I'm working on an elasticity problem which, as I understand it, can be

solved using Maxwell's Reciprocal Theorem. The problem is as follows:

Given an inextensible ring subjected to a pair of diametrically opposing

forces, show that the area bound by the ring remains unchanged. The

ring can deform only by bending. Assume small deformation. (Note:

This is all the information I have...)

F

*/---\ F*

\---/

Ring

\---/

My understanding of this theorem is that so long as the system is linear

and elastic, it can be used to relate one loading scenario to another.

In this particular case, we know nothing about the applied forces, other

than the fact they are equal and opposite and serve to stretch (or

rather bend) the ring.

Therefore, I expect the need for another generalized force (like gravity

or pressure or something) in order to make the theorem work.

Unfortunately, I really have no idea what that generalized force would be.

Anybody have any ideas how to approach this problem? I appreciate any

input!

Thanks,

Kevin