In this paper,the authors investigate the sharp threshold of a three-dimensional nonlocal nonlinear Schr?dinger system.It is a coupled system which provides the mathe- matical modeling of the spontaneous generation of...In this paper,the authors investigate the sharp threshold of a three-dimensional nonlocal nonlinear Schr?dinger system.It is a coupled system which provides the mathe- matical modeling of the spontaneous generation of a magnetic field in a cold plasma under the subsonic limit.The main difficulty of the proof lies in exploring the inner structure of the system due to the fact that the nonlocal effect may bring some hinderance for establishing the conservation quantities of the mass and of the energy,constructing the corresponding variational structure,and deriving the key estimates to gain the expected result.To overcome this,the authors must establish local well-posedness theory,and set up suitable variational structure depending crucially on the inner structure of the system under study,which leads to define proper functionals and a constrained variational problem.By building up two invariant manifolds and then making a priori estimates for these nonlocal terms,the authors figure out a sharp threshold of global existence for the system under consideration.展开更多
We perform a linear analysis of the elastic fields and stability of epitaxially strained thin films based on nonlocal elasticity.We derive expressions of perturbed stresses to the first order of perturbation amplitude...We perform a linear analysis of the elastic fields and stability of epitaxially strained thin films based on nonlocal elasticity.We derive expressions of perturbed stresses to the first order of perturbation amplitude,which show that the stresses are directly proportional to the lattice mismatch and the perturbation amplitude,and decrease with an increase in the perturbation wavelength.The critical perturbation wavelength distinguishes whether the fiat film for the perturbation is stable,which is inversely proportional to the square of the mismatch and decreases with the thickness of the film.展开更多
In this paper, we investigate the Cauchy problem for the nonlocal diffusion system with localized source ut = J*u-u + a(x)v~p, v_t = J*v-v + a(x)u~q. We first prove that the Fujita curve is(pq)_c*-= 1+max{p+1, q+1}bas...In this paper, we investigate the Cauchy problem for the nonlocal diffusion system with localized source ut = J*u-u + a(x)v~p, v_t = J*v-v + a(x)u~q. We first prove that the Fujita curve is(pq)_c*-= 1+max{p+1, q+1}based on whether there exist global solutions, thatis, if 1 < pq(pq)_c,then every nonnegative solution blows up in finite time, but for pq >(pq)_c,there exist both global and non-global solutions to the problem. Furthermore, we establish the secondary critical curve on the space-decay of initial value at infinity.展开更多
The nonlinear vibration characteristics of the piezoelectric circular cylindri- cal nanoshells resting on an elastic foundation are analyzed. The small scale effect and thermo-electro-mechanical loading are taken into...The nonlinear vibration characteristics of the piezoelectric circular cylindri- cal nanoshells resting on an elastic foundation are analyzed. The small scale effect and thermo-electro-mechanical loading are taken into account. Based on the nonlocal elastic- ity theory and Donnell’s nonlinear shell theory, the nonlinear governing equations and the corresponding boundary conditions are derived by employing Hamilton’s principle. Then, the Galerkin method is used to transform the governing equations into a set of ordinary differential equations, and subsequently, the multiple-scale method is used to obtain an approximate analytical solution. Finally, an extensive parametric study is conducted to examine the effects of the nonlocal parameter, the external electric potential, the temperature rise, and the Winkler-Pasternak foundation parameters on the nonlinear vibration characteristics of circular cylindrical piezoelectric nanoshells.展开更多
From a two-vortex interaction model in atmospheric and oceanic systems, a nonlocal counterpart with shifted parity and delayed time reversal is derived by a simple AB reduction. To obtain some approximate analytic sol...From a two-vortex interaction model in atmospheric and oceanic systems, a nonlocal counterpart with shifted parity and delayed time reversal is derived by a simple AB reduction. To obtain some approximate analytic solutions of this nonlocal system, the multi-scale expansion method is applied to get an AB-Burgers system. Various exact solutions of the AB-Burgers equation, including elliptic periodic waves, kink waves and solitary waves, are obtained and shown graphically.To show the applications of these solutions in describing correlated events, a simple approximate solution for the two-vortex interaction model is given to show two correlated dipole blocking events at two different places. Furthermore, symmetry reduction solutions of the nonlocal AB-Burgers equation are also given by using the standard Lie symmetry method.展开更多
