A three-dimensional(3D)asymptotic theory is reformulated for the static analysis of simply-supported,isotropic and orthotropic single-layered nanoplates and graphene sheets(GSs),in which Eringen’s nonlocal elasticity...A three-dimensional(3D)asymptotic theory is reformulated for the static analysis of simply-supported,isotropic and orthotropic single-layered nanoplates and graphene sheets(GSs),in which Eringen’s nonlocal elasticity theory is used to capture the small length scale effect on the static behaviors of these.The perturbation method is used to expand the 3D nonlocal elasticity problems as a series of two-dimensional(2D)nonlocal plate problems,the governing equations of which for various order problems retain the same differential operators as those of the nonlocal classical plate theory(CST),although with different nonhomogeneous terms.Expanding the primary field variables of each order as the double Fourier series functions in the in-plane directions,we can obtain the Navier solutions of the leading-order problem,and the higher-order modifications can then be determined in a hierarchic and consistent manner.Some benchmark solutions for the static analysis of isotropic and orthotropic nanoplates and GSs subjected to sinusoidally and uniformly distributed loads are given to demonstrate the performance of the 3D nonlocal asymptotic theory.展开更多
The present study enlightens the two-dimensional analysis of the thermo-mechanical response for a mi-cropolar double porous thermoelastic material with voids(MDPTMWV)by virtue of Eringen’s theory of nonlocal elastici...The present study enlightens the two-dimensional analysis of the thermo-mechanical response for a mi-cropolar double porous thermoelastic material with voids(MDPTMWV)by virtue of Eringen’s theory of nonlocal elasticity.Moore-Gibson-Thompson(MGT)heat equation is introduced to the considered model in the context of memory-dependent derivative and variable conductivity.By employing the normal mode technique,the non-dimensional coupled governing equations of motion are solved to determine the an-alytical expressions of the displacements,temperature,void volume fractions,microrotation vector,force stress tensors,and equilibrated stress vectors.Several two-dimensional graphs are presented to demon-strate the influence of various parameters,such as kernel functions,thermal conductivity,and nonlocality.Furthermore,different generalized thermoelasticity theories with variable conductivity are compared to visualize the variations in the distributions associated with the prior mentioned variables.Some particu-lar cases are also discussed in the presence and absence of different parameters.展开更多
The current paper presents a thorough study on the pull-in instability of nanoelectromechanical rectangular plates under intermolecular, hydrostatic, and thermal actuations. Based on the Kirchhoff theory along with Er...The current paper presents a thorough study on the pull-in instability of nanoelectromechanical rectangular plates under intermolecular, hydrostatic, and thermal actuations. Based on the Kirchhoff theory along with Eringen's nonlocal elasticity theory, a nonclassical model is developed. Using the Galerkin method(GM), the governing equation which is a nonlinear partial differential equation(NLPDE) of the fourth order is converted to a nonlinear ordinary differential equation(NLODE) in the time domain. Then, the reduced NLODE is solved analytically by means of the homotopy analysis method. At the end, the effects of model parameters as well as the nonlocal parameter on the deflection, nonlinear frequency, and dynamic pull-in voltage are explored.展开更多
Micromorphic theory(MMT)envisions a material body as a continuous collection of deformable particles;each possesses finite size and inner structure.It is considered as the most successful top-down formulation of a two...Micromorphic theory(MMT)envisions a material body as a continuous collection of deformable particles;each possesses finite size and inner structure.It is considered as the most successful top-down formulation of a two-level continuum model,in which the deformation is expressed as a sum of macroscopic continuous deformation and internal microscopic deformation of the inner structure.In this work,the kinematics including the objective Eringen tensors is introduced.Balance laws are derived by requiring the energy equation to be form-invariant under the generalized Galilean transformation.The concept of material force and the balance law of pseudomomentum are generalized for MMT.An axiomatic approach is demonstrated in the formulation of constitutive equations for a generalized micromorphic thermoviscoelastic solid,generalized micromorphic fluid,micromorphic plasticity,and micromorphic electromagnetic-thermoelastic solid.Applications of MMT in micro/nanoscale are discussed.展开更多
Nonlocal continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with micro-or nanostructures.This paper deals with the lateral-torsional buckling of elastic n...Nonlocal continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with micro-or nanostructures.This paper deals with the lateral-torsional buckling of elastic nonlocal small-scale beams.Eringen’s model is chosen for the nonlocal constitutive bendingcurvature relationship.The effect of prebuckling deformation is taken into consideration on the basis of the Kirchhoff-Clebsch theory.It is shown that the application of Eringen’s model produces small-length scale terms in the nonlocal elastic lateraltorsional buckling moment of a hinged-hinged strip beam.Clearly,the non-local parameter has the effect of reducing the critical lateral-torsional buckling moment.This tendency is consistent with the one observed for the in-plane stability analysis,for the lateral buckling of a hinged-hinged axially loaded column.The lateral buckling solution can be derived from a physically motivated variational principle.展开更多
