?`Qué forma adquiere una membrana elástica circular al aplicarle una diferencia de presión?

Abstract

An elastic circular membrane of uniform density and thickness and subjected to a constant pressure difference is studied theoretically and experimentally. Two solutions of the deformation of an elastic circular membrane and their comparisons with the numerical values of the measured deformations of a surgical rubber glove membrane. The first solution is an analogical calculations using the geometry of soap bubbles, and the second one is the analytical solution of the differential equation of the elastic deformation in the approximation of constant elastic modulus. Both solutions predict a spherical shape which is confirmed by the experimental data. Comparisons with the solution of a deformed plate and with the paraboloidal shape desirable for solar mirrors are also included.