Dynamic modal rotation method with inertial nonlinearity for large deformation analysis of slender structures

As high-aspect-ratio wings can suppress induced drag, they are used for next-generation aircraft such as high-altitude long-endurance (HALE) aircraft. High-fidelity models such as nonlinear shell/plate or solid finite element models, which analyze large dynamic deformations with many degrees of freedom, are computationally intensive. The modal rotation method (MRM) is a static analysis method that efficiently analyzes large deformations based on modes and stiffness matrices obtained from any linear or linearized model. MRM targets slender structures with small strains and large displacements and considers geometrical nonlinearity rather than material nonlinearity. Dynamic MRM (DMRM), which was developed by extending the MRM to a dynamic analysis method, can efficiently perform nonlinear dynamic analyses using a modal approach. However, the conventional DMRM was formulated under the assumption that the inertial nonlinearity can be neglected. In this study, a novel DMRM that takes inertial nonlinearity into account was proposed. To achieve this, emphasis was placed on the similarities between MRM and rigid multibody systems. In addition, a damping term has been included in the equation of motion in the proposed method. This enables a comparison between the analytical results of the proposed method and the experimental results with damping effects. The proposed method can account for the inertial nonlinearity in a simulation performed and reduce the calculation time by 98% compared to the nonlinear plate finite element method. Moreover, the proposed method with damping showed good agreement with the experimental results for large beam deformations.