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Well-posedness of two-phase local/nonlocal integral polar models for consistent axisymmetric bending of circular microplates

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Applied Mathematics and Mechanics(English Edition) 2022年第5期43卷 637-652页

作者： hai qing State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China

Previous studies have shown that Eringen’s differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular *** on the nonlocal integral models along the radial and circumferential directions,we propose nonlocal integral polar models in this *** proposed strainand stress-driven two-phase nonlocal integral polar models are applied to model the axisymmetric bending of circular *** governing differential equations and boundary conditions(BCs)as well as constitutive constraints are *** is found that the purely strain-driven nonlocal integral polar model turns to a traditional nonlocal differential polar model if the constitutive constraints are ***,the purely strain-and stress-driven nonlocal integral polar models are ill-posed,because the total number of the differential orders of the governing equations is less than that of the BCs plus constitutive *** nominal variables are introduced to simplify the mathematical expression,and the general differential quadrature method(GDQM)is applied to obtain the numerical *** results from the current models(CMs)are compared with the data in the *** is clearly established that the consistent softening and toughening effects can be obtained for the strain-and stress-driven local/nonlocal integral polar models,*** proposed two-phase local/nonlocal integral polar models(TPNIPMs)may provide an efficient method to design and optimize the plate-like structures for microelectro-mechanical systems.

关键词： softening effect toughening effect circular microplate nonlocal integral model general differential quadrature method(GDQM)

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Finite Element Analysis of the Microstructure–Strength Relationships of Metal Matrix Composites

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Acta Metallurgica Sinica(English Letters) 2014年第5期27卷 844-852页

作者： hai qing State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics and Astronautics

The influence of the shape and spatial distribution of reinforced particles on strength and damage of metal matrix composite （MMC） is investigated through finite element method under uniaxial tensile, simple shear, biaxial tensile, as well as combined tensile/shear loadings. The particle shapes change randomly from circular to regular n-sided polygon （3 ≤ n ≤ 10）; the particle alignments are determined through a sequentially random number stream and the particle locations are defined through the random sequential adsorption algorithm. The ductile failure in metal matrix and brittle failure in particles are described through damage models based on the stress triaxial indicator and maximum principal stress criterion, respectively, while the debonding behavior of interface between particles and matrix is simulated through cohesive elements. The simulation results show that, under different loadings, interface debonding is the dominated failure mechanism in MMCs and plastic deformation and ductile failure of matrix also play very important roles on the failure of MMCs.

关键词： Metal matrix composites Finite element analysis Damage Strength

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On the consistency of two-phase local/nonlocal piezoelectric integral model

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Applied Mathematics and Mechanics(English Edition) 2021年第11期42卷 1581-1598页

作者： Yanming REN hai qing State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China

In this paper,we propose general strain-and stress-driven two-phase local/nonlocal piezoelectric integral models,which can distinguish the difference of nonlocal effects on the elastic and piezoelectric behaviors of *** nonlocal piezoelectric model is transformed from integral to an equivalent differential form with four constitutive boundary conditions due to the difficulty in solving intergro-differential equations *** nonlocal piezoelectric integral models are used to model the static bending of the Euler-Bernoulli piezoelectric beam on the assumption that the nonlocal elastic and piezoelectric parameters are coincident with each *** governing differential equations as well as constitutive and standard boundary conditions are *** is found that purely strain-and stress-driven nonlocal piezoelectric integral models are ill-posed,because the total number of differential orders for governing equations is less than that of boundary ***,the traditional nonlocal piezoelectric differential model would lead to inconsistent bending response for Euler-Bernoulli piezoelectric beam under different boundary and loading *** nominal variables are introduced to normalize the governing equations and boundary conditions,and the general differential quadrature method(GDQM)is used to obtain the numerical *** results from current models are validated against results in the *** is clearly established that a consistent softening and toughening effects can be obtained for static bending of the Euler-Bernoulli beam based on the general strain-and stress-driven local/nonlocal piezoelectric integral models,respectively.