In this paper,multi-scale modeling for nanobeams with large deflection is conducted in the framework of the nonlocal strain gradient theory and the Euler-Bernoulli beam theory with exact bending curvature.The proposed...In this paper,multi-scale modeling for nanobeams with large deflection is conducted in the framework of the nonlocal strain gradient theory and the Euler-Bernoulli beam theory with exact bending curvature.The proposed size-dependent nonlinear beam model incorporates structure-foundation interaction along with two small scale param-eters which describe the stiffness-softening and stiffness-hardening size effects of nano-materials,respectively.By applying Hamilton’s principle,the motion equation and the associated boundary condition are derived.A two-step perturbation method is intro-duced to handle the deep postbuckling and nonlinear bending problems of nanobeams analytically.Afterwards,the influence of geometrical,material,and elastic foundation parameters on the nonlinear mechanical behaviors of nanobeams is discussed.Numerical results show that the stability and precision of the perturbation solutions can be guaran-teed,and the two types of size effects become increasingly important as the slenderness ratio increases.Moreover,the in-plane conditions and the high-order nonlinear terms appearing in the bending curvature expression play an important role in the nonlinear behaviors of nanobeams as the maximum deflection increases.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
The nonlocal means(NLM)has been widely used in image processing.In this paper,we introduce a modified weight function for NLM denoising,which will compute the nonlocal similarities among the pre-processing pixel patch...The nonlocal means(NLM)has been widely used in image processing.In this paper,we introduce a modified weight function for NLM denoising,which will compute the nonlocal similarities among the pre-processing pixel patches instead of the commonly used similarity measure based on noisy observations.By the law of large number,the norm for the pre-processing pixel patches is closer to the norm of the original clean pixel patches,so the proposed weight functions are more optimized and the selected similar patches are more accurate.Experimental results indicate the proposed algorithm achieves better restored results compared to the classical NLM s method.展开更多
The one-dimensional monoatomic lattice chain connected by nonlinear springs is investigated,and the asymptotic solution is obtained through the Lindstedt-Poincar′e perturbation method.The dispersion relation is deriv...The one-dimensional monoatomic lattice chain connected by nonlinear springs is investigated,and the asymptotic solution is obtained through the Lindstedt-Poincar′e perturbation method.The dispersion relation is derived with the consideration of both the nonlocal and the active control effects.The numerical results show that the nonlocal effect can effectively enhance the frequency in the middle part of the dispersion curve.When the nonlocal effect is strong enough,zero and negative group velocities will be evoked at different points along the dispersion curve,which will provide different ways of transporting energy including the forward-propagation,localization,and backwardpropagation of wavepackets related to the phase velocity.Both the nonlinear effect and the active control can enhance the frequency,but neither of them is able to produce zero or negative group velocities.Specifically,the active control enhances the frequency of the dispersion curve including the point at which the reduced wave number equals zero,and therefore gives birth to a nonzero cutoff frequency and a band gap in the low frequency range.With a combinational adjustment of all these effects,the wave propagation behaviors can be comprehensively controlled,and energy transferring can be readily manipulated in various ways.展开更多
A nonlocal elastic micro/nanobeam is theoretically modeled with the consideration of the surface elasticity,the residual surface stress,and the rotatory inertia,in which the nonlocal and surface effects are considered...A nonlocal elastic micro/nanobeam is theoretically modeled with the consideration of the surface elasticity,the residual surface stress,and the rotatory inertia,in which the nonlocal and surface effects are considered.Three types of boundary conditions,i.e.,hinged-hinged,clamped-clamped,and clamped-hinged ends,are examined.For a hinged-hinged beam,an exact and explicit natural frequency equation is derived based on the established mathematical model.The Fredholm integral equation is adopted to deduce the approximate fundamental frequency equations for the clamped-clamped and clamped-hinged beams.In sum,the explicit frequency equations for the micro/nanobeam under three types of boundary conditions are proposed to reveal the dependence of the natural frequency on the effects of the nonlocal elasticity,the surface elasticity,the residual surface stress,and the rotatory inertia,providing a more convenient means in comparison with numerical computations.展开更多
