Figure 1.
Morphology of Allomyrina dichotoma beetle's hind wing.
(A) The Allomyrina dichotoma beetle and its flexible hind wing, and (B) its right hind wing showing veins. (AA, anal anterior; CuA, cubitus anterior; af, anal fold; cf, claval fold; lf, longitudinal fold; mf, median flexion line; MP1+2, media posterior; AP3+4, anal posterior; RA, radius anterior; RP, radius posterior; ScA, subcosta anterior; tf, transverse fold; the circle denotes the marginal joint (MJ) position and the star denotes the movable vein joint (MVJ) position.). (C) Spanwise and chordwise camber of the wing at the rest condition.
Figure 2.
Finite element models based on the Allomyrina dichotoma beetle's hind wing.
(A) Chord-spanwise camber intact model. (B) Chord-spanwise camber cutting model. The membrane elements are yellow and the vein elements are blue. The circle and star indicate the MJ and MVJ, respectively. The displacement is applied to MJ and MVJ. XX' and YY' show two cross sections of the model.
Figure 3.
Force and area distribution along a single wingspan.
The average force included the aerodynamic and inertial forces during a flapping cycle were considered as a reference force to investigate the bending asymmetry of the wing.
Figure 4.
The stress stiffening effects on the chord-spanwise camber intact model.
(A) The free body forces (NFOR) and moments (NMOM) in the ANSYS® model in the linear and nonlinear solutions. The NFOR is indicated using pink, and the NMOM is green. (B) Displacement contour when pressure was applied to the dorsal and ventral sides in the linear and nonlinear solutions.
Figure 5.
Finite element results for the force versus deflection of the chordwise camber intact model and chord-spanwise intact model at two load positions.
(A) Load applied at MJ. (B) Load applied at MVJ.
Figure 6.
Deformations of the chord-spanwise camber intact model.
(A) Deformations of the wing under 1 mm displacement applied to the MVJ (red arrow). The black lines without contours indicate the undeformed shape of the wing. The black lines with contours indicate the deformed shape of the wing. (B) Deformations of the wing due to pressure.
Figure 7.
Finite element results for the force versus deflection of the beetle hind wing for the spanwise camber intact model.
(A) Load applied at MJ. (B) Load applied at MVJ.
Figure 8.
Finite element results for the force versus deflection of the chord-spanwise camber cutting model at two load positions.
(A) Load applied at MJ. (B) Load applied at MVJ.
Figure 9.
Schematic of the spanwise camber intact model under a load.
(A) Load on the dorsal side, where the force tends to decrease the effective length. (B) Load on the ventral side, where the force tends to increase the effective length. The curve in the figure shows the spanwise camber. The dashed lines indicate the initial position; the solid lines indicate the deformed position.
Figure 10.
Contour plot of the normal stresses in the x and y directions (σx and σy) due to the pressure load in both sides (dorsal and ventral sides) of the chord-spanwise camber intact model.
Figure 11.
Orientation of the principal stresses (σ1, σ2, and σ3) due to the pressure load on both sides (dorsal and ventral sides) of the chord-spanwise camber intact model.