Polynomial series expansion for optimisation of wing plane structures in idealised critical flutter conditions

Abstract

Abstract A numerical procedure, which utilises polynomial power series expansions for the optimisation of multipanel wing structures in idealised critical flutter conditions, is introduced and developed. It arises from the Rayleigh-Ritz method and employes trial polynomial describing functions both for the flexural displacement and for the thickness variation over the multipanel surface. An idealised structural plate model, according to the Kirchhoff’s theory, together with a linearised supersonic aerodynamic approach, are supposed. The classical Euler-Lagrange optimality criterion, based on variational principles, has been utilised for the optimisation operations, where by imposing the stationary conditions of the Lagrangian functional expression, a nonlinear algebraic equations system is obtained, whose solution is found by an appropriate algorithm. By utilising an iterative process it is possible to reach the reference structure critical conditions, with an optimised thickness distribution throughout the multipanel surface. The final part of the work consists in searching the minimum weight of the multipanel planform wing structure with optimised thickness profile vs the flutter frequency, considered as a variable imput parameter, for fixed flutter speed and equal to the critical one of the reference uniform structure.