The meshing dilema uncovered

Finally I got the time to wrap up this subject and uncover this mystery. Actually none of the curves I presented was correct. Let me recap.

  1. I used the default mesh – option 1,
  2. I used a course mesh with general surface refinement – option 2
  3. I used a bit finer mesh with local surface refinement – option 3
Meshing Sensitivity
Meshing Sensitivity

I got the above graph. Next I decided to cut the solid but shared the boundary conditions so that it was a single entity just sectioned. On my target edge/surface I defined a volume mesh (more refined) and on top of that near the edge I was studying and measuring I place a volume refinement. I got just about as much elements as before but now they were concentrated on my target zone.

The final mesh had the following

Meshing dilema Final Mesh
Meshing dilema Final Mesh

And the final result:

Meshing Final Result Dilema
Meshing Final Result Dilema

And here you go. The yellow curve has nothing to do with the blue curve which was my starting point and eventually converged with my previous 2 attempts.

Lessons learned:

Carefull usage of meshes, it is always good practice to verify mesh sensitivity. This example applies to any thing you do in simulation, it is always good to verify if the result we have in hand are actually trustable.

Comments to the starter: When ever your boss demands results immediately it is always tempting not to do a sensitivity analysis to rush and give something. If for instance this was a professional case (which it’s not) and one feed the blue line there would be some opportunity for mistakes. It is always important to verify how accurate a result the requester desires. On some clients the blue line would be wonderful for others it would be useless.

Ultimately the simulation result needs to fit the expectations of the requester. And the simulation effort, accuracy and time should fit those expectations.

The meshing dilema

Some times we use the default mesh and get happy with the result,s others we don’t. It is hard to develop a test setup or expensive to buy the test setup equipment to calibrate the model. On these cases that we can’t compare results we have to take simulation results as final. This presents a few chalenges since how do we know the model is good enough for our purpose? Normally I follow two paths either by analytically calculating a rough value or by carefully analysing mesh sensitivty, analysing energy balances and whatnot. Although it is tempting to take a rough model as final, bad consequences can come from that decision, since we can end up with divergent results that relate more to model deficiencies than to the actual physics in hand.
Look at this example where I have 3 result set’s for varying thicknesses, however with different meshing strategies.

Meshing Sensitivity
Meshing Sensitivity

Which of the lines is the truth? Just a small change and such a big difference. You have to trust me on this, there is a big difference 200MPa from bottom blue to top grey.

The mystery of the train seat uncovered

Will the train seat withstand 120Kg? was I seeing things? Maybe the weight was more since the person had a backpack. But the load was extreme.

Seat deformation
Seat deformation

I calculated 5 mm deformation on the cushion. Could I have seen it? Well maybe. Stresses were far away from the plasticity limit, however the structure feels loaded.

From my analysis the structure could take even more load and wobble even more. Maybe the squeaking sound over exaggerated my notion of wobbling.

Undeformed to undeformed seat
Undeformed to deformed seat comparison

The light blue image is the deformed state,  we can see the deformation direction, which moves in a expected direction.

Close up of seat
Close up of seat

In this close up we can see a slight displacement. But very small.

So my conclusions:

The heavy train traveller was safe, the seat could stand a few extra Kg’s of weight with some more camping equipment.

The design seems fairly robust, however it actually wobbles.

Train seat analysing

Finally I got time to mesh and solve my imaginary problem. I will not dive into meshing since it is a chapter on its own. I used a tetrahedron mesh as standard as it gets. The work flow is simple; get a CAD model, get material data, mesh it, add supports and loads and finally get some results, either by stresses or displacements.

Train seat mesh & Result
Train seat mesh & Result

My results for a small load of 1.2Kg shows that the T tube element will suffer most when we sit on it. I would say that if it breaks it will be there. Ok this case is more then evident since the only thing holding my weight is this connection.

But will it wobble with 120Kg weight?