fixes

nafems4.md

@@ -48,7 +48,7 @@ In the years following [Enrico Fermi](https://en.wikipedia.org/wiki/Enrico_Fermi
 
 After further years passed by, engineers (probably the same people that forked section\ III) 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 previously amended body of knowledge. This is how knowledge evolves, and it is this kind of complexities that engineers are faced with during their professional lives. We have to face it, it would be a very hard work to re-write everything from scratch every time something changes.
 
-![A real-life piping system.](real-piping.png){#fig:real-life}
+![A section of a real-life piping system.](real-piping.png){#fig:real-life}
 
 Actually, this article does not focus on a single case study but on some general ideas regarding analysis of fatigue in piping systems in nuclear power plants. There is no single case study but a compendium of ideas obtained by studying many different systems which are directly related to the safety of a real nuclear reactor.
 
@@ -235,7 +235,8 @@ This section is not (just) about different kinds of elements like tetrahedra, he
     - buckling
     - modal
  * element features
-    - full elements
+    - isoparametric elements
+    - serendipity elements
     - sub-integrated elements
     - incomplete elements
 
@@ -389,7 +390,7 @@ On the one hand, a reasonable number of nodes (remember it is the number of node
 
 There is a wonderful essay by [Isaac Asimov](https://en.wikipedia.org/wiki/Isaac_Asimov) called [“The Relativity of Wrong”](https://en.wikipedia.org/wiki/The_Relativity_of_Wrong) where he introduces the idea that even if something cannot be computed exactly, there are different levels of error. For instance, believing that the Earth is a sphere is less wrong than believing that the Earth is flat, but wrong nonetheless, since it really deviates from a perfect sphere and resembles more an oblate spheroid.
 
-We can then merge this idea by Asimovve with an adapted version of the [Saint-Venant's principle](https://en.wikipedia.org/wiki/Saint-Venant%27s_principle) and note that the detailed transient temperature distribution is important only around the location of the SCLs. We can then make an engineering approximation and
+We can then merge this idea by Asimov with an adapted version of the [Saint-Venant's principle](https://en.wikipedia.org/wiki/Saint-Venant%27s_principle) and note that the detailed transient temperature distribution is important only around the location of the SCLs. We can then make an engineering approximation and
 
  1. compute the transient thermal problem using a reduced mesh around the SCLs, and
  2. assume the part of the full system which is not contained in the reduced mesh is at an uniform (though not constant) temperature equal to the average of the inner and outer temperatures at each side of the reduced mesh.
@@ -872,7 +873,7 @@ Back to the two-material interface, all the discussion above about non-continuou
 
 # 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. 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