The influence of shell element thickness on the calculation of moment of inertia

[chuankaia]

I wrote a piece of code to test the calculation of mass related information.
mapdl = launch_mapdl()
mapdl.clear()
mapdl.prep7()

mapdl.et(1, "SHELL181")
mapdl.sectype(1, "SHELL")
mapdl.secdata(0.2, 1)
mapdl.mp('DENS', 1, 7800)

v0 = mapdl.cylind(2, z1=0, z2=5)
mapdl.vatt(1, 1)
mapdl.vsum(lab='fine')
volume = mapdl.get('volume', 'VOLU', 0, "VOLU")
cent = mapdl.get('volume', 'VOLU', 0, 'CENT', 'z')
imc_x = mapdl.get('volume', 'VOLU', 0, 'IMC', 'x')
imc_y = mapdl.get('volume', 'VOLU', 0, 'IMC', 'y')
imc_z = mapdl.get('volume', 'VOLU', 0, 'IMC', 'z')
print(f"{volume}")
print(f"{cent}")
print(f"{imc_x} {imc_y} {imc_z}")

When I changed the value of the thickness, I found that it had no effect on the result of the moment of inertia. What is the reason for this
Best wishes

[mikerife]

Hi @chuankaia just so we are on the same page; none of the volume areas were meshed so the value of the shell thickness does not matter in this example.

Also the example is not enough to show the issue - there is only one volume, which is missing R2 in its definition, and so any comment may not actually address the issue.

So here is an example that does show that two different cylinders of the same height and outer radius, but different inner radius, does result in differing moments of inertial:

import os
from ansys.mapdl.core import launch_mapdl
path = os.getcwd()
mapdl = launch_mapdl(run_location=path)
mapdl.clear()
mapdl.prep7()

v0 = mapdl.cylind(1, 2, z1=0, z2=5)
v1 = mapdl.cylind(1.5, 2, z1=0, z2=5)

mapdl.vsel('s', 'volu', '', v0)
mapdl.vsum(lab='fine')
volume = mapdl.get('volume', 'VOLU', v0, "VOLU")
cent = mapdl.get('volume', 'VOLU', v0, 'CENT', 'z')
imc_x = mapdl.get('volume', 'VOLU', v0, 'IMC', 'x')
imc_y = mapdl.get('volume', 'VOLU', v0, 'IMC', 'y')
imc_z = mapdl.get('volume', 'VOLU', v0, 'IMC', 'z')

mapdl.vsel('s', 'volu', '', v1)
mapdl.vsum(lab='fine')
volume1 = mapdl.get('volume', 'VOLU', v1, "VOLU")
cent1 = mapdl.get('volume', 'VOLU', v1, 'CENT', 'z')
imc_x1 = mapdl.get('volume', 'VOLU', v1, 'IMC', 'x')
imc_y1 = mapdl.get('volume', 'VOLU', v1, 'IMC', 'y')
imc_z1 = mapdl.get('volume', 'VOLU', v1, 'IMC', 'z')

print(f"{volume}")
print(f"{cent}")
print(f"{imc_x} {imc_y} {imc_z}")
print("")
print(f"{volume1}")
print(f"{cent1}")
print(f"{imc_x1} {imc_y1} {imc_z1}")

The printout is:

Mike

[chuankaia]

Thank you very much for your response; your approach is effective. However, using the R2 parameter has resulted in the structure becoming a hollow cylinder. I would like to create a cylindrical structure with wall thicknesses of 0.05m for both the top and bottom surfaces, as well as the sidewall. Could you please advise me on how to achieve this?
Best wishes

[mikerife]

Hi @chuankaia
Do you really want a CAD model of the described cyliner or a FEM of the thin walled cylinder? Since your original posting PyMAPDL listing had a shell element defined I'm tending towards FEM...but don't want to assume so could you please clarify.

If you wanted a FEM then you were close and just needed to mesh the cylinders areas with the shell elements. And change the shell section definition to be 0.05 thickness instead of 0.2.

