# Deflection of ring

1. Aug 17, 2011

### vishal007win

How to calculate the deflection in ring, fixed at center, with a radial point force acting at some point(let say at theta=0) ?
I have derived complete set of equations. Now how to apply boundary conditions ?
to get a complete solution of 4th order equation, I need 4 B.C's, but here displacements are not specified at any point. Imposing periodicity I can get 2 more conditions
u(0)=u(2*pi)
w(0)=w(2*pi)
where u and w are radial and tangential displacements respectively
and how to apply force boundary condition in this case?

2. Aug 18, 2011

### Studiot

This does not make sense.

A ring has no material centre, do you mean a disk?

Perhaps a diagram?

3. Aug 18, 2011

### vishal007win

consider the thin ring on elastic foundation(shaded portion shown in the figure is an elastic foundation(elastic membrane) which provide a support from center to ring)
The inner circle shown can be taken as mass-less and inertia-less disc.
actually resembling the tyre geometry with side walls and inner wheel drum.
now if a point load is applied at the circumference of ring. How to calculate the static deflection in this case?

#### Attached Files:

• ###### Untitled.jpg
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4. Aug 18, 2011

### Studiot

If h is your applied load, and the wheel does not touch the ground I still don't see equilibrium in your diagram.

How is the elastic centre supported?

5. Aug 18, 2011

### vishal007win

h is the width of the ring.
the attachment in the above post actually resembles kind of set up shown in the figure below.. where elastic membrane resembles the sidewalls of tires and the ring represents the belt of tire and the inner disc represents the wheel drum. Now equilibrium is maintained by the reaction from the centre which is fixed(force getting transmitted by elastic membrane). i hope that makes the problem clear.
now instead of modelling contact region, if radial point force is applied at bottom, assuming the centre of wheel fixed, how to find the static deflection of ring?

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