An Enhanced Modal Approach for Large Deformation Modeling of Wing-Like Structures

Abstract

A new modal-based method that captures the geometric nonlinear effects that arise in the regime of large deformations of wing-like structures is presented. The most limiting factors of the modal approach are the linear force-displacement relationship and the representation of the nodal displacement field based on normal modes. The proposed extension includes stiffness terms that cubically depend on the generalized coordinates. The structural deformation is calculated not only by normal modes but also by higher order mode components that account for the foreshortening effect at beam-type structures. The approach is applied to a cantilever slender wing. Static and dynamic results are presented together with results from a commercial finite element solver and from the UM/NAST aeroelastic solver from the University of Michigan. The numerical study highlights the capability of the new approach to capture nonlinear effects while keeping the simplicity of the modal approach.