Radial deflection from an axial load
Radial deflection from an axial load
(OP)
I've got a polyethylene disk with a short width compared to the diameter. The disk will have an axial pressure placed upon it, and I wish to find the radial displacement as a result of this axial pressure. It will form a bulge in the center of the disk around the circumference, and the height of that bulge is what I'm looking to find.
Looking through my books, the only similar case is delta = PL/E (from PL/AE); however, the displacement is only axial displacement.
Any ideas? Thanks in advance!
Looking through my books, the only similar case is delta = PL/E (from PL/AE); however, the displacement is only axial displacement.
Any ideas? Thanks in advance!





RE: Radial deflection from an axial load
RE: Radial deflection from an axial load
It can be easy to forget where our everyday values come from.
RE: Radial deflection from an axial load
If you are asking for that motion due to a pressure on the disk, then you can find it in Rourke's book on stresses and strains for various edge conditions.
RE: Radial deflection from an axial load
The disk is within a cylinder, and I am trying to find the pressure at which that disk contacts the wall of the cylinder. Using Poisson's ratio:
nu = -lateral strain / axial strain
nu = (gap/ID)/(deltaX/L)
I can solve for deltaX, then use
deltaX = PL/E
to find the pressure at which I will make contact.
However, the results I get from this do not agree with the results I am getting from Pro/E Mechanica. I trust these hand calcs more than I trust Pro/E, but it would be nice if they lined up.
RE: Radial deflection from an axial load
RE: Radial deflection from an axial load
Perhaps this is the incorrect method to use when analyzing the deformation of a plastic? I have been using my Strength of Materials textbook to determine the proper method of calculation; I have never studied elasticity theory.
Thank you for your advice.
RE: Radial deflection from an axial load
RE: Radial deflection from an axial load
RE: Radial deflection from an axial load
prex
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RE: Radial deflection from an axial load
RE: Radial deflection from an axial load
-Is it loaded uniformly across the surface on both sides?
Yes
-If gap is the radial gap, then the lateral strain is (2*gap/ID). Does this correction, if applicable, result in a better agreement with Pro/E?
The gap I am using in my calculations is diametrical gap, not radial.
-Are you plastically deforming the disk? Poisson's ratio is only accurate for elastic deformation.
I can't say for sure here, but since the disc is a polyethylene and the gap is only a few thousandths of an inch, I would think that the disk is deforming elastically, although I would like to check the numbers against plastic deformation. However, I do not believe there are equations for finding the deformation in the plastic region. Any ideas?
Thanks for your input.
RE: Radial deflection from an axial load
RE: Radial deflection from an axial load
In your first post you refer of a bulge in the middle of the lateral surface. This is not exact for the ideal case of your hand calc and you should check what Pro/E gives. In fact, if the pressure is really uniform on both faces and there are no tangential forces, such as those that would be applied by a piston and due to friction, the disk will be uniformly compressed in the axial direction and also uniformly extended in the radial direction (see Timoshenko & Goodier 3rd ed., page 226).
However those ideal conditions are very difficult to be implemented in practice, I wonder what you can realistically obtain for a relatively hard material and a correspondingly small gap.
prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads