Isogeometric Analysis For Nonlinear Mechanical Behaviors Of FG-GPLRC Plates And Shells Based On Non-classical Elasticity

Functionally graded graphene platelet reinforced composite(FG-GPLRC)is a novel lightweight composite material with great application prospect in the field of micro-and nano-mechanical systems.It is found that size effect appears in micro-and nano-structures.In this dissertation,nonlinear mechanical behaviors of size-dependent novel composite plates and shells in micro-and nano-scales are investigated within the framework of isogeometric analysis.Three non-classical elasticity theories,i.e.,modified couple stress theory,modified strain gradient theory and nonlocal strain gradient theory are introduced to capture size effect.Based on first-order shear deformation theory,higher-order shear deformation theory and the four-variable higher-order shear deformation theory,a series of size-dependent isogeometric model are presented to investigate scientifically the nonlinear buckling,nonlinear free vibration,nonlinear static bending and nonlinear transient dynamic responses of the FG-GPLRC micro-and nano-plates,which has a certain guiding significance for the design and application of micro-and nano-structures made of new materials.The modified couple stress-based isogeometric model of the shallow spherical shells is established for the first time and the model is applied to analyze the nonlinear buckling behaviors of the FG-GPLRC shallow spherical shells.On the basis of modified couple stress theory,first-order shear deformation theory,the von Kármán geometric nonlinearity and variation principle,the weak form of the equilibrium equation of the size-dependent FG-GPLRC shallow shell panels subjected to transverse loadings is established within the framework of isogeometric analysis(IGA).The arclength continuation and Newton-Raphson’s iterative method are utilized synthetically to capture successfully the snap point and to obtain the equilibrium paths for the panels numerically.Parametric studies are performed in detail to demonstrate the influences of distribution of graphene platelet(GPL),weight fraction of GPL,material length scale parameter and radius of the shallow shell on the nonlinear load-deflection curves for the FG-GPLRC shallow shell panels.The size-dependent nonlinear free vibration of the FG-GPLRC plates is studied by taking higher-order shear deformation theory into account.A novel non-elementary function is proposed as the shear deformation function.Based on modified couple stress theory,higher-order shear deformation theory,the von Kármán geometric nonlinearity and variation principle,the weak form of the governing equation for nonlinear free vibrations of the FG-GPLRC circular and annular sectorial plates is established within the framework of isogeometric analysis.The displacement control strategy associated with iterative technique are employed to obtain the nonlinear amplitude-frequency curves(or backbone curves)of the FG-GPLRC plates.Detailed parametric studies are performed to present an insight into the influences of distribution pattern and weight fraction of GPL,size dimensions of plates and material length scale parameter on the behaviors of linear natural frequencies and large amplitude responses of the plates under different boundary conditions.In addition,the comparative investigations show the validity of the proposed shear deformation function.The size-dependent nonlinear static bending and nonlinear transient dynamic responses of the FG-GPLRC plates under transverse loadings are carried out.Based on modified couple stress theory,the four-variable higher-order shear deformation theory,the von Kármán geometric nonlinearity and variation principle,the weak forms of the governing equations for static and dynamic behaviors of the FG-GPLRC rectangular plates are established within the framework of isogeometric analysis.The nonlinear static bending responses are obtained by load increment and iterative procedure,while the transient dynamic responses are obtained by Newmark time integration scheme and iterative method.In numerical examples,the influences of distribution pattern of GPL and material length scale parameter on the bending and transient responses are discussed.In addition,the distinction of linear and nonlinear transient responses are elaborated.A nonlinear isogeometric model based the four-variable refined plate theory and modified strain gradient theory is presented for the first time and it is applied to analyze the size-dependent postbuckling behavior of a lightweight sandwich plate with FGGPLRC face layers and porous core subjected to in-plane uniaxial compression.Based on modified strain gradient theory,the four-variable higher-order shear deformation theory,the von Kármán geometric nonlinearity and variation principle,the weak form of the governing equation for postbuckling behavior of the porous sandwich FGGPLRC rectangular plates is established within the framework of isogeometric analysis.The equilibrium equation is regarded as a nonlinear eigenvalue problem to obtain postbuckling paths.Several numerical cases are provided to reveal the influences of weight fraction of GPL,coefficient of porosity and three material length scale parameters on postbuckling behavior of porous sandwich FG-GPLRC plates.As for the porous sandwich FG-GPLRC plates in nano-scale,the nonlinear transient dynamic responses are investigated.On the basis of nonlocal strain gradient theory,first-order shear deformation theory,the von Kármán geometric nonlinearity and variation principle,the nonlinear equation of motion of the plate under transient loadings is established within the framework of isogeometric analysis.The structural damping is introduced to the discrete equation.The nonlinear static bending and nonlinear transient dynamic responses are obtained by iterative method.In numerical examples,the influences of damping coefficient,nonlocal parameter,strain gradient parameter and coefficient of porosity on the nonlinear static and transient responses are examined.