Comparative analysis of deformation behaviors of dragonfly wing under aerodynamic and inertial forces.

Insect wings are typically deformed under aerodynamic and inertial forces. Both the forces are related to kinematic and morphology parameters of the wing. However, how the insects utilize complex wing morphologies and kinematics to generate the forces, and what the exact contributions of the two forces in wing deformation are still unclear. In the study, the aerodynamic and inertial forces produced by a dragonfly forewing are compared quantitively. Then the dynamic deformation behaviors are studied with a three-dimensional finite element model. Finally, roles of the two forces in wing deformation are fully discussed. The two forces increase along the wingspan every moment and they reach maximal consistently near the pterostigma. Because of the asymmetry of angle of attack, the maximal resultant aerodynamic force is about 4 times of that in upstroke. By comparison, the normal component of aerodynamic force plays the leading role in downstroke while the inertial force works mainly in tangential in upstroke. The finite element simulation demonstrates the bending and twisting deformation behaviors of the wing considering both flapping and rotation. The average strain energy in one flapping cycle is 1.23×10 mJ under inertial force and 0.43×10 mJ under aerodynamics respectively. In addition, the rapid rotation can enhance inertial deformation by 6 times. As a result, deformation of dragonfly wing is dominated by its own inertia in flight. The deformation mechanism addressed could inspire the design of flexible flapping airfoils in morphology and kinematics.