Topology Optimization of a Reinforced Wing Box for Enhanced Roll Maneuvers

Abstract

In this paper, the aileron reversal speed of a wing torsion box is maximized by reinforcing its upper skin. We propose a topology optimization approach using the spectral level set methodology. This is based on the level set methods,which represent theinterface describing thereinforcements asthe zerolevel setofafunction. Accordingto the proposed methodology, this function is discretized using its Fourier coefficients. These coefficients become the design variables of the optimization problem assigned to define the reinforcing layout. Results show that approximately the sameoptimal reinforcement layout isobtained from topologically different initialconfigurations. The two underlying ideas of the present work are to propose the spectral level set methodology as a framework for topology optimization, given its potential for reducing the design space dimension, and, considering the possibilities of new custom-made materials, to readdress the reinforcement perspective in aircraft structures without the weight penalty. Nomenclature ai,bi = problem domain boundaries corresponding to componenti ofx at = � t smoothness parameter aV = � V smoothness parameter a0 = lift curve slope bt = minimum thickness C = positive constant Cl� = derivative of the rolling moment coefficient of the rigid airplane with respect to� C �� � y;n� = twist aty produced by a unit moment at