Aeroelastic optimisation of composite wings using the dynamic stiffness method

Abstract

A computer program for use in the conceptual stage of aircraft design has been developed. The program obtains minimum mass designs for high aspect ratio, composite wings, subject to constraints on flutter speed, divergence speed and material stress. The wing is modelled as a series of composite beam elements and both flutter speed and divergence speed are calculated using a normal mode approach. Modal analysis is carried out by applying the Wittrick-Williams algorithm to the dynamic stiffness method, whereas unsteady aerodynamic loads are calculated from strip theory, although an option which uses lifting-surface theory is also presented. A previously published example is given to validate the analysis. Single level optimisation is carried out using a sequential quadratic programming strategy combined with the modified methods of feasible directions optimizer, for which flutter sensitivities are obtained by an efficient determinant interpolation technique. Design variables include topological variables such as spar and engine positions as well as layer thicknesses, which are modelled using quadratic functions. The wing of a regional turboprop aircraft is optimized to illustrate the use of the program. The problem was modelled using 10 elements and had 43 design variables, 162 constraints and required just over 20 minutes of CPU time on a workstation. This, coupled with the fact that a full three-dimensional FE model of the same wing would require over 1000 elements, illustrates the suitability of the dynamic stiffness method to the conceptual design stage.