| The constant evolution of the computer science gives rise to many research areas especially in computer aided design. This study is part, of the advancement of the numerical methods in engineering computer aided design, specifically in aerospace science. The geometric modeling based on NURBS has been applied successfully to generate a parametric wing surface for aerodynamic design while satisfying manufacturing constraints. The goal of providing a smooth geometry described with few parameters has been achieved. In that case, a wing design including ruled surfaces at the leading edge slat and at the flap, and, curved central surfaces with intrinsic geometric property coming from conic curves, necessitates 130 control points and 15 geometric design variables. The 3D character of the wing need to be analyzed by techniques of investigation of surfaces in order to judge conveniently the visual aspect and detect any sign inversion in both directions of parametrization u and nu. Color mapping of the Gaussian curvature appears to be a very effective tools in visualization. The automation of the construction has been attained using an heuristic optimization algorithm, simulated annealing. The relative high speed of convergence to the solutions confirms its practical interest in engineering problems nowadays. The robustness of the geometric model has been tested successfully with an academic inverse design problem. The results obtained allow to foresee multiple possible applications from an extension to a complete geometric description of an airplane to the interaction with others disciplines belonging to a preliminary aeronautical design process. |
