Absolute Nodal Coordinate Formulation With Vector-Strain Transformation for High Aspect Ratio Wings

Abstract

High aspect ratio wings are potential candidates for use in atmospheric satellites and civil aircraft as they exhibit a low induced drag, which can reduce the fuel consumption. Owing to their slender and light weight configuration, such wings undergo highly flexible aeroelastic static and dynamic deformations that cannot be analyzed using conventional linear analysis methods. An aeroelastic analysis framework based on the absolute nodal coordinate formulation (ANCF) can be used to analyze the static and dynamic deformations of high aspect ratio wings. However, owing to the highly nonlinear elastic force, the statically deformed wing shape during steady flight cannot be efficiently obtained via static analyses. Therefore, an ANCF with a vector-strain transformation (ANCF-VST) was proposed in this work. Considering the slender geometry of high aspect ratio wings, the nodal vectors of an ANCF beam element were transformed to the strains. In this manner, a constant stiffness matrix and reduced degrees-of-freedom could be generated while capturing the highly flexible deformations accurately. The ANCF-VST exhibited superior convergence performance and accuracy compared to those of analytical approaches and other nonlinear beam formulations. Moreover, an aeroelastic analysis flow coupling the ANCF-VST and an aerodynamic model based on the unsteady vortex lattice method was proposed to perform the static and dynamic analyses successively. The proposed and existing aeroelastic frameworks exhibited a good agreement in the analyses, which demonstrated the feasibility of employing the proposed framework to analyze high aspect ratio wings.