Since the pillars of quantum theory were established, it was already noted that quantum physics may allow certain correlations defying any local realistic picture of nature, as first recognized by Einstein,Podolsky an...Since the pillars of quantum theory were established, it was already noted that quantum physics may allow certain correlations defying any local realistic picture of nature, as first recognized by Einstein,Podolsky and Rosen. These quantum correlations, now termed quantum nonlocality and tested by violation of Bell’s inequality that consists of statistical correlations fulfilling local realism, have found loophole-free experimental confirmation. A more striking way to demonstrate the conflict exists, and can be extended to the multipartite scenario. Here we report experimental confirmation of such a striking way, the multipartite generalized Hardy’s paradoxes, in which no inequality is used and the conflict is stronger than that within just two parties. The paradoxes we consider here belong to a general framework [S.-H. Jiang et al., Phys. Rev. Lett. 120(2018) 050403], including previously known multipartite extensions of Hardy’s original paradox as special cases. The conflict shown here is stronger than in previous multipartite Hardy’s paradox. Thus, the demonstration of Hardy-typed quantum nonlocality becomes sharper than ever.展开更多
This paper is concerned with a buckling analysis of an embedded nanoplate integrated with magnetoelectroelastic(MEE)layers based on a nonlocal magnetoelectroe-lasticity theory.A surrounding elastic medium is simulated...This paper is concerned with a buckling analysis of an embedded nanoplate integrated with magnetoelectroelastic(MEE)layers based on a nonlocal magnetoelectroe-lasticity theory.A surrounding elastic medium is simulated by the Pasternak foundation that considers both shear and normal loads.The sandwich nanoplate(SNP)consists of a core that is made of metal and two MEE layers on the upper and lower surfaces of the core made of BaTiO3/CoFe2O4.The refined zigzag theory(RZT)is used to model the SNP subject to both external electric and magnetic potentials.Using an energy method and Hamilton’s principle,the governing motion equations are obtained,and then solved analytically.A detailed parametric study is conducted,concentrating on the combined effects of the small scale parameter,external electric and magnetic loads,thicknesses of MEE layers,mode numbers,and surrounding elastic medium.It is concluded that in-creasing the small scale parameter decreases the critical buckling loads.展开更多
By means of a comprehensive theory of elasticity,namely,a nonlocal strain gradient continuum theory,size-dependent nonlinear axial instability characteristics of cylindrical nanoshells made of functionally graded mate...By means of a comprehensive theory of elasticity,namely,a nonlocal strain gradient continuum theory,size-dependent nonlinear axial instability characteristics of cylindrical nanoshells made of functionally graded material(FGM)are examined.To take small scale effects into consideration in a more accurate way,a nonlocal stress field parameter and an internal length scale parameter are incorporated simultaneously into an exponential shear deformation shell theory.The variation of material properties asso-ciated with FGM nanoshells is supposed along the shell thickness,and it is modeled based on the Mori-Tanaka homogenization scheme.With a boundary layer theory of shell buck-ling and a perturbation-based solving process,the nonlocal strain gradient load-deflection and load-shortening stability paths are derived explicitly.It is observed that the strain gradient size effect causes to the increases of both the critical axial buckling load and the width of snap-through phenomenon related to the postbuckling regime,while the nonlocal size dependency leads to the decreases of them.Moreover,the influence of the nonlocal type of small scale effect on the axial instability characteristics of FGM nanoshells is more than that of the strain gradient one.展开更多
