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DE Seminar: Prof. Rouben Rostamian (UMBC)

First of Our UMBC Faculty DE Series


Mathematics/Psychology : 401

Date & Time

October 4, 2021, 11:00 am12:00 pm


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

Abstract: Calculating the shape of an inflated balloon presents a series
of challenges, including the formulation of the mathematical
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.