What you are dealing with here is not as simple as adding a pressure to the inside of the cylinder, you are wanting to perform a thick walled pressure vessel analysis according to Lames theory.
The stress results you are wanting to plot are the circumfrential or hoop stresses, can you describe the dimensions of the cylinder?
Thanks for your reply. Yes, I'm trying to analysis a thick walled pressure vessel. i just begin to use simulation and i don't know how to do it.
The dimensions of the cylinder are as follows: inner diameter φ10mm，outer diameter φ30mm, length 50mm; material ANSI 304,yield strength 206Mpa. I fixed one end of the cylinder, only add a pressure of 150Mpa in it. The result of stress is show in von mises.
The calculations you are referring to are a very simple alternative to doing a FEA simulation if you have studied mechanical engineering.
What you have to do is to use Lames equations to calculate the radial and hoop stresses, these are defined as:
Radial Stress (id) = A - B / ri^2 where ri = inner radius (5mm in your case).
Radial Stress (od) = A - B / ro^2 where ro = outer radius (15mm in your case).
The radial stress is also the pressure, therefore in your case inner radial = -150 MPa and outer radial = 0 since you are applying an internal pressure of 150 MPa and nothing to the outer wall.
Knowing the pressures internally and externally and knowing the inner and outer radii you can calculate the constant A and B.
In your case A = 18.75 and B = 0.0042. You can double check these constants by inputting them back into the equation.
Therefore 0 = 18.75 - 0.0042 / 0.015^2.
You can now calculate the internal and external hoop or circumfrential stresses by using the same constants A and B using:
Hoop Stress (id) = A + B / ri^2 = 186.75 MPa (in your case).
Hoop Stress (od) = A + B / ro^2 = 37.42 MPa (in your case).
Like I say, very simple.
In terms of FEA, you are best making the assumption that the strain in the axial direction = 0 and using a 2D simplification and also take advantage of symmetry and only solve for a 1/4 model as shown.
In terms of output stress you need to define an axis in the z-direction through the cylinders diameter i.e. intersection of the x and z planes and use this to define:
SX (X Normal Stress) for the Radial Stress (-150 MPa @ r = 5mm and 0 MPa @ r = 15mm).
SY (Y Normal Stress for the Hoop Stress.
Please note the stress vectors will depend on the plane you have decided to sketch on.
The following images show the radial and hoop stresses calculated by FEA:
As you can see, the values correlate very well.
I hope this helps you.
I'll add just one note to Matthew's excellent post. Solidworks has an axisymmetric 2d simplification which would allow you to analyze an arbitrarily small length of pipe.
Hi Matthew & Mike
Sorry for the delay of reply because of weekend, i was unable to use my account. Your excellent advices do help me, thanks a lot!
I addition, if i want to calculate the safety factor, which stress i need to use. After all, the stresses outside and inside of the cylinder are quite different.
You need to use the maximum Hoop Stress to calculate your safety factor i.e. 187 MPa, not 38 MPa.
That is why thick walled cylinders have very poor efficiency since majority of the walled is lightly stressed in comparision to the wall where the pressure is applied. An alternative is to use a composite cylinder or in other words more than one cylinder shrunk together.
In your case:
FOS = 206 / 187 = 1.1
Aim for at least 2 so that the end caps are taken into consideration.
Thank you very much for your patient answer. I think i know how to do it now, thanks!