Buckling Analysis Of Functionally Graded Carbon Nanotube Reinforced Composite Nano-plates

In this thesis,based on the new couple stress theory for the microscale mechanical properties of anisotropic elasticity,a new model of functionally graded carbon nanotube-reinforced composite nano-plates,orthotropic functionally graded piezoelectric micro-plate as well as electrostatically actuated anisotropic micro-plate were proposed.The governing equations and related boundary conditions for buckling problem,bending and Pull-in phenomenon were derived by the principle of minimum energy and virtual work principle,according to numerical example capture the size effect of microscale structure.Studies in the thesis can be concluded as follows:(1)Based on a new modified couple stress theory and Mindlin plate theory,functionally graded carbon nanotube-reinforced composite nano-plates model were proposed.A simply supported square plate was taken as illustrative to respectively discuss the influence of material scale parameters,volume fraction and distributional patterns of the Carbon nanotube on the critical buckling load.The results indicate that the critical buckling loads predicted by the present model are always higher than those by the classical macroscopic theory,mean capture the size effect.In addition,The volume fraction and distribution pattern of Carbon nanotube have conspicuous influences on the critical buckling load,which should be considered in engineering design.(2)Bending model of the special plane orthotropic functionally graded piezoelectric(FGP)micro-plate was firstly presented based on the re-modified couple stress theory.This model contain two material size parameters,which considered bending stiffness and electric potential energy enhancement caused by size effect in two orthotropic directions caused by size effect.Through concrete comparision of results and paremeter,the influences of material paremeters on bending deflection and electric potential energy.Subsequently,the influence of functionally graded index on the size effects and bending defection were embodied in the present paper.(3)A size dependent model of electrostatically actuated anisotropic micro-plate was proposed based on a modified couple stress theory.This model simultaneously take into account macroscopic and microscopic anisotropy on the structural Pull-in characteristic.The explicit expressions of pull-in voltage and transverse deflection were given by utilizing a novel reduced-order method.Numerical results demonstrate that the presented model tends to predict higher/lower Pull-in voltage/transverse deflection than classical model,i.e.the size effect can be well depicted.The influence of size effect are most noticeable when the ratio of plate thickness to material size parameter approaches to 1,and the size effect would be gradually weak and neglectable if the ratio increases.In addition,the effects of microscopic anisotropy and initial gap on Pull-in voltage and size effect were also discussed.