In practical engineering construction,multi-layered barriers containing geomembranes are extensively applied to retard the migration of pollutants.However,the associated analytical theory on pollutants diffusion still...In practical engineering construction,multi-layered barriers containing geomembranes are extensively applied to retard the migration of pollutants.However,the associated analytical theory on pollutants diffusion still needs to be further improved.In this work,general analytical solutions are derived for one-dimensional diffusion of degradable organic contaminant(DOC)in the multi-layered media containing geomembranes under a time-varying concentration boundary condition,where the variable substitution and separated variable approaches are employed.These analytical solutions with clear expressions can be used not only to study the diffusion behaviors of DOC in bottom and vertical composite barrier systems,but also to verify other complex numerical models.The proposed general analytical solutions are then fully validated via three comparative analyses,including comparisons with the experimental measurements,an existing analytical solution,and a finite-difference solution.Ultimately,the influences of different factors on the composite cutoff wall’s(CCW,which consists of two soil-bentonite layers and a geomembrane)service performance are investigated through a composite vertical barrier system as the application example.The findings obtained from this investigation can provide scientific guidance for the barrier performance evaluation and the engineering design of CCWs.This application example also exhibits the necessity and effectiveness of the developed analytical solutions.展开更多
In recent years,magneto-electro-elastic(MEE)cylindrical shells with step-wise thicknesses have shown significant potential in the field of vibration energy harvesting.To aid the design of such energy harvesting device...In recent years,magneto-electro-elastic(MEE)cylindrical shells with step-wise thicknesses have shown significant potential in the field of vibration energy harvesting.To aid the design of such energy harvesting devices,an accurate free vibration analysis of embedded MEE cylindrical shells with step-wise thicknesses is performed within the framework of symplectic mechanics.By using the Legendre transformation,a new known vector is defined to transform the higher-order partial differential governing equations into a set of lower-order ordinary differential equations.Therefore,the original vibration analysis is regarded as an eigen problem in the symplectic space,and analytical solutions can be represented by the symplectic series.In numerical examples,the new analytical solutions are compared with the existing results,and good agreement is observed.Furthermore,the effects of critical design parameters on free vibration characteristics are thoroughly investigated.All numerical results can serve as benchmarks for the development of other approximate or numerical methods.展开更多
The study of transient heat conduction in multilayered slabs is widely used in various engineering fields. In this paper, the transient heat conduction in multilayered slabs with general boundary conditions and arbitr...The study of transient heat conduction in multilayered slabs is widely used in various engineering fields. In this paper, the transient heat conduction in multilayered slabs with general boundary conditions and arbitrary heat generations is analysed. The boundary conditions are general and include various combinations of Dirichlet, Neumann or Robin boundary conditions at either surface. Moreover, arbitrary heat generations in the slabs are taken into account. The solutions are derived by basic methods, including the superposition method, separation variable method and orthogonal expansion method. The simplified double-layered analytical solution is validated by a numerical method and applied to predicting the temporal and spatial distribution of the temperature inside a landfill. It indicates the ability of the proposed analytical solutions for solving the wide range of applied transient heat conduction problems.展开更多
Analytical solutions for the elastic properties of a variety of binary nanotubes with arbitrary chirality are obtained through the study of systematic molecular mechanics. This molecular mechanics model is first exten...Analytical solutions for the elastic properties of a variety of binary nanotubes with arbitrary chirality are obtained through the study of systematic molecular mechanics. This molecular mechanics model is first extended to chiral binary nanotubes by introducing an additional out-of-plane inversion term into the so-called stick-spiral model, which results from the polar bonds and the buckling of binary graphitic crystals. The closed-form expressions for the longitudinal and circumferential Young's modulus and Poisson's ratio of chiral binary nanotubes are derived as functions of the tube diameter. The obtained inversion force constants are negative for all types of binary nanotubes, and the predicted tube stiffness is lower than that by the former stick-spiral model without consideration of the inversion term, reflecting the softening effect of the buckling on the elastic properties of binary nanotubes. The obtained properties are shown to be comparable to available density functional theory calculated results and to be chirality and size sensitive. The developed model and explicit solutions provide a systematic understanding of the mechanical performance of binary nanotubes consisting of III-V and II-VI group elements.展开更多
