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# Benchmark plate with hole and mesh-sizes

## Benchmark plate with hole and mesh-sizes

(OP)
This can be the more basic and stupid question for any FEA analyst but for a chemical engineer is not so clear.

In a typical bench mark of a hole in a plate, the stress concentration factor is 3, but one I "re-mesh" and " re-mesh" (trying to have the more "dense" fine mesh in the interest area), the level off stress increase all the time when I try to get a fine dense mesh around the hole.

Is a basic concept that a stress concentration can produce an infinite stress level, but how to know until "when"  I can "re-mesh" my model.. (in this case if obvious because I got one equation to compare, but what happen in those case where we don't have ANY single equation to compare).

If I got a non-lineal material model ("plastic analysis" and off course a software that can solve this model) is phenomenon will still happen?.

### RE: Benchmark plate with hole and mesh-sizes

The stress concentration factor of x3 is associated with a hole in a plate of infinite width and the stress that it implies is the maximum pricipal stress.  The applied stress (in your case a pressure load) will need to be applied at the ends of the plate far away from the hole and acting in a direction normal (or transverse) to the hole axis.  If the hole that you have is located very near a side wall of the plate your results will not match this particular analytical model.

The theoretical model you mention is for linear elastic mechanics.  Therefore, utilizing a software package capable of inelastic deformations (such as Ansys) will either be: a) useless if the stress is below the yield point of the material because Mechanica would produce the same results or b) useless because the analytical model you are basing your results on is for a linear elastic analysis as mentioned above.

Mechanica is a P type finite element solver.  Therefore, excessive refinement near a stress concentration should not be needed, given that the variation of stress/strain throughout the element will be mapped with an element having a maximum polynomial order of 9.

It sounds like you have some constraints or loads mixed up.  Check your boundary conditions again.  Use Roark's Handbook for a more detailed explination regarding the analytical model you are basing your results on.

Steve

### RE: Benchmark plate with hole and mesh-sizes

(OP)
Hello Seymours2571,,
my model is a 1/4 shell model, the BC in the planes edges are the normal ones for symmetri and the load edges are far away from the hole..

my point is that I get a max stress that change all the time when i re-fine my mesh in that place.. but I must admite that the stress "near" to this "hot point" come around to 3 the normal stress.

my question: is this hot point to stabilize to 3 times the normal stress or it is going to increase all the time due to this local stress concnetration hole feature.

this question comes, because when your are rediang results,, you just see this max stress reported by the software

### RE: Benchmark plate with hole and mesh-sizes

Hey Mark,

Theoretically the stress should top out at 3x the nominal stress.  Which type of convergence option are you using: Single Pass or Multi-Pass?  If you are using the Multi-Pass (MPA) then just check to see if the max polynomial order is being reached by choosing p order from the results drop down list.

You could also run a 1/2 symmetry model with the plane of symmetry being parallel to the appplied stress (e.g. stress being applied in +y and the symmetry plane splitting the part along the y coordinate).

I believe also there is an option to insert a measure in th vicinity of the edge of the hole.  If the measure is located at a point or vertex you will receive an option to specify a radius of a sphere in which the particular measure will be measured.

Finally, what is the size of the changes in stress that you are seeing from mesh to mesh.  Mechanica normally does a good job at converging on non-singular type geometry so I am just curious if it is very small percentages of change from mesh to mesh.

Steve

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