The Influence Of Surface Effects Of Nanostructures On Several Problems Based On Surface Energy Density Elasticity Theory

Nanomaterials and nanotechnology,which are initiated and rapidly developed in the 20 th century,have been applied in many basic researches and engineering applications.From the perspective of electronics,the atomic size of nanostructures is very close to the coherence length of electrons,so the strong coherence between atoms results in self-organization of their internal structures.From the optical point of view,the original periodic boundary condition is destroyed when the structure scale is very close to the wavelength of light.All these make the properties of nanomaterials change greatly,which makes them have excellent mechanical,optical,magnetic,thermal and electrical properties.Therefore,it is widely used as structural components in micro/nano electromechanical systems,such as nano sensors,nano vibrators,nano energy capture devices,etc.When the size of the material reaches the nanoscale or smaller,the surface area to volume ratio of the material increases rapidly,which will lead to the surface effect will have a significant impact on the mechanical properties of the material.Therefore,it is of great significance and necessity to analyze the influence of surface effect on the mechanical behavior of nanometer components.In this paper,the influence of surface effect on the mechanical behavior of several nanostructure problems is studied based on the theory of surface energy density elasticity theory.The analytical expressions of the related problems are obtained by combined with the mathematical method in mechanics.The details are as follows:(1)The influences of surface effect on contact problems at the nanoscale are investigated.By combining the variation principle and the generalized Young-Laplace equation,the stress boundary conditions of the elastic field with surface energy density are derived,and the analytical expressions of the stress and displacement in the elastic half-space under uniform distributed load and concentrated force are given by using the Fourier integral transform method.The results show that the contact stress and displacement of the deformed surface can change steadily along the loading boundary.In addition,the surface effect has a significant influence on the stiffness of the material.The higher the surface energy density is,the harder the material surface becomes.(2)The influences of surface effects in heterogeneous structures with elliptic hole at nanoscale are studied.Based on the theory of complex function,the closed solutions of the deformation around elliptic holes under different far field loading including surface effect are obtained by using the stress function method and conformal transformation.The results show that the stress state around the elliptic hole not only depends on the shape of the hole,but also obviously depends on the surface effects.(3)The influences of surface effects on the bending and force-electrical coupling behavior of piezoelectric nanowires were investigated.Based on the principle of minimum potential energy,the governing equation of piezoelectric nanowires bending with surface effect and the corresponding boundary conditions are derived,and the analytical expressions of deflection,effective bending stiffness and induced charge of two piezoelectric nanowires under concentrated force are given.The results show that the surface effect increases the effective stiffness of the stiffened nanowires,and the cantilever nanowires have the opposite effect.In addition,the induced charge of both types of nanowires significantly higher than that without surface effect under the same external load.(4)The influence of surface effect on the free vibration and buckling behavior of piezoelectric nanowires was studied.The governing equations of motion and buckling of piezoelectric nanowires containing surface effects are derived by using Hamiltonian principle and solved the vibration natural frequency and buckling critical voltage.The theoretical results show that the surface effect has more significant influence on the vibration natural frequency and buckling critical voltage change of slender nanowires.