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
Ordinary energy and dark energy density are determined using a Cosserat-Cartan and killing-Yano reinterpretation of Einstein’s special and general relativity. Thus starting from a maximally symmetric space with 528 k...Ordinary energy and dark energy density are determined using a Cosserat-Cartan and killing-Yano reinterpretation of Einstein’s special and general relativity. Thus starting from a maximally symmetric space with 528 killing vector fields corresponding to Witten’s five Branes model in eleven dimensional M-theory we reason that 504 of the 528 are essentially the components of the relevant killing-Yano tensor. In turn this tensor is related to hidden symmetries and torsional coupled stresses of the Cosserat micro-polar space as well as the Einstein-Cartan connection. Proceeding in this way the dark energy density is found to be that of Einstein’s maximal energy mc2 where m is the mass and c is the speed of light multiplied with a Lorentz factor equal to the ratio of the 504 killing-Yano tensor and the 528 states maximally symmetric space. Thus we have E (dark) = mc2 (504/528) = mc2 (21/22) which is about 95.5% of the total maximal energy density in astounding agreement with COBE, WMAP and Planck cosmological measurements as well as the type 1a supernova analysis. Finally theory and results are validated via a related theory based on the degrees of freedom of pure gravity, the theory of nonlocal elasticity as well as ‘t Hooft-Veltman renormalization method.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
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Ordinary energy and dark energy density are determined using a Cosserat-Cartan and killing-Yano reinterpretation of Einstein’s special and general relativity. Thus starting from a maximally symmetric space with 528 killing vector fields corresponding to Witten’s five Branes model in eleven dimensional M-theory we reason that 504 of the 528 are essentially the components of the relevant killing-Yano tensor. In turn this tensor is related to hidden symmetries and torsional coupled stresses of the Cosserat micro-polar space as well as the Einstein-Cartan connection. Proceeding in this way the dark energy density is found to be that of Einstein’s maximal energy mc2 where m is the mass and c is the speed of light multiplied with a Lorentz factor equal to the ratio of the 504 killing-Yano tensor and the 528 states maximally symmetric space. Thus we have E (dark) = mc2 (504/528) = mc2 (21/22) which is about 95.5% of the total maximal energy density in astounding agreement with COBE, WMAP and Planck cosmological measurements as well as the type 1a supernova analysis. Finally theory and results are validated via a related theory based on the degrees of freedom of pure gravity, the theory of nonlocal elasticity as well as ‘t Hooft-Veltman renormalization method.
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.