This paper aims to reveal the multi-optimal mechanisms for dynamic control in drag- onfly wings. By combining the Arnold circulation with such micro/nano structures as the hollow inside constructions of the pterostigma, veins and spikes, dragonfly wings can create variable mass, variable rotating inertia and variable natural frequency. This marvelous ability enables dragonflies to overcome the contradictory requirements of both light-weight-wing and heavy-weight-wing, and displays the multi-optimal mechanisms for the excellent flying ability and dynamic control capac- ity of dragonflies. These results provide new perspectives for understanding the wings＇ functions and new inspirations for bionic manufactures.
Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.
Based on the negative exponential pair-potential （I/R）n, the interaction potential between the micro/nano planar curve and the particle located outside the curve is studied. We verified that, whatever the value of exponent n may be the potential of particle/plane-curve is always of unified curvature form. Furthermore, we proved that the driving forces acted on the particle may be induced by the highly curved micro/nano curve, and the curvature and gradient of curvature are confirmed to be the essential factors forming the driving force. Through the idealized numerical experiments, the accuracy and reliability of the curvature-based potential are examined.
Xugui WangYajun YinJiye WuKun HuangDan WangQinshan Fan
Based on the viewpoint of duality, this paper studies the interaction between a curved surface body and an inside particle. By convex/concave bodies with geometric duality, interaction potentials of particles located outside and inside the curved surface bodies are shown to have duality. With duality, the curvature-based potential between a curved surface body and an inside particle is derived. Furthermore, the normal and tangential driving forces exerted on the particle are studied and expressed as a function of curvatures and curvature gradients. Numerical experiments are designed to test accuracy of the curvature-based potential.
Wrinkling and buckling of nano-films on the compliant substrate are always induced due to thermal deformation mismatch.This paper proposes effective means to control the surface wrinkling of thin film on the compliant substrate,which exploits the curvatures of the curve cracks designed on the stiff film.The procedures of the method are summarized as:1)curve patterns are fabricated on the surface of PDMS(Polydimethylsiloxane)substrate and then the aluminum film with the thickness of several hundred nano-meters is deposited on the substrate;2)the curve patterns are transferred onto the aluminum film and lead to cracking of the film along the curves.The cracking redistributes the stress in the compressed film on the substrate;3)on the concave side of the curve,the wrinkling of the film surface is suppressed to be identified as shielding effect and on the convex side the wrinkling of the film surface is induced to be identified as inductive effect.The shielding and inductive effects make the dis-ordered wrinkling and buckling controllable.This phenomenon provides a potential application in the fabrication of flexible electronic devices.
This paper reports the new progresses in the axiomatization of tensor anal- ysis, including the thought of axiomatization, the concept of generalized components, the axiom of covariant form invariability, the axiomatized definition, the algebraic structure, the transformation group, and the simple calculation of generalized covariant differentia- tions. These progresses strengthen the tendency of the axiomatization of tensor analysis.
