Nonlinear Aeroelastic Method for Flapping Wings with Coupled Twisting and Bending

The aeroelastic behavior of insect-inspired flexible flapping wings (FFWs) directly dictates flight performance and is critical for the efficient operation of FFW-based aerial vehicles. However, most existing FFW models fail to simultaneously account for coupled twisting and bending, limiting their ability to accurately capture how leading-edge (LE) local flexibility affects aerodynamics. To address this, an FFW aeroelastic modeling method is proposed. Structurally, an analytical model coupling LE bar bending with wing membrane twisting is introduced, using nonlinear displacement–strain relations for geometric equations. Aerodynamically, the total aerodynamic load is decomposed into four components, and the dynamic equations are derived using Lagrange’s principle. Comprehensive validation shows that the Rayleigh dissipation-integrated model agrees well with high-fidelity computational fluid dynamics (CFD)/computational structural dynamics (CSD) simulations, with its computing time reduced to less than one-thousandth of [Formula: see text], realizing a remarkable improvement in computational efficiency. Parametric studies under the adopted kinematic conditions (sweeping amplitude 60 deg, frequency 25 Hz, passive pitching motion) reveal that 1) maximum vertical force and efficiency are achieved at an aspect ratio (AR) of 3; 2) reducing LE bar stiffness increases peak vertical force by 31% and results in a more pronounced “8”-shaped wingtip trajectory; and 3) increasing membrane stiffness from [Formula: see text] to [Formula: see text] boosts peak vertical force by 12%. In conclusion, this low-cost method accurately captures FFW deformation and aerodynamics under aerodynamic-inertial coupling, supporting high-efficiency FFW vehicle design.