This paper first gives the general solution of two-dimensional orthotropic media expressed with two harmonic displacement functions by using the governing equations. Then, based on the general solution in the case of ...This paper first gives the general solution of two-dimensional orthotropic media expressed with two harmonic displacement functions by using the governing equations. Then, based on the general solution in the case of distinct eigenvalues, a series of beam problems, including the problem of cantilever beam under uniform loads, cantilever beam with axial load and bending moment at the free end, cantilever beam under the first, second, third and fourth power ofx tangential loads, is solved by the superposition principle and the trial-and-error methods.展开更多
In this paper, the specific solutions of orthotropic plane problems with body forces are derived. Then, based on the general solution in the case of distinct eigenvalues and the specific solution for density functiona...In this paper, the specific solutions of orthotropic plane problems with body forces are derived. Then, based on the general solution in the case of distinct eigenvalues and the specific solution for density functionally graded orthotropic media, a series of beam problem, including the problems of cantilever beam with body forces depending only on z or on x coordinate and expressed by z or x polynomial is solved by the principle of superposition and the trial-and-error method.展开更多
To efficiently and accurately design satellite constellations equipped with Reentry Glide Vehicles(RGVs),new analytical solutions are developed for calculating their coverage perfor-mance.Specifically,a new coverage m...To efficiently and accurately design satellite constellations equipped with Reentry Glide Vehicles(RGVs),new analytical solutions are developed for calculating their coverage perfor-mance.Specifically,a new coverage model is established by approximating the Reentry Reachable Domain(RRD).However,the computation of real-time relative distances between satellites and targets,which is essential for coverage analysis based on this model,imposes a significant compu-tational burden.To address this challenge,a coverage analysis method based on two-dimensional map theory is proposed.This method represents the coverage conditions of a target as a fixed area on a two-dimensional map and transforms the satellite trajectory into a series of parallel lines.By determining the intersection points between these lines and the area boundaries,the coverage ana-lytical solutions for a target point are derived.On this basis,coverage theorems are presented for rapid calculation of the constellation coverage performance for an area.Simulation results demon-strate the effectiveness and high precision of the proposed analytical solutions.展开更多
In recent years, as the composite laminated plates are widely used in engineering practice such as aerospace, marine and building engineering, the vibration problem of the composite laminated plates is becoming more a...In recent years, as the composite laminated plates are widely used in engineering practice such as aerospace, marine and building engineering, the vibration problem of the composite laminated plates is becoming more and more important. Frequency, especially the fundamental frequency, has been considered as an important factor in vibration problem. In this paper, a calculation method of the fundamental frequency of arbitrary laminated plates under various boundary conditions is proposed. The vibration differential equation of the laminated plates is established at the beginning of this paper and the frequency formulae of specialty orthotropic laminated plates under various boundary conditions and antisymmetric angle-ply laminated plates with simply-supported edges are investigated. They are proved to be correct. Simple algorithm of the fundamental frequency for multilayer antisymmetric and arbitrary laminated plates under various boundary conditions is studied by a series of typical examples. From the perspective of coupling, when the number of laminated plates layers N〉8-10, some coupling influence on the fundamental frequency can be neglected. It is reasonable to use specialty orthotropic laminated plates with the same thickness but less layers to calculate the corresponding fundamental frequency of laminated plates. Several examples are conducted to prove correctness of this conclusion. At the end of this paper, the influence of the selected number of layers of specialty orthotropic laminates on the fundamental frequency is investigated. The accuracy and complexity are determined by the number of layers. It is necessary to use proper number of layers of special orthotropic laminates with the same thickness to simulate the fundamental frequency in different boundary conditions.展开更多
Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric d...Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie functions of scattering states on the ＂k/2π scale＂ and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.展开更多
Within the context of Gurtin-Murdoch surface elasticity theory,closed-form analytical solutions are derived for an isotropic elastic half-plane subjected to a concentrated/uniform surface load.Both the effects of resi...Within the context of Gurtin-Murdoch surface elasticity theory,closed-form analytical solutions are derived for an isotropic elastic half-plane subjected to a concentrated/uniform surface load.Both the effects of residual surface stress and surface elasticity are included.Airy stress function method and Fourier integral transform technique are used.The solutions are provided in a compact manner that can easily reduce to special situations that take into account either one surface effect or none at all.Numerical results indicate that surface effects generally lower the stress levels and smooth the deformation profiles in the half-plane.Surface elasticity plays a dominant role in the in-plane elastic fields for a tangentially loaded half-plane,while the effect of residual surface stress is fundamentally crucial for the out-of-plane stress and displacement when the half-plane is normally loaded.In the remaining situations,combined effects of surface elasticity and residual surface stress should be considered.The results for a concentrated surface force serve essentially as fundamental solutions of the Flamant and the half-plane Cerruti problems with surface effects.The solutions presented in this work may be helpful for understanding the contact behaviors between solids at the nanoscale.展开更多
