### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** Edward W. Swim, Mathematics, US Military Academy, West Point

**Title: ***
Nonlinear fluid-structure interaction models for biologically inspired elastic membrane wings
*

**Abstract:**

Micro air vehicles (MAVs), which typically have a wing span of at most six inches, flight speeds of twenty to forty miles per hour, and a
total weight less than half a pound, encounter flight conditions with Reynolds numbers similar to that of an insect or bird (10^3-10^5). As a result, stall may
occur for moderate angles of attack due to flow separation near the leading edge spar. This aerodynamic regime results in vastly different flight dynamics
than is usually observed in traditional aircraft.

As the size of MAVs decreases for usage in urban and interior environments, the ability to mimic flight behavior of insects and other small creatures is
an important part of creating a vehicle that can be easily maneuvered in such settings and still maintain anonymity when necessary. Stability and responsiveness
of MAVs improves whenever a thin material, similar to that used for sailboats and parachutes, is the primary surface of the wing. Moreover, wings constructed
in this way can delay the onset of stall. But as in nature, the payload and function of a MAV can significantly influence the optimal shape of a membrane wing.
As a result, it is necessary to construct an efficient numerical scheme which allows for the coupling of a viscous incompressible fluid and a nonlinear membrane in
a dynamic fluid-structure interaction simulation. In particular, the membrane solver should allow for a wide variety of material nonlinearity so that many
different constitutive models can be explored during the development phase of MAV production.

In this talk we present a new nonlinear framework for membrane dynamics in the numerical simulation of micro air vehicle performance.
A finite element approach to approximating the solutions to the resulting initial-boundary value problem is constructed and analyzed based on
manufactured solutions that mimic deformations frequently observed for flexible wing MAVs.

**Time:** Friday, February 1, 2008, 1:30-2:30 p.m.
**Place:** Research I, Room 301

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491