*Proceedings of the 5th World Congress on Computational
Mechanics (WCCM-V)*
(Eds. H.A. Mang, F.G. Rammerstorfer, J. Eberhardsteiner),
paper # 80870, 2002

### MEMBRANE STRUCTURES IN UNSTEADY POTENTIAL FLOW

N. Friedl

Institute of Lightweight Structures and Aerospace
Engineering,

TU Wien,
Vienna, Austria

**Abstract** -
In this contribution a method will be described, which allows the simulation of
membrane wings in unsteady potential flow.
Typical examples for membrane wings are hanggliders, kites and sails of boats.
In the case of hanggliders the wing has very little torsional stiffness.
The wing shape, i.e. the angle of attack along the wingspan, is governed by
both the nonlinear membrane structure and the aerodynamic loads, which in turn
depend on the geometry of the structure.
Therefore this system is dominated by fluid-structure interaction.
A method for solving the stationary problem can be found in [1], where the
aerodynamic flow was calculated by the VLM-QCM-method, a specialized
vortex-lattice procedure.
The membrane structure is simulated by the Finite Element Method (FEM).
The coupling between both models is carried out by exchanging pressure
distributions and displacement fields between the models.
This way of coupling can, however, cause poor convergence or even diverging
solutions.

For the unsteady procedure presented in this work a more complex approach was
implemented to simulate the fluid-structure interaction.
The nonlinear FEM-analysis uses a Newmark scheme for the implicit stepwise time
integration.
The unsteady flow is calculated by a novel procedure which was developed by
combining [2] and [3] to a higher order vorticity panel method.
Starting from a known solution (steady solution or converged solution of a
previous timestep), a Predictor-Corrector algorithm calculates the aerodynamic
loads for the next timestep (predictor step).
Furthermore the aerodynamic stiffness and damping matrices for the predicted
state are found.
They describe the changes in aerodynamic loads with respect to deviations from
the predicted position and velocity (corrector terms).
This formulation of the aerodynamic loads is used in the nonlinear
FEM-analysis and allows a simultanuous solution of the aerodynamic and the
structural problem.

Numerical examples for the Predictor-Corrector-algorithm and results of the
simulation of simple hangglider structures are presented.

[1] H. Schoop, N. Bessert, L. Taenzer,
*On the Elastic Membrane in a Potential Flow*,
Int.J.Numer.Meth.Engng. **41**(2), 271-291, 1998.

[2] C.P. Mracek, M.J. Kim, D.T. Mook,
*Three-Dimensional Potential Flows by a Vorticity-Panel Method*,
Comput.Fluids **21**(1), 31-42, 1992.

[3] K.-H. Horstmann,
*Ein Mehrfach-Traglinienverfahren und seine Verwendung für Entwurf und
Nachrechnung nichtplanarer Flügelanordnungen*,
Deutsches Zentrum für Luft- und Raumfahrt,
Forschungsbericht DFVLR-FB 87-51, 1987.

(hjb,020529)