Elasticity Solutions For Functionally Graded Plates And Shells Reinforced With Graphene Nanoplatelets

Graphene is a kind of two-dimensional crystal with only one layer of atom thickness,which is separated from graphite material and composed of carbon atoms.Because of its excellent optical,electrical and mechanical properties,graphene is considered as a revolutionary material.It has an extremely important application prospect in material science,micro nano processing,energy and other fields.Considering the super mechanical properties of graphene,as one of the materials with the highest strength know n,it also has excellent toughness and bendability.As a reinforcement material,graphene can effectively improve the mechanical properties of the matrix material.FGM is a kind of material which combines two or more materials with different properties,by continuously changing the composition and structure of the material,the properties of FGM will change continuously and uniformly with the change of the components of the material.FGM overcomes the shortcomings of traditional composite materials,effectively avoids the residual stress caused by material adaptation,and has the advantages that traditional composite materials do not have.FGM can improve the deformation and damage resistance of materials,which has been widely used in civil engineering and aviation.Due to the large contact area and excellent mechanical properties,graphene can be used as a gradient distribution in the matrix material to obtain graphene reinforced functional gradient material,which can effectively improve the mechanical properties of the material.With the further study of graphene materials,graphene reinforced functionally gradient materials have a deep research significance and a wide range of applications.In this paper,based on the three-dimensional elastic theory,the accurate three-dimensional elastic mechanics solution of the plate and shell structure is established by combining the motion equation,geometric relationship and constitutive equation.The static and dynamic problems of the plate and shell structure reinforced by functional gradient graphene are analyzed by introducing different boundary conditions with differential quadrature method.In this paper,it is assumed that the graphene nanocomposites are uniformly and randomly dispersed in the matrix,and their mass fraction / volume fraction changes linearly along the thickness direction.The equivalent material properties of graphene nanocomposites are determined by the improved Halpin-Tsai micromechanical model and the compound rule.Finally,the influence of the distribution pattern,mass fraction,size and shape of graphene nanoplatelets on the static and dynamic properties of the structure is discussed by numerical examples.The results of this paper are based on the three-dimensional elastic theory,without introducing other basic assumptions,which can provide information for solving the static and dynamic problems of nano reinforced composite structures.The study found that:(1)A small amount of graphene nanoplatelets dispersed in the polymer matrix can significantly reduce the bending deformation of the structure and increase its natural frequency.In addition,it was found ed that graphene nanoplatelets with large surface area could notable enhance the properties of the reinforced materials;(2)The distribution pattern of graphene nanoplatelets in polymer matrix has a great influence on the free vibration and bending characteristics of graphene reinforced structure.Among the five graphene distribution patterns considered in this paper,GPL-X distribution pattern is more efficient in enhancing stiffness,and the structure of this distribution pattern has the highest natural frequency and the smallest bending deformation;(3)The influence of elastic foundation parameters on the fundamental frequency of annular plate is also great.With the increase of Winkler coefficient and shear layer elastic coefficient of elastic foundation,the fundamental frequency of graphene reinforced structure increases.However,when the elastic coefficient of the shear layer is large,the influence of the increase of the Winkler elastic coefficient on the dimensionless frequency is limited.