Eringen’s two-phase local/nonlocal model is applied to an Euler-Bernoulli nanobeam considering the bending-induced axial force,where the contribution of the axial force to bending moment is calculated on the deformed...Eringen’s two-phase local/nonlocal model is applied to an Euler-Bernoulli nanobeam considering the bending-induced axial force,where the contribution of the axial force to bending moment is calculated on the deformed state.Basic equations for the corresponding one-dimensional beam problem are obtained by degenerating from the three-dimensional nonlocal elastic equations.Semi-analytic solutions are then presented for a clamped-clamped beam subject to a concentrated force and a uniformly distributed load,respectively.Except for the traditional essential boundary conditions and those required to be satisfied by transferring an integral equation to its equivalent differential form,additional boundary conditions are needed and should be chosen with great caution,since numerical results reveal that non-unique solutions might exist for a nonlinear problem if inappropriate boundary conditions are used.The validity of the solutions is examined by plotting both sides of the original integro-differential governing equation of deflection and studying the error between both sides.Besides,an increase in the internal characteristic length would cause an increase in the deflection and axial force of the beam.展开更多
In this paper, a nonlocal two-wave interaction system from the Manakov hierarchy is investigated via the Riemann–Hilbert approach. Based on the spectral analysis of the Lax pair, a Riemann–Hilbert problem for the no...In this paper, a nonlocal two-wave interaction system from the Manakov hierarchy is investigated via the Riemann–Hilbert approach. Based on the spectral analysis of the Lax pair, a Riemann–Hilbert problem for the nonlocal two-wave interaction system is constructed. By discussing the solutions of this Riemann–Hilbert problem in both the regular and nonregular cases, we explicitly present the N-soliton solution formula of the nonlocal two-wave interaction system. Moreover,the dynamical behaviour of the single-soliton solution is shown graphically.展开更多
Peridynamics (PD)is a nonlocal continuum theory based on integro-differential equations without spatial derivatives.The fracture criterion is implicitly incorporated in the PD theory and fracture is a natural outcome ...Peridynamics (PD)is a nonlocal continuum theory based on integro-differential equations without spatial derivatives.The fracture criterion is implicitly incorporated in the PD theory and fracture is a natural outcome of the simulation.However,capturing of complex mixed-mode crack patterns has been proven to be difficult with PD.On the other hand,the extended finite element method (XFEM)is one of the most popular methods for fracture which allows crack propagation with minimal remeshing.It requires a fracture criterion which is independent of the underlying discretization though a certain refinement is needed in order to obtain suitable results.This article presents a comparative study between XFEM and PD.Therefore,two examples are studied.The first example is crack propagation in a double notched specimen under uniaxial tension with different crack spacings in loading direction.The second example is the specimens with two center cracks.The results show that PD as well as XFEM are well suited to capture this type of behaviour.展开更多
基金the National Natural Science Foundation of China (No.11571254).
文摘In this paper,the authors investigate the sharp threshold of a three-dimensional nonlocal nonlinear Schr?dinger system.It is a coupled system which provides the mathe- matical modeling of the spontaneous generation of a magnetic field in a cold plasma under the subsonic limit.The main difficulty of the proof lies in exploring the inner structure of the system due to the fact that the nonlocal effect may bring some hinderance for establishing the conservation quantities of the mass and of the energy,constructing the corresponding variational structure,and deriving the key estimates to gain the expected result.To overcome this,the authors must establish local well-posedness theory,and set up suitable variational structure depending crucially on the inner structure of the system under study,which leads to define proper functionals and a constrained variational problem.By building up two invariant manifolds and then making a priori estimates for these nonlocal terms,the authors figure out a sharp threshold of global existence for the system under consideration.
基金the Zhejiang Provincial Natural Science Foundation of China under Grant Nos LY18A020011 and LQ17A020001the National Natural Science Foundation of China under Grant No 11702247.
文摘We perform a linear analysis of the elastic fields and stability of epitaxially strained thin films based on nonlocal elasticity.We derive expressions of perturbed stresses to the first order of perturbation amplitude,which show that the stresses are directly proportional to the lattice mismatch and the perturbation amplitude,and decrease with an increase in the perturbation wavelength.The critical perturbation wavelength distinguishes whether the fiat film for the perturbation is stable,which is inversely proportional to the square of the mismatch and decreases with the thickness of the film.
