Membrane Analogy
The elastic membrane analogy, also known as the soap-film analogy, was first published by pioneering aerodynamicist Ludwig Prandtl in 1903. It describes the stress distribution on a long bar in torsion. The cross section of the bar is constant along its length, and need not be circular. The differential equation that governs the stress distribution on the bar in torsion is of the same form as the equation governing the shape of a membrane under differential pressure. Therefore, in order to discover the stress distribution on the bar, all one has to do is cut the shape of the cross section out of a piece of wood, cover it with a soap film, and apply a differential pressure across it. Then the slope of the soap film at any area of the cross section is directly proportional to the stress in the bar at the same point on its cross section.
Read more about Membrane Analogy: Application To Thin-walled, Open Cross Sections, Other Applications
Famous quotes containing the word analogy:
“The whole of natural theology ... resolves itself into one simple, though somewhat ambiguous proposition, That the cause or causes of order in the universe probably bear some remote analogy to human intelligence.”
—David Hume (1711–1776)