If CAD then you could create two cylinders the larger with surfaces that represent the outer surface of the hollow cylinder that you want. Then the smaller whose outer surfaces represent the inner surfaces of the hollow cylinder. Then boolean subtract the smaller from the larger.

Mike

[chuankaia]

Apologies for any confusion in my previous explanation. Here is a more detailed description of my goal: I want to calculate the moment of inertia for a complex structure made of steel, with a thickness of 0.05m. Therefore, I set the material and its density in the commands and assigned them to the structure. However, I found that when I modify the material's density, the moment of inertia changes, but when I modify the thickness, there is no change. I found some descriptions about this in the help documentation, which indicate that if no thickness value is assigned, the default is 1. I checked the moment of inertia calculation, and this is indeed the case. However, after assigning a value to the thickness, the result for the moment of inertia did not change. Therefore, I am unsure what went wrong. As you mentioned, although Boolean operations can achieve this, the complexity of the structure could make the commands more cumbersome. Therefore, I am looking for a simpler way to accomplish this task.

[mikerife]

Hi @chuankaia ok - perhaps the confusion is that the volume and areas can have different attribute values. Here is an example that shows that the area have different moments of inertia based on the attibutes assigned:

import os
from ansys.mapdl.core import launch_mapdl
path = os.getcwd()
mapdl = launch_mapdl(run_location=path)

mapdl.clear()
mapdl.prep7()

mapdl.et(1, "SHELL181")
mapdl.sectype(1, "SHELL")
mapdl.secdata(0.2, 1)
mapdl.mp('DENS', 1, 7800)

# use 1 for thickness of first calculation of cylinder areas MoI
# and 0.5 for second cylinder areas MoI
mapdl.r(1, 1)
mapdl.r(2, .5)

v0 = mapdl.cylind(1, 2, z1=0, z2=5)

mapdl.aatt(1, 1)
mapdl.asum('fine')
imc_x = mapdl.get_value('area', 0, 'IMC', 'x')
imc_y = mapdl.get_value('area', 0, 'IMC', 'y')
imc_z = mapdl.get_value('area', 0, 'IMC', 'z')

mapdl.aatt(1, 2)
mapdl.asum('fine')
imc_x1 = mapdl.get_value('area', 0, 'IMC', 'x')
imc_y1 = mapdl.get_value('area', 0, 'IMC', 'y')
imc_z1 = mapdl.get_value('area', 0, 'IMC', 'z')

print(f"{imc_x} {imc_y} {imc_z}")
print("")
print(f"{imc_x1} {imc_y1} {imc_z1}")

And we can see that the values are different:

Mike

[chuankaia]

Thank you very much for your patient answer, but no matter how to define the value of thickness, I can't seem to get the correct value of moment of inertia. For my purposes, I used the Boolean operation you mentioned to get the correct result, and here is my code:
mapdl = launch_mapdl()
mapdl.clear()
mapdl.prep7()

mapdl.mp('DENS', 1, 7800)
mapdl.et(1, "SHELL181")
mapdl.sectype(1, "SHELL")

v0 = mapdl.cylind(2, z1=0, z2=5)
v1 = mapdl.cylind(1.95, z1=0.05, z2=4.95)
mapdl.vsbv(v0, v1)
mapdl.vplot()

mapdl.vatt(1, 1)
mapdl.vsum('fine')
volume = mapdl.get('volume', 'VOLU', 0, "VOLU")
cent = mapdl.get('volume', 'VOLU', 0, 'CENT', 'z')
imc_x = mapdl.get('volume', 'VOLU', 0, 'IMC', 'x')
imc_y = mapdl.get('volume', 'VOLU', 0, 'IMC', 'y')
imc_z = mapdl.get('volume', 'VOLU', 0, 'IMC', 'z')

print(f"{volume}")
print(f"{cent}")
print(f"{imc_x} {imc_y} {imc_z}")

We can get the right result：
4.29713708
2.50000041
163560.822 163557.517 112129.607

However, it has to be said that if the structure is a complex one, this will cause the command to be used repeatedly. I would like to ask you to see if you can achieve this using thickness attribute assigned (aatt/vatt).
Best wishes