Welcome to MathOverflow

Question

5

2

I take an rectangular sheet of paper, of height $H$ and Young's Modulus $E$, and in the absence of gravity, I bend it into a "teardrop" shape so that the edges along the top and bottom touch only along a single line.

What analytic function describes this "teardrop" shape?

flag	asked Jan 24 2012 at 23:30 PaperHouse 53●2

1

Are you specifying the boundary condition that the tangent cones of the edges coincide, or that they form some specified dihedral angle? – S. Carnahan♦ Jan 24 2012 at 23:45

1

You may find this question on MSE useful: math.stackexchange.com/questions/51539/… – Samuel Reid Jan 25 2012 at 0:02

Joseph O'Rourke · Accepted Answer · 2012-01-25 01:09:25Z UTC

7

All in here (if using Euler Bernoulli beam theory)

http://sci-toys.com/bent_paper_problem.pdf

(Added by Joseph O'Rourke). Here is Fig.1 from the paper by Antoni Colom, "Analysis of the shape of a sheet of paper when two opposite edges are joined," PDF link above.
Tear Drop

edited Jan 25 2012 at 1:09

Joseph O'Rourke

answered Jan 24 2012 at 23:53

Paul B
176●1●2

1

@Paul: I took the liberty of adding detail to your answer. – Joseph O'Rourke Jan 25 2012 at 1:34

Bending an elastic, inextensible sheet of paper into a teardrop shape

Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

1 Answer

You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.