It seems to me that everyone focusing on a 1° arc is assuming that the axisymmetric component touches at the centerline.
We deal with this situation often in the world of pressure vessel evaluation for the process industries. Picture a vertical cylinder 20' (~7m) diameter x 3" thick shell say 30' tall. I have a conical transition (similar to a piping reducer) which has a 30° off vertical profile and transitions me to a 10' diameter shell. Let's say teh Inspection group has discovered a thin spot (due to corrosion) near the large diameter to cone transition and for simplicity I want to model it as though it is a full band extending 6" on the 20' diameter shell and 6" onto the cone. It has corroded down to 2" thick. As a first pass, I'm only going to include internal pressure. Its full of pressurized hydrocarbons and bad things would happen if it fails to contain the pressure. On the other hand, an immediate unplanned shutdown of the plant is not only costly but carries with it the not-insignificant hazards of taking the process through a shutdown and startup sequence. Keep in mind, BP Texas city
killed fifteen people during a startup in 2005. So, you, the analyst, get a call: Is is safe to keep operating until we can get to the next planned shutdown (or at least limp along for a month while we plan a quick one) or do we need to shut 'er down NOW? This type of scenario happens a lot more often than most folks realize.
We now enter the world of Fitness For Service, since we are well past the "new design" code limits.
I could go to my trusty old full blown FEA package and use true axisymmetric elements, or I could use my solid modeling package with the same FEA solver, but restricted to solid elements. If I choose (for whatever reasons) to go with the solid modeling package, I will build a profile of the geometry, which looks just like the axisymmetric model, and sweep it one degree for an inside arc length of about one inch. If I use more than one element through the 2" thickness, I can easily have well-conditioned tetrahedral elements. I apply internal pressure, fix the bottom section cut in the vertical direction, and apply the calculated longitudinal stress as a pressure along the top boundary on my small diameter section. I apply symmetrical boundary conditions on the edges of the slice. Within a few hours of the initial phone call I can have some feel for how dire the situation is, and at that point can either recommend an immediate shutdown or move on to a more detailed model incorporating a more realistic degraded area and additional loads.
gfbotha said:
Using 3D tetrahedral elements, with what minimum wedge or sector (included) angle would you, generally speaking, still feel comfortable to analyse an axisymmetric problem? 15°? I realise it depends..., and might vary; but surely there must be some rule of thumb to generally deliver robust results (almost code-like).
My perspective is that it depends. Perhaps one way to look at it would be to put at least enough of a swept arc to have several elements through the swept section. If the profile goes all the way to the centerline, then the concerns expressed in prior posts regarding sharp angles become applicable.
jt