## DE Seminar: Prof. Rouben Rostamian (UMBC)

#### First of Our UMBC Faculty DE Series

Monday, October 4, 2021 · 11 AM - 12 PM

**Title:**Inflating a balloon, and what it takes to get there

**Abstract:**Calculating the shape of an inflated balloon presents a series

model (large elastic deformations), reduction of the 3D

elasticity equations to those of a 2D membrane (differential

geometry), evaluating the equations of equilibrium on a membrane

whose shape is not known a priori (free boundary problem),

and solving the resulting nonlinear boundary value problem

for a system of ODEs (in the axially symmetric case) or PDEs

(in the general case).

In this talk I will touch upon some of the interesting aspects

of the issues outlined above without delving too deeply into the

technical minutia, and then demonstrate how one calculates the

inflated shape of a balloon corresponding to a prescribed

internal pressure P.