基金the National Natural Science Foundation of China(Grant No.11301419)the Meritocracy Research Funds of China West Normal University(Grant No.17YC382).
文摘In this paper, we investigate the Cauchy problem for the nonlocal diffusion system with localized source ut = J*u-u + a(x)v~p, v_t = J*v-v + a(x)u~q. We first prove that the Fujita curve is(pq)_c*-= 1+max{p+1, q+1}based on whether there exist global solutions, thatis, if 1 < pq(pq)_c,then every nonnegative solution blows up in finite time, but for pq >(pq)_c,there exist both global and non-global solutions to the problem. Furthermore, we establish the secondary critical curve on the space-decay of initial value at infinity.
基金the National Natural Science Foundation of China (No. 11672071)the Fun- damental Research Funds for the Central Universities (No.N170504023).
文摘The nonlinear vibration characteristics of the piezoelectric circular cylindri- cal nanoshells resting on an elastic foundation are analyzed. The small scale effect and thermo-electro-mechanical loading are taken into account. Based on the nonlocal elastic- ity theory and Donnell’s nonlinear shell theory, the nonlinear governing equations and the corresponding boundary conditions are derived by employing Hamilton’s principle. Then, the Galerkin method is used to transform the governing equations into a set of ordinary differential equations, and subsequently, the multiple-scale method is used to obtain an approximate analytical solution. Finally, an extensive parametric study is conducted to examine the effects of the nonlocal parameter, the external electric potential, the temperature rise, and the Winkler-Pasternak foundation parameters on the nonlinear vibration characteristics of circular cylindrical piezoelectric nanoshells.
基金the National Natural Science Foundation of China(Grant Nos.11405110,11275129,and 11472177)the Natural Science Foundation of Zhejiang Province of China(Grant No.LY18A050001).
文摘From a two-vortex interaction model in atmospheric and oceanic systems, a nonlocal counterpart with shifted parity and delayed time reversal is derived by a simple AB reduction. To obtain some approximate analytic solutions of this nonlocal system, the multi-scale expansion method is applied to get an AB-Burgers system. Various exact solutions of the AB-Burgers equation, including elliptic periodic waves, kink waves and solitary waves, are obtained and shown graphically.To show the applications of these solutions in describing correlated events, a simple approximate solution for the two-vortex interaction model is given to show two correlated dipole blocking events at two different places. Furthermore, symmetry reduction solutions of the nonlocal AB-Burgers equation are also given by using the standard Lie symmetry method.
基金the National Natural Science Foundation of China(Nos.11672252 and 11602204)the Fundamental Research Funds for the Central Universities,Southwest Jiaotong University(No.2682016CX096).
文摘In this paper,multi-scale modeling for nanobeams with large deflection is conducted in the framework of the nonlocal strain gradient theory and the Euler-Bernoulli beam theory with exact bending curvature.The proposed size-dependent nonlinear beam model incorporates structure-foundation interaction along with two small scale param-eters which describe the stiffness-softening and stiffness-hardening size effects of nano-materials,respectively.By applying Hamilton’s principle,the motion equation and the associated boundary condition are derived.A two-step perturbation method is intro-duced to handle the deep postbuckling and nonlinear bending problems of nanobeams analytically.Afterwards,the influence of geometrical,material,and elastic foundation parameters on the nonlinear mechanical behaviors of nanobeams is discussed.Numerical results show that the stability and precision of the perturbation solutions can be guaran-teed,and the two types of size effects become increasingly important as the slenderness ratio increases.Moreover,the in-plane conditions and the high-order nonlinear terms appearing in the bending curvature expression play an important role in the nonlinear behaviors of nanobeams as the maximum deflection increases.
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.
基金Foundation items:National Natural Science Foundations of China(Nos.U1504603,61301229)Key Scientific Research Project of Colleges and Universities in Henan Province,China(Nos.18A120002,19A110014).
