  We study investigate a long, thin rectangular elastic membrane that is bent
through an angle $2 \alpha$, using the Foppl--von Karman ansatz in a
geometrically linear setting. We study the associated variational problem, and
show the existence of a minimizer for the elastic energy. We also prove
rigorous upper and lower bounds for the minimum energy of this configuration in
terms of the plate thickness and the bending angle, and we also obtain results
for the structure of the elastic ridge along it's length.
