low-cycle fatigue using such results further illustrates the complexities of real-life engineering analysis.