The improved near crack line analysis method was used to investigate an eccentric cracked plate loaded by two pairs of anti_plane point forces at the crack surface in an elastic_perfectly plastic solid. The analytical...The improved near crack line analysis method was used to investigate an eccentric cracked plate loaded by two pairs of anti_plane point forces at the crack surface in an elastic_perfectly plastic solid. The analytical solutions of the elastic_plastic stress fields and displacements near the crack line have been found without the assumptions of the small scale yielding. The law that the length of the plastic zone along the crack line is varied with an external loads and the bearing capacity of an eccentric cracked plate are obtained.展开更多
The present study has obtained the new model of the reservoir filtration problem by taking into account the effect of wellbore storage and skin and by making use of the coupled equations of doubled porous media filtra...The present study has obtained the new model of the reservoir filtration problem by taking into account the effect of wellbore storage and skin and by making use of the coupled equations of doubled porous media filtration and consequently has got, through various forms of limits, the exact analytical solutions of the three common reservoirs (fissure, homogeneous and the two-layered) pressure distribution under the conditions of three boundaries, i.e., infinite boundary, sealed finite boundary and the finite boundary at constant pressures.展开更多
The analytical solutions to the Schrodinger equation with the Eckart potential in arbitrary dimension D is investigated by using the Nikiforov-Uvarov method, and the centrifugal term is treated approximatively with th...The analytical solutions to the Schrodinger equation with the Eckart potential in arbitrary dimension D is investigated by using the Nikiforov-Uvarov method, and the centrifugal term is treated approximatively with the scheme of Greene and Aldrich. The discrete spectrum is obtained and the wavefunetion is expressed in terms of the Jacobi polynomial or the hypergeometric function. Some special cases of the Eckart potential are discussed for D=3, and the resulting energy equation agrees well with that obtained by other methods.展开更多
Using the Boussinesq approximation, the vortex in the boundary layer is assumed to be axisymmetrical and thermal-wind balanced system forced by diabatic heating and friction, and is solved as an initial-value problem ...Using the Boussinesq approximation, the vortex in the boundary layer is assumed to be axisymmetrical and thermal-wind balanced system forced by diabatic heating and friction, and is solved as an initial-value problem of linearized vortex equation set in cylindrical coordinates. The impacts of thermal forcing on the flow field structure of vortex are analyzed. It is found that thermal forcing has significant impacts on the flow field structure, and the material representative forms of these impacts are closely related to the radial distribution of heating. The discussion for the analytical solutions for the vortex in the boundary layer can explain some main structures of the vortex over the Tibetan Plateau.展开更多
In the scenario that a solid-fuel launch vehicle maneuvers in outer space at high angles of attack and sideslip for energy management,Approximate Analytical Solutions(AAS)for the threedimensional(3D)ascent flight stat...In the scenario that a solid-fuel launch vehicle maneuvers in outer space at high angles of attack and sideslip for energy management,Approximate Analytical Solutions(AAS)for the threedimensional(3D)ascent flight states are derived,which are the only solutions capable of considering time-varying Mass Flow Rate(MFR)at present.The uneven MFR makes the thrust vary nonlinearly and thus increases the difficulty of the problem greatly.The AAS are derived based on a 3D Generalized Ascent Dynamics Model(GADM)with a normalized mass as the independent variable.To simplify some highly nonlinear terms in the GADM,several approximate functions are introduced carefully,while the errors of the approximations relative to the original terms are regarded as minor perturbations.Notably,a finite series with positive and negative exponents,called Exponent-Symmetry Series(ESS),is proposed for function approximation to decrease the highest exponent in the AAS so as to reduce computer round-off errors.To calculate the ESS coefficients,a method of seeking the Optimal Interpolation Points(OIP)is proposed using the leastsquares-approximation theory.Due to the artful design of the approximations,the GADM can be decomposed into two analytically solvable subsystems by a perturbation method,and thus the AAS are obtained successfully.Finally,to help implement the AAS,two indirect methods for measuring the remaining mass and predicting the burnout time in flight are put forward using information from accelerometers.Simulation results verify the superiority of the AAS under the condition of time-varying MFR.展开更多
