A methodology for the shape optimization of flexible wings

M. Vázquez (INRIA, Sophia‐Antipolis, France)
A. Dervieux (INRIA, Sophia‐Antipolis, France)
B. Koobus (Department of Mathématiques, Université de Montpellier II, Montpellier, France)

Engineering Computations

ISSN: 0264-4401

Publication date: 1 June 2006



To propose an integrated algorithm for aerodynamic shape optimization of aircraft wings under the effect of aeroelastic deformations at supersonic regime.


A methodology is proposed in which a high‐fidelity aeroelastic analyser and an aerodynamic optimizer are loosely coupled. The shape optimizer is based on a “CAD‐free” approach and an exact gradient method with a single adjoint state. The global iterative process yields optimal shapes in the at‐rest condition (i.e. with the aeroelastic deformations substracted).


The methodology was tested under different conditions, taking into account a combined optimization goal: to reduce the sonic boom production, while preserving the aerodynamic performances of flexible wings. The objective function model contains both aerodynamic parameters and an acoustic term based on the sonic boom downwards emission.

Practical implications

This paper proposes a shape optimization methodology developed by researchers but aiming at the final strategic goal of creating tools that can be really integrated in design processes.


The paper presents an original loosely coupled method for the shape optimization of flexible wings in which recent and modern techniques are used at different levels of the global algorithm: the aerodynamic optimizer, the aeroelastic analyser, the shape parametrization and the objective function model.



Vázquez, M., Dervieux, A. and Koobus, B. (2006), "A methodology for the shape optimization of flexible wings", Engineering Computations, Vol. 23 No. 4, pp. 344-367. https://doi.org/10.1108/02644400610661145

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