文摘The nonlocal means(NLM)has been widely used in image processing.In this paper,we introduce a modified weight function for NLM denoising,which will compute the nonlocal similarities among the pre-processing pixel patches instead of the commonly used similarity measure based on noisy observations.By the law of large number,the norm for the pre-processing pixel patches is closer to the norm of the original clean pixel patches,so the proposed weight functions are more optimized and the selected similar patches are more accurate.Experimental results indicate the proposed algorithm achieves better restored results compared to the classical NLM s method.
基金Project supported by the National Natural Science Foundation of China(Nos.11532001 and 11621062)and the Fundamental Research Funds for the Central Universities of China(No.2016XZZX001-05)
文摘The one-dimensional monoatomic lattice chain connected by nonlinear springs is investigated,and the asymptotic solution is obtained through the Lindstedt-Poincar′e perturbation method.The dispersion relation is derived with the consideration of both the nonlocal and the active control effects.The numerical results show that the nonlocal effect can effectively enhance the frequency in the middle part of the dispersion curve.When the nonlocal effect is strong enough,zero and negative group velocities will be evoked at different points along the dispersion curve,which will provide different ways of transporting energy including the forward-propagation,localization,and backwardpropagation of wavepackets related to the phase velocity.Both the nonlinear effect and the active control can enhance the frequency,but neither of them is able to produce zero or negative group velocities.Specifically,the active control enhances the frequency of the dispersion curve including the point at which the reduced wave number equals zero,and therefore gives birth to a nonzero cutoff frequency and a band gap in the low frequency range.With a combinational adjustment of all these effects,the wave propagation behaviors can be comprehensively controlled,and energy transferring can be readily manipulated in various ways.
文摘A nonlocal elastic micro/nanobeam is theoretically modeled with the consideration of the surface elasticity,the residual surface stress,and the rotatory inertia,in which the nonlocal and surface effects are considered.Three types of boundary conditions,i.e.,hinged-hinged,clamped-clamped,and clamped-hinged ends,are examined.For a hinged-hinged beam,an exact and explicit natural frequency equation is derived based on the established mathematical model.The Fredholm integral equation is adopted to deduce the approximate fundamental frequency equations for the clamped-clamped and clamped-hinged beams.In sum,the explicit frequency equations for the micro/nanobeam under three types of boundary conditions are proposed to reveal the dependence of the natural frequency on the effects of the nonlocal elasticity,the surface elasticity,the residual surface stress,and the rotatory inertia,providing a more convenient means in comparison with numerical computations.
基金the National Natural Science Foun-dation of China (11475089 and 11875167)the Chinese Academy of Sciences,the National Fundamental Research Programthe China Postdoctoral Science Foundation (2018M630063).
文摘Since the pillars of quantum theory were established, it was already noted that quantum physics may allow certain correlations defying any local realistic picture of nature, as first recognized by Einstein,Podolsky and Rosen. These quantum correlations, now termed quantum nonlocality and tested by violation of Bell’s inequality that consists of statistical correlations fulfilling local realism, have found loophole-free experimental confirmation. A more striking way to demonstrate the conflict exists, and can be extended to the multipartite scenario. Here we report experimental confirmation of such a striking way, the multipartite generalized Hardy’s paradoxes, in which no inequality is used and the conflict is stronger than that within just two parties. The paradoxes we consider here belong to a general framework [S.-H. Jiang et al., Phys. Rev. Lett. 120(2018) 050403], including previously known multipartite extensions of Hardy’s original paradox as special cases. The conflict shown here is stronger than in previous multipartite Hardy’s paradox. Thus, the demonstration of Hardy-typed quantum nonlocality becomes sharper than ever.
