figs

nafems4.md

@@ -813,7 +813,7 @@ 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
+# Adding complexity: 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.
 
@@ -925,9 +925,9 @@ Location of the three radial SCLs: cyan, yellow and green.
 :::::
 
 ::::: {#fig:tee-MB}
-![Membrane stress](M.svg){#fig:M}
+![Membrane stress](M.svg){#fig:M width=90%}
 
-![Bending stress](B.svg){#fig:B}
+![Bending stress](B.svg){#fig:B width=90%}
 
 Parametric membrane and bending stresses as a function of the nominal diameter\ $d_b$ of the branch.
 :::::
@@ -998,13 +998,32 @@ And this last equation is linear in\ $\vec{u}$. In effect, the discretization st
 
 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%}\  
+::::: {#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%}\  
+![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.
-::::
+:::::
+
+::::: {#fig:case-mesh}
+![General view](case-mech-mesh1.png){#fig:case-mesh1 width=70%}
+
+![Detail of the refinement around the interface](case-mech-mesh2.png){#fig:case-mesh2 width=100%}
+
+Unstructured grid for the mechanical analysis. Volumetric elements (i.e. tetrahedra) corresponding to carbon steel are magenta and to stainless steel are green. Surface elements (i.e. triangles) corresponding to the internal pressurised face are yellow.
+:::::
+
+![Location of the 15\ SCLs](case-scls.pdf){#fig:case-scls width=70%}
+
+::::: {#fig:case-temp}
+![Simplified axi-symmetric domain](case-temp-4-0015.png){#fig:case-temp1 width=70%}
+
+![Generalisation](case-temp-gen-4-0015.png){#fig:case-temp2 width=100%}
+
+Temperature distribution for a certain instant of the transient, computed in the simplified two-dimensional axi-symmetric domain and its generalisation to the three-dimensional mechanical domain as discussed in\ [@sec:thermal].
+:::::
+
 
 # Fatigue
 
@@ -1021,7 +1040,7 @@ do you trust your FEM program?
 
 # 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.
+Back in college, we all learned how to solve engineering problems. And once we graduated, we felt we could solve and fix the world (if you did not graduate yet, you will feel it shortly). 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.
 
  * use and exercise your imagination
  * practise math