Based on the Landau-Lifshitz-Gilbert(LLG)equation,the precession relaxation of magnetization is studied when the external field H is parallel to the uniaxial anisotropic field H_(k).The evolution of three-component ma...Based on the Landau-Lifshitz-Gilbert(LLG)equation,the precession relaxation of magnetization is studied when the external field H is parallel to the uniaxial anisotropic field H_(k).The evolution of three-component magnetization is solved analytically under the condition of H=nH_(k)(n=3,1 and 0).It is found that with an increase of H or a decrease of the initial polar angle of magnetization,the relaxation time decreases and the angular frequency of magnetization increases.For comparison,the analytical solution for H_(k)=0 is also given.When the magnetization becomes stable,the angular frequency is proportional to the total effective field acting on the magnetization.The analytical solutions are not only conducive to the understanding of the precession relaxation of magnetization,but also can be used as a standard model to test the numerical calculation of LLG equation.展开更多
By using a two-mode mean-field approximation, we study the dynamics of the microcavities containing semiconductor quantum wells. The exact analytical solutions are obtained in this study. Based on these solutions, we ...By using a two-mode mean-field approximation, we study the dynamics of the microcavities containing semiconductor quantum wells. The exact analytical solutions are obtained in this study. Based on these solutions, we show that the emission from the microcavity manifests periodic oscillation behaviour and the oscillation can be suppressed under a certain condition.展开更多
This paper presents analytieal solutions to the partial differential equations for unsteady flow of the second-order fluid and Maxwell fluid in tube by using the integral transform method. It can be used to analyse th...This paper presents analytieal solutions to the partial differential equations for unsteady flow of the second-order fluid and Maxwell fluid in tube by using the integral transform method. It can be used to analyse the behaviour of axial velocity and shear stress for unsteady flow of nun-Newtonian visco-elastie fluids in tube, and to provide a theoretical base for the projection of pipe-line engineering.展开更多
On the basis of the concept of finite element methods, the rigorous analytical solutions of structural response in terms of the design variables are researched in this paper. The spatial trusses are taken as an exampl...On the basis of the concept of finite element methods, the rigorous analytical solutions of structural response in terms of the design variables are researched in this paper. The spatial trusses are taken as an example for the solution of the analytical expressions of the explicit displacements which are proved mathematically; then some conclusions are reached that are useful to structural sensitivity analysis and optimization. In the third part of the paper, a generalized geometric programming method is sugviped for the optimal model with the explicit displacement. Finally, the analytical solutions of the displacements of three trusses are given as examples.展开更多
It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analyt...It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analytical solutions. In this paper, exact solutions for the periodic forcing by surface heat flux and wind stress are given by solving the linearized equations of motion neglecting the rotation, advection and horizontal diffusion terms. The temperature at the bottom is set to a prescribed periodic value and a slip condition on flow is enforced at the bottom. The geometry of the quarter annulus, which has been extensively studied for two- and three-dimensional analytical solutions of unstratified water bodies, is used with a general power law variation of the bottom slope in the radial direction and is constant in the azimuthal direction. The analytical solutions are derived in a cylindrical coordinate system, which describes the three-dimensional fluid field in a Cartesian coordinate system. The results presented in this paper should provide a foundation for studying and verifying the baroclinic term over a varied topography in a three-dimensional numerical model.展开更多
基金Project(2023YFC3707800)supported by the National Key Research and Development Program of China。
文摘In practical engineering construction,multi-layered barriers containing geomembranes are extensively applied to retard the migration of pollutants.However,the associated analytical theory on pollutants diffusion still needs to be further improved.In this work,general analytical solutions are derived for one-dimensional diffusion of degradable organic contaminant(DOC)in the multi-layered media containing geomembranes under a time-varying concentration boundary condition,where the variable substitution and separated variable approaches are employed.These analytical solutions with clear expressions can be used not only to study the diffusion behaviors of DOC in bottom and vertical composite barrier systems,but also to verify other complex numerical models.The proposed general analytical solutions are then fully validated via three comparative analyses,including comparisons with the experimental measurements,an existing analytical solution,and a finite-difference solution.Ultimately,the influences of different factors on the composite cutoff wall’s(CCW,which consists of two soil-bentonite layers and a geomembrane)service performance are investigated through a composite vertical barrier system as the application example.The findings obtained from this investigation can provide scientific guidance for the barrier performance evaluation and the engineering design of CCWs.This application example also exhibits the necessity and effectiveness of the developed analytical solutions.