基金Project supported by the University of Kashan(No.574600/33)
文摘This paper is concerned with a buckling analysis of an embedded nanoplate integrated with magnetoelectroelastic(MEE)layers based on a nonlocal magnetoelectroe-lasticity theory.A surrounding elastic medium is simulated by the Pasternak foundation that considers both shear and normal loads.The sandwich nanoplate(SNP)consists of a core that is made of metal and two MEE layers on the upper and lower surfaces of the core made of BaTiO3/CoFe2O4.The refined zigzag theory(RZT)is used to model the SNP subject to both external electric and magnetic potentials.Using an energy method and Hamilton’s principle,the governing motion equations are obtained,and then solved analytically.A detailed parametric study is conducted,concentrating on the combined effects of the small scale parameter,external electric and magnetic loads,thicknesses of MEE layers,mode numbers,and surrounding elastic medium.It is concluded that in-creasing the small scale parameter decreases the critical buckling loads.
文摘By means of a comprehensive theory of elasticity,namely,a nonlocal strain gradient continuum theory,size-dependent nonlinear axial instability characteristics of cylindrical nanoshells made of functionally graded material(FGM)are examined.To take small scale effects into consideration in a more accurate way,a nonlocal stress field parameter and an internal length scale parameter are incorporated simultaneously into an exponential shear deformation shell theory.The variation of material properties asso-ciated with FGM nanoshells is supposed along the shell thickness,and it is modeled based on the Mori-Tanaka homogenization scheme.With a boundary layer theory of shell buck-ling and a perturbation-based solving process,the nonlocal strain gradient load-deflection and load-shortening stability paths are derived explicitly.It is observed that the strain gradient size effect causes to the increases of both the critical axial buckling load and the width of snap-through phenomenon related to the postbuckling regime,while the nonlocal size dependency leads to the decreases of them.Moreover,the influence of the nonlocal type of small scale effect on the axial instability characteristics of FGM nanoshells is more than that of the strain gradient one.
基金Project supported by the National Natural Science Foundation of China(No.11472130)
文摘Eringen’s two-phase local/nonlocal model is applied to an Euler-Bernoulli nanobeam considering the bending-induced axial force,where the contribution of the axial force to bending moment is calculated on the deformed state.Basic equations for the corresponding one-dimensional beam problem are obtained by degenerating from the three-dimensional nonlocal elastic equations.Semi-analytic solutions are then presented for a clamped-clamped beam subject to a concentrated force and a uniformly distributed load,respectively.Except for the traditional essential boundary conditions and those required to be satisfied by transferring an integral equation to its equivalent differential form,additional boundary conditions are needed and should be chosen with great caution,since numerical results reveal that non-unique solutions might exist for a nonlinear problem if inappropriate boundary conditions are used.The validity of the solutions is examined by plotting both sides of the original integro-differential governing equation of deflection and studying the error between both sides.Besides,an increase in the internal characteristic length would cause an increase in the deflection and axial force of the beam.
基金the National Natural Science Foundation of China (Grant Nos.11331008and 11522112).
文摘In this paper, a nonlocal two-wave interaction system from the Manakov hierarchy is investigated via the Riemann–Hilbert approach. Based on the spectral analysis of the Lax pair, a Riemann–Hilbert problem for the nonlocal two-wave interaction system is constructed. By discussing the solutions of this Riemann–Hilbert problem in both the regular and nonregular cases, we explicitly present the N-soliton solution formula of the nonlocal two-wave interaction system. Moreover,the dynamical behaviour of the single-soliton solution is shown graphically.
基金the Ministry of Science and Technology of China(No.SLDRCE14一B-03Natural Science Foundation of Shanghai(No.17ZR1431900).
文摘Peridynamics (PD)is a nonlocal continuum theory based on integro-differential equations without spatial derivatives.The fracture criterion is implicitly incorporated in the PD theory and fracture is a natural outcome of the simulation.However,capturing of complex mixed-mode crack patterns has been proven to be difficult with PD.On the other hand,the extended finite element method (XFEM)is one of the most popular methods for fracture which allows crack propagation with minimal remeshing.It requires a fracture criterion which is independent of the underlying discretization though a certain refinement is needed in order to obtain suitable results.This article presents a comparative study between XFEM and PD.Therefore,two examples are studied.The first example is crack propagation in a double notched specimen under uniaxial tension with different crack spacings in loading direction.The second example is the specimens with two center cracks.The results show that PD as well as XFEM are well suited to capture this type of behaviour.