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Aiming at exploring the excellent structural performance of the vein-stiffening membrane structure of dragonfly hind wings, we analyzed two planar computational models and three 3D computational models with cambered corrugation based on the finite element method. It is shown that the vein size in different zones is proportional to the magnitude of the vein internal force when the wing structure is subjected to uniform out-of-plane transverse loading. The membrane contributes little to the flexural stiffness of the planar wing models, while exerting an immense impact upon the stiffness of the 3D wing models with cambered corrugation. If a lumped mass of 10% of the wing is fixed on the leading edge close to the wing tip, the wing fundamental frequency decreases by 10.7%∼13.2%; if a lumped mass is connected to the wing via multiple springs, the wing fundamental frequency decreases by 16.0%∼18.0%. Such decrease in fundamental frequency explains the special function of the wing pterostigma in alleviating the wing quivering effect. These particular features of dragonfly wings can be mimicked in the design of new-style reticulately stiffening thin-walled roof systems and flapping wings in novel intelligent aerial vehicles.

Review of the book Hanger, W.W., and Pardalos, P. (Eds) [1998], Optimal Control, Kluwer Academic Publishers

We present an elastoplastic normal force–displacement (NFD) model for spheres in collision. Among several possible applications of this model are the granular–flow simulations using a discrete–element method. The proposed NFD model is consistent with the formalism of the continuum theory of elastoplasticity, and is validated with nonlinear finite–element analyses. A key feature of this NFD model is the additive decomposition of the radius of the contact area into an elastic part and a plastic part. Further, the contact curvature is corrected, and the Hertzian contact mechanics generalized, to account for plastic deformation. The present displacement–driven version of the elastoplastic NFD model—whose force–driven version was presented by Vu–Quoc, Zhang and Lesburg in 1988—is developed particularly for granular flow simulations. Results of sphere–on–sphere collisions are discussed. In particular, the resulting coefficient of restitution varies with the incoming velocity. A comparison of the results obtained from the present NFD models with those from other models is given.

A new theory of sandwich beams/one-dimensional plates is presented with finite rotations and shear allowed in each layer. The layers, variable in number from one to three, need not have the same thickness and the same length, thus allowing for ply drop-off. Restricting to planar deformation, the cross section has a motion identical to that of a multibody system that consists of rigid links connected by hinges. Large deformation and large overall motion are accommodated, with the beam dynamics referred directly to an inertial frame. An important approximated theory is developed from the general nonlinear equations. The classical linear theory is recovered by consistent linearization.

A Galerkin projection of the equations of equilibrium for a recent theory of geometrically exact sandwich beams that allow finite rotations and shear deformation in each layer is presented. The continuity of the displacement across the layers is exactly satisfied. The resulting finite element formulation can accommodate large deformation. The number of layers is variable, with layer lengths and thicknesses not required to be the same, thus allowing the modeling of sandwich structures with ply drop-off. Numerical examples are presented which underline the salient features of the formulation. Saint-Venant principle is demonstrated for very short sandwich beams.