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Collapsing mode of a circular cylindrical shell

From:
http://www.beachpackagingdesign.com/wp/2014/05/pseudo-cylindrical-concave-polyhedral-packaging.html

Also see:
"The Imperfection Data Bank and its Applications" by Jan de Vries, PhD dissertation, Department of Aerospace Engineering, 2009-05-11, Delft University of Technology
http://repository.tudelft.nl/search/ir/?q=The+Imperfection+Data+Bank+and+its+Applications&faculty=&department=&type=&year=

de Vries' introduction:
"The beer can was denied its original purpose in life. Before it got to the filling station in the beer plant, it got removed from the machine to be of use in the investigation of imperfection sensitivity of thin-walled shells. As it found out what was going to happen, the beer can reconsidered what to do. It could not taste the beer it had waited for for so long. However, this was not an unrealistic thought. Serving as a container for some liquid, whilst not being able to drink, and waiting for some person to come along and empty you and then get thrown out of the window if you were unlucky, or get recycled if you weren’t. No, one had to look for new opportunities. What was this imperfection sensitivity all about? Thin-walled shells, that is me, it thought. Am I alone in this world or are there more like me? Yes, I know lots of fellow beer cans. Even some vague far away families who prefer cola or orange juice even. But they are all small like me. The can then found out that there are huge shells, dinosaur tall compared to him, but not extinct. They did not contain stuff like beer, or coke, but very interesting sounding stuff like LOX or LH2. The can did not know what kind of stuff this was, but realized this: these big brothers were about to fly to the moon, to Mars or even maybe out of the solar system. No short life time, no low mile coverage, no, just your ordinary Saturday evening getting sold, getting drunk and getting thrown away. These guys really went somewhere. Now this was something to think about. The little can thought that even though he could not fly into space, it would also mean a lot to him if he could in some way help his big friends to safely fly into the sky.

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