Vein-Membrane Interaction in Cambering of Flapping Insect Wings.

It is still unclear how elastic deformation of flapping insect wings caused by the aerodynamic pressure results in their significant cambering. In this study, we present that a vein-membrane interaction (VMI) can clarify this mechanical process. In order to investigate the VMI, we propose a numerical method that consists of (a) a shape simplification model wing that consists of a few beams and a rectangular shell structure as the structural essence of flapping insect wings for the VMI, and (b) a monolithic solution procedure for strongly coupled beam and shell structures with large deformation and large rotation to analyze the shape simplification model wing. We incorporate data from actual insects into the proposed numerical method for the VMI. In the numerical analysis, we demonstrate that the model wing can generate a camber equivalent to that of the actual insects. Hence, the VMI will be a mechanical basis of the cambering of flapping insect wings. Furthermore, we present the mechanical roles of the veins in cambering. The intermediate veins increase the out-of-plane deflection of the wing membrane due to the aerodynamic pressure in the central area of the wing, while they decrease it in the vicinity of the trailing edge. As a result, these veins create the significant camber. The torsional flexibility of the leading-edge veins increases the magnitude of cambering.