Solution of a Nonplanar Lifting-Line Model Using the Finite Element Method

Abstract

A reduction in the structural wing weight is generally followed by an increase in the structural flexibility, leading to a significantly deformed wing configuration. A modified Prandtl’s lifting-line model proposed herein aims to approximate the spanwise lift distribution and the induced drag using a finite element method approach. A numerical validation considering planar elliptical wings is carried out for several mesh configurations. The proposed approach has an optimal agreement to the analytical solution, showing a global error inferior to in terms of the spanwise circulation distribution. Next, analyses of nonplanar wings are made compared to the available literature data. For the first case, the relative difference regarding the lift coefficient is less than 0.3%, whereas for the induced drag, it is less than 2.2%. For the second case, a maximum difference for the lift coefficient is less than 0.5%. The numerical strategy proposed in this paper approximates the solution of the aerodynamic problem to the approach via finite element methods used in structural analysis. The presented approach can later lead to a hybrid finite element with aerodynamic and structural degrees of freedom, which can be helpful for the development of a monolithic approach.