Flexural stiffness in insect wings I. Scaling and the influence of wing venation

Abstract

SUMMARYDuring flight, many insect wings undergo dramatic deformations that are controlled largely by the architecture of the wing. The pattern of supporting veins in wings varies widely among insect orders and families, but the functional significance of phylogenetic trends in wing venation remains unknown, and measurements of the mechanical properties of wings are rare. In this study, we address the relationship between venation pattern and wing flexibility by measuring the flexural stiffness of wings (in both the spanwise and chordwise directions) and quantifying wing venation in 16 insect species from six orders. These measurements show that spanwise flexural stiffness scales strongly with the cube of wing span, whereas chordwise flexural stiffness scales with the square of chord length. Wing size accounts for over 95% of the variability in measured flexural stiffness; the residuals of this relationship are small and uncorrelated with standardized independent contrasts of wing venation characters. In all species tested, spanwise flexural stiffness is 1-2 orders of magnitude larger than chordwise flexural stiffness. A finite element model of an insect wing demonstrates that leading edge veins are crucial in generating this spanwise-chordwise anisotropy.

Structural Analysis of a Dragonfly Wing

“…Previous studies [13,15,29,33,34] suggested that the inertial loads are higher than the aerodynamic loads, from 2 [31] up to 10 times [34]. If such a load ratio also holds for dragonfly wings is unknown.…”

“…To check if the number of elements in our FEM model was appropriate for numerical convergence we performed a literature survey. Combes and Daniel [13][14][15] found an asymptotic solution for their FEM model of a Manduca sexta wing for 865 elements and up (FEM solver MSC Marc/Mentat 2001). Considering the similarity in wing dimensions and number of elements and the quality of the solution we obtained, we are confident we performed an accurate FEM analysis.…”

“…The material density of wing cuticle ρ c is taken as 1,200 kg/m3 (measured in biological materials by Wainwright et al [23], and confirmed by Vincent and Wegst [24]) and we used a Poisson's ratio ν of 0.49 [23]. Combes and Daniel [13][14][15] also used a Poisson's ratio of 0.49 and tested the effects of using a Poisson's ratio of 0.3 and found the effect to be negligible. In our analysis we took the material stiffness of the wing (Young's modulus, E) constant throughout the wing for both the veins and membranes, similar to Smith [10] and Kesel et al [11].…”

“…Counter-intuitively the corrugated wings of insects provide good aerodynamic performance at low Reynolds numbers [5][6][7][8][9], while providing good structural strength and stiffness [6]. Numerical analyses of insect wings have been performed by Smith [10], Kesel et al [11], Herbert et al [12], Combes and Daniel [13][14][15] and Wootton et al [16] to better understand the structural function of insect wings under different loading regimes. Smith [10] performed a modal analysis of a quasi-two-dimensional finite element model (FEM) of the fore-and hindwing of a moth, to correlate the distribution of mass and stiffness.…”

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

“…For our purpose, it is sufficient to address only the chordwise flexibility and represent the flexible wing as a homogeneous elastic flat plate [24]. While three-dimensional effects, such as spanwise flow that seem to stabilize the LEVs [25] or LEV-tip-vortex interaction [26] are notable in general, the chordwise flexibility is essential and warrants an independent study [18].…”