关键词： nonlocal piezoelectric integral model softening effect toughening effect general differential quadrature method(GDQM)

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Nonlocal stress gradient formulation for damping vibration analysis of viscoelastic microbeam in thermal environment

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Applied Mathematics and Mechanics(English Edition) 2023年第5期44卷 773-786页

作者： hai qing Huidiao SONG State Key Laboratory of Mechanics and Control for Aerospace Structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China

An integral nonlocal stress gradient viscoelastic model is proposed on the basis of the integral nonlocal stress gradient model and the standard viscoelastic model,and is utilized to investigate the free damping vibration analysis of the viscoelastic BernoulliEuler microbeams in thermal ***'s principle is used to derive the differential governing equations and corresponding boundary *** integral relations between the strain and the nonlocal stress are converted into a differential form with constitutive *** size-dependent axial thermal stress due to the variation of the environmental temperature is derived *** Laplace transformation is utilized to obtain the explicit expression for the bending deflection and *** the boundary conditions and constitutive constraints,one can get a nonlinear equation with complex coefficients,from which the complex characteristic frequency can be determined.A two-step numerical method is proposed to solve the elastic vibration frequency and the damping *** effects of length scale parameters,viscous coefficient,thermal stress,vibration order on the vibration frequencies,and critical viscous coefficient are investigated numerically for the viscoelastic Bernoulli-Euler microbeams under different boundary conditions.

关键词： damping vibration size effect integral nonlocal stress gradient model standard viscoelastic model Laplace transformation

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Torsional static and vibration analysis of functionally graded nanotube with bi-Helmholtz kernel based stress-driven nonlocal integral model

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Applied Mathematics and Mechanics(English Edition) 2021年第3期42卷 425-440页

作者： Peiliang BIAN hai qing State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China

A torsional static and free vibration analysis of the functionally graded nanotube(FGNT)composed of two materials varying continuously according to the power-law along the radial direction is performed using the bi-Helmholtz kernel based stress-driven nonlocal integral *** differential governing equation and boundary conditions are deduced on the basis of Hamilton’s principle,and the constitutive relationship is expressed as an integral equation with the bi-Helmholtz *** nominal variables are introduced to simplify the differential governing equation,integral constitutive equation,and boundary *** than transforming the constitutive equation from integral to differential forms,the Laplace transformation is used directly to solve the integro-differential *** explicit expression for nominal torsional rotation and torque contains four unknown constants,which can be determined with the help of two boundary conditions and two extra constraints from the integral constitutive relation.A few benchmarked examples are solved to illustrate the nonlocal influence on the static torsion of a clamped-clamped(CC)FGNT under torsional constraints and a clamped-free(CF)FGNT under concentrated and uniformly distributed torques as well as the torsional free vibration of an FGNT under different boundary conditions.

关键词： integro-differential equation bi-Helmholtz kernel stress-driven nonlocal integral model Laplace transform technique free vibration

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Two-phase nonlocal integral models with a bi-Helmholtz averaging kernel for nanorods

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Applied Mathematics and Mechanics(English Edition) 2021年第10期42卷 1379-1396页

作者： Pei ZHANG hai qing State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China

In this work,the static tensile and free vibration of nanorods are studied via both the strain-driven(Strain D)and stress-driven(Stress D)two-phase nonlocal models with a bi-Helmholtz averaging *** adjusting the limits of integration,the integral constitutive equation of the Fredholm type is converted to that of the Volterra type and then solved directly via the Laplace transform *** unknown constants can be uniquely determined through the standard boundary conditions and two constrained conditions accompanying the Laplace transform *** the numerical examples,the bi-Helmholtz kernel-based Strain D(or Stress D)two-phase model shows consistently softening(or stiffening)effects on both the tension and the free vibration of nanorods with different boundary *** effects of the two nonlocal parameters of the bi-Helmholtz kernel-based two-phase nonlocal models are studied and compared with those of the Helmholtz kernel-based models.

