Study On The Mechanical Behavior Of Functionally Graded Graphene Reinforced Composite Shallow Shells

Graphene and its derivatives,rich in the nature,have excellent electrical,mechanical and thermal properties.Studies have shown that a small weight percentage of graphene platelet as the reinforcement in the composite,can significantly enhance the stiffness and strength of the compositescompared with the traditional carbon fibers.Functionally graded graphene reinforced composite,in which graphene platelets as reinforcement are randomly or evenly distributed in the matrix with gradient or uniform arrangement according to a certain rule along the thickness,have attracted increasing attention in science and engineering fields.As a promising material,it's necessary to study the mechanical behavior of the structures for their future applications.In this paper,the mechanical behaviors of functionally graded graphene reinforced composite shallow shells with different graphene distribution patterns are studied.The high order shear deformation theory and the von-Karman type strain and displacement relationship are used,and the Young's modulus is guaranteed by modified Halpin-Tsai model.Poisson's ratio as well as density is conducted via rule of mixtures.According to the Hamilton's principle,the kinetic equations of the shallow shells are obtained.In this paper,the mechanical behaviors of functionally graded graphene reinforced composite shallow shells are investigatedin the following aspects:(1)Free vibration and static bending of functionally graded graphene nanoplatelet reinforced composite doubly-curved shallow shells with three distinguished distributions are analyzed.Material properties with gradient variation in the thickness aspect are evaluated by the modified Halpin-Tsai model.Mathematical model of the simply supported doubly-curved shallow shells rests upon Hamilton Principle and a higher order shear deformation theory(HSDT).The free vibration frequencies and bending deflections are gained by taking into account Navier technique.The agreement between the obtained results and ANSYS as well as the prior results in the open literature verifies the accuracy of the theory in this article.Further,parametric studies are accomplished to highlight the significant influence of GPL distribution patterns and weight fraction,stratification number,dimensions of GPLs and shells on the mechanical behavior of the system.(2)Nonlinear dynamics of functionally graded graphene reinforced composite spherical shallow shell subjected to transverse excitation and in-plane excitation are studied.By applying Galerkinmethod,a series of coupled nonlinear ordinary differential equations(ODEs)is formed.Further,numerical results depended on the fourth-order Runge-Kutta method including bifurcation diagram,the maximum Lyapunov exponent diagrams,waveforms as well as phase portrait are presented to illustrate the influence of graphene platelet weight fraction,distribution patterns and length-to-thickness ratios on the nonlinear dynamics responses of the structure.(3)The nonlinear transientdynamic response of functionally graded graphene reinforced compositeshallowsphericalshell has been investigated under time dependent blast load.Then a second ordinary differential equation is obtained by Galerkin method andsolved by the Newton-Raphson method.Further,a parametric study is conducted to consider the influence of the content of graphene platelet,distribution types,the total layers number,the size of graphene platelet,parameters related to blast loading and aspect ratio of shallow spherical shell on the nonlinear transient dynamics responses of the structure.(4)The flutter characteristics of functionally graded graphene reinforced composite shallow spherical shells considering aerodynamic force with curvature correction term are carried out.The truncated flutter equations of six-degrees-of-freedom are obtainedusing the Galerkin methodand the flutter characteristics of the shallow shell systems with different graphene platelet contents and distribution patterns are analyzed by eigenvalue response curve of the system and the numerical results obtained by Runge-Kutta method.