基金Project supported by the Science and Technology Plan Joint Program of Liaoning Province of China(Natural Science Foundation-Doctoral Research Launch Project)(No.2024-BSLH-027)the Fundamental Research Funds for Undergraduate Universities of Liaoning Province of China(No.LJBKY2024033)+1 种基金the National Natural Science Foundation of China(No.12472064)the Natural Science Foundation of Liaoning Province of China(No.2023-MS-118)。
文摘In recent years,magneto-electro-elastic(MEE)cylindrical shells with step-wise thicknesses have shown significant potential in the field of vibration energy harvesting.To aid the design of such energy harvesting devices,an accurate free vibration analysis of embedded MEE cylindrical shells with step-wise thicknesses is performed within the framework of symplectic mechanics.By using the Legendre transformation,a new known vector is defined to transform the higher-order partial differential governing equations into a set of lower-order ordinary differential equations.Therefore,the original vibration analysis is regarded as an eigen problem in the symplectic space,and analytical solutions can be represented by the symplectic series.In numerical examples,the new analytical solutions are compared with the existing results,and good agreement is observed.Furthermore,the effects of critical design parameters on free vibration characteristics are thoroughly investigated.All numerical results can serve as benchmarks for the development of other approximate or numerical methods.
基金Projects(41530637,41877222,41702290)supported by the National Natural Science Foundation of China
文摘The study of transient heat conduction in multilayered slabs is widely used in various engineering fields. In this paper, the transient heat conduction in multilayered slabs with general boundary conditions and arbitrary heat generations is analysed. The boundary conditions are general and include various combinations of Dirichlet, Neumann or Robin boundary conditions at either surface. Moreover, arbitrary heat generations in the slabs are taken into account. The solutions are derived by basic methods, including the superposition method, separation variable method and orthogonal expansion method. The simplified double-layered analytical solution is validated by a numerical method and applied to predicting the temporal and spatial distribution of the temperature inside a landfill. It indicates the ability of the proposed analytical solutions for solving the wide range of applied transient heat conduction problems.
基金supported by the 973 Program (Grants 2013CB932604, 2012CB933403)a project funded by the Priority Academic Program Development of Jiangsu Higher Education InstitutionsJiangsu Innovation Program for Graduate Education (Grant CXZZ12_0140)
文摘Analytical solutions for the elastic properties of a variety of binary nanotubes with arbitrary chirality are obtained through the study of systematic molecular mechanics. This molecular mechanics model is first extended to chiral binary nanotubes by introducing an additional out-of-plane inversion term into the so-called stick-spiral model, which results from the polar bonds and the buckling of binary graphitic crystals. The closed-form expressions for the longitudinal and circumferential Young's modulus and Poisson's ratio of chiral binary nanotubes are derived as functions of the tube diameter. The obtained inversion force constants are negative for all types of binary nanotubes, and the predicted tube stiffness is lower than that by the former stick-spiral model without consideration of the inversion term, reflecting the softening effect of the buckling on the elastic properties of binary nanotubes. The obtained properties are shown to be comparable to available density functional theory calculated results and to be chirality and size sensitive. The developed model and explicit solutions provide