文摘A three-dimensional(3D)asymptotic theory is reformulated for the static analysis of simply-supported,isotropic and orthotropic single-layered nanoplates and graphene sheets(GSs),in which Eringen’s nonlocal elasticity theory is used to capture the small length scale effect on the static behaviors of these.The perturbation method is used to expand the 3D nonlocal elasticity problems as a series of two-dimensional(2D)nonlocal plate problems,the governing equations of which for various order problems retain the same differential operators as those of the nonlocal classical plate theory(CST),although with different nonhomogeneous terms.Expanding the primary field variables of each order as the double Fourier series functions in the in-plane directions,we can obtain the Navier solutions of the leading-order problem,and the higher-order modifications can then be determined in a hierarchic and consistent manner.Some benchmark solutions for the static analysis of isotropic and orthotropic nanoplates and GSs subjected to sinusoidally and uniformly distributed loads are given to demonstrate the performance of the 3D nonlocal asymptotic theory.
文摘The present study enlightens the two-dimensional analysis of the thermo-mechanical response for a mi-cropolar double porous thermoelastic material with voids(MDPTMWV)by virtue of Eringen’s theory of nonlocal elasticity.Moore-Gibson-Thompson(MGT)heat equation is introduced to the considered model in the context of memory-dependent derivative and variable conductivity.By employing the normal mode technique,the non-dimensional coupled governing equations of motion are solved to determine the an-alytical expressions of the displacements,temperature,void volume fractions,microrotation vector,force stress tensors,and equilibrated stress vectors.Several two-dimensional graphs are presented to demon-strate the influence of various parameters,such as kernel functions,thermal conductivity,and nonlocality.Furthermore,different generalized thermoelasticity theories with variable conductivity are compared to visualize the variations in the distributions associated with the prior mentioned variables.Some particu-lar cases are also discussed in the presence and absence of different parameters.
文摘The current paper presents a thorough study on the pull-in instability of nanoelectromechanical rectangular plates under intermolecular, hydrostatic, and thermal actuations. Based on the Kirchhoff theory along with Eringen's nonlocal elasticity theory, a nonclassical model is developed. Using the Galerkin method(GM), the governing equation which is a nonlinear partial differential equation(NLPDE) of the fourth order is converted to a nonlinear ordinary differential equation(NLODE) in the time domain. Then, the reduced NLODE is solved analytically by means of the homotopy analysis method. At the end, the effects of model parameters as well as the nonlocal parameter on the deflection, nonlinear frequency, and dynamic pull-in voltage are explored.
文摘Micromorphic theory(MMT)envisions a material body as a continuous collection of deformable particles;each possesses finite size and inner structure.It is considered as the most successful top-down formulation of a two-level continuum model,in which the deformation is expressed as a sum of macroscopic continuous deformation and internal microscopic deformation of the inner structure.In this work,the kinematics including the objective Eringen tensors is introduced.Balance laws are derived by requiring the energy equation to be form-invariant under the generalized Galilean transformation.The concept of material force and the balance law of pseudomomentum are generalized for MMT.An axiomatic approach is demonstrated in the formulation of constitutive equations for a generalized micromorphic thermoviscoelastic solid,generalized micromorphic fluid,micromorphic plasticity,and micromorphic electromagnetic-thermoelastic solid.Applications of MMT in micro/nanoscale are discussed.
文摘Nonlocal continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with micro-or nanostructures.This paper deals with the lateral-torsional buckling of elastic nonlocal small-scale beams.Eringen’s model is chosen for the nonlocal constitutive bendingcurvature relationship.The effect of prebuckling deformation is taken into consideration on the basis of the Kirchhoff-Clebsch theory.It is shown that the application of Eringen’s model produces small-length scale terms in the nonlocal elastic lateraltorsional buckling moment of a hinged-hinged strip beam.Clearly,the non-local parameter has the effect of reducing the critical lateral-torsional buckling moment.This tendency is consistent with the one observed for the in-plane stability analysis,for the lateral buckling of a hinged-hinged axially loaded column.The lateral buckling solution can be derived from a physically motivated variational principle.
