Finite element models of Manduca sexta wings (Combes, 2002)

homogeneous wing: model wing with membrane (blue) and vein (pink) elements each of homogeneous material stiffness (E).	exponential wing: model wing in which declining material stiffness (E) of membrane (memb 1-12) and vein (vein 1-12) elements results in an exponential decline in flexural stiffness (EI) in both the spanwise and chordwise directions, as measured in real wings.

Results of static loading tests on finite element model (FEM) wings. Homogeneous wing is shown on left and exponential wing on right. Wings are fixed at the base (no rotation or displacement) and a point force of 0.003 N is applied at the wing tip (green arrow). Note that displacement at the tip is the same in both models, and is comparable to displacements measured on real wings (results in the chordwise direction are similar). The overall flexural stiffness (EI averaged over the entire span or chord) is therefore the same in both models, and the models differ only in the spatial distribution of flexural stiffness throughout the wing.

Movies of flapping FEM wings. Homogeneous wing is on the left and exponential wing on the right. Wings are rotated around one axis at their base. Rotation amplitude is increased gradually to a sinusoidal motion, with a frequency of 26 Hz (comparable to flapping frequency in Manduca sexta). See Combes (2002) for further details.