关键词： two-phase nonlocal integral model bi-Helmholtz kernel tensile analysis free vibration exact solution Laplace transform

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On well-posedness of two-phase nonlocal integral models for higher-order refined shear deformation beams

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Applied Mathematics and Mechanics(English Edition) 2021年第7期42卷 931-950页

作者： Pei ZHANG hai qing State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China

Due to the conflict between equilibrium and constitutive requirements,Eringen’s strain-driven nonlocal integral model is not applicable to nanostructures of engineering *** an alternative,the stress-driven model has been recently *** this paper,for higher-order shear deformation beams,the ill-posed issue(i.e.,excessive mandatory boundary conditions(BCs)cannot be met simultaneously)exists not only in strain-driven nonlocal models but also in stress-driven *** well-posedness of both the strain-and stress-driven two-phase nonlocal(TPN-Strain D and TPN-Stress D)models is pertinently evidenced by formulating the static bending of curved beams made of functionally graded(FG)*** two-phase nonlocal integral constitutive relation is equivalent to a differential law equipped with two restriction *** using the generalized differential quadrature method(GDQM),the coupling governing equations are solved *** results show that the two-phase models can predict consistent scale-effects under different supported and loading conditions.

关键词： well-posedness strain-and stress-driven two-phase nonlocal(TPN-Strain D and TPN-Stress D)models refined shear deformation theory functionally graded(FG)curved beam generalized differential quadrature method(GDQM)

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Learning topological defects formation with neural networks in a quantum phase transition

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Communications in Theoretical Physics 2024年第5期76卷 68-76页

作者： Han-qing Shi hai-qing Zhang Center for Gravitational Physics Department of Space ScienceBeihang UniversityBeijing 100191China Peng Huanwu Collaborative Center for Research and Education Beihang UniversityBeijing 100191China

Neural networks possess formidable representational power,rendering them invaluable in solving complex quantum many-body *** they excel at analyzing static solutions,nonequilibrium processes,including critical dynamics during a quantum phase transition,pose a greater challenge for neural *** address this,we utilize neural networks and machine learning algorithms to investigate time evolutions,universal statistics,and correlations of topological defects in a one-dimensional transverse-field quantum Ising ***,our analysis involves computing the energy of the system during a quantum phase transition following a linear quench of the transverse magnetic field *** excitation energies satisfy a power-law relation to the quench rate,indicating a proportional relationship between the excitation energy and the kink ***,we establish a universal power-law relationship between the first three cumulants of the kink numbers and the quench rate,indicating a binomial distribution of the ***,the normalized kink-kink correlations are also investigated and it is found that the numerical values are consistent with the analytic formula.

关键词： neural networks machine learning transverse-field quantum Ising model kibble-zurek mechanism

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Theoretical analysis on elastic buckling of nanobeams based on stress-driven nonlocal integral model

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Applied Mathematics and Mechanics(English Edition) 2020年第2期41卷 207-232页

作者： Peng JIANG hai qing Cunfa GAO State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China

Several studies indicate that Eringen's nonlocal model may lead to some inconsistencies for both Euler-Bernoulli and Timoshenko beams, such as cantilever beams subjected to an end point force and fixed-fixed beams subjected a uniform distributed load. In this paper, the elastic buckling behavior of nanobeams, including both EulerBernoulli and Timoshenko beams, is investigated on the basis of a stress-driven nonlocal integral model. The constitutive equations are the Fredholm-type integral equations of the first kind, which can be transformed to the Volterra integral equations of the first kind. With the application of the Laplace transformation, the general solutions of the deflections and bending moments for the Euler-Bernoulli and Timoshenko beams as well as the rotation and shear force for the Timoshenko beams are obtained explicitly with several unknown constants. Considering the boundary conditions and extra constitutive constraints, the characteristic equations are obtained explicitly for the Euler-Bernoulli and Timoshenko beams under different boundary conditions, from which one can determine the critical buckling loads of nanobeams. The effects of the nonlocal parameters and buckling order on the buckling loads of nanobeams are studied numerically, and a consistent toughening effect is obtained.

关键词： Laplace transformation Volterra integral equation Fredholm integral equation stress-driven nonlocal integral model

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Brightening and controlling dark excitons in monolayer TMDCs

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Science China Materials 2018年第9期61卷 1245-1247页

作者： qing-hai Tan Jun Zhang State Key Laboratory of Superlattices and Microstructures Institute of Semiconductors Chinese Academy of Sciences CAS Center of Excellence in Topological Quantum Computation College of Materials Science and Opto-Electronic Technology University of Chinese Academy of Sciences

An exciton is a bound state formed by an excited electron and hole via the Coulomb *** bound states often play an important role in the optical properties of low dimensional materials such as quantum dots,nanowires an... 详细信息

关键词：激发态引力材料学量子点

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