case figs

nafems4.md

@@ -813,6 +813,10 @@ Detailed mathematics show that the location where the derivatives of the interpo
 In any case, this step takes a non-negligible amount of time. The most-common approach, i.e. the node-averaging method is driven mainly by the number of nodes of course. So all-in-all, these are the reasons to use the number of nodes instead of the numbers of elements as a basic parameter to measure the complexity of a FEM problem.
 
 
+# The truth is out there
+
+Let us review some issues that appear during our real-world piping system and that might not have been thoroughly addressed back during our college days.
+
 ## Two (or more) materials {#sec:two-materials}
 
 The main issue with fatigue in nuclear piping during operational transients is that at the welds between two materials with different thermal expansion coefficients there can appear potentially-high stresses during temperature changes. If these transients are repeated cyclically, fatigue may occur. We already have risen a warning flag about stresses at material interfaces. Besides all the open questions about computing stresses at nodes, this case also adds the fact that the material properties (say the Young Modulus\ $E$) is different in the elements that are at each side of the interface.
@@ -990,8 +994,17 @@ $$ K(\vec{x}) \cdot \vec{u}(\vec{x}) = \vec{b}(\vec{x})$$
 
 And this last equation is linear in\ $\vec{u}$. In effect, the discretization step means to integrate over\ $\vec{x}$. As\ $K$, $\vec{u}$ and\ $\vec{b}$ depend only on\ $\vec{x}$, then after integration one gets just numbers with the matrix representation of\ [@eq:kub]. Again, you can either trust me, ask a teacher or go through with the maths.
 
-**33410 1D-403**
+\medskip
+
+To recapitulate, here are some partial and non-sensitive results of an actual system of a certain nuclear power plant. The main issues to study were the interfaces between a carbon-steel pipe and a stainless-steel orifice plate used to measure the (heavy) water flow through the line.
+
+:::: {fig:case-cad}
+![General view. Carbon steel is gray and stainless steel is green.](case-cad1.png){#fig:case-cad1 width=90%}\  
+
+![Detail of the orifice plate.](case-cad2.png){#fig:case-cad2 width=90%}\  
 
+Three-dimensional\ CAD model of a section of the piping system between aproppriate supports.
+::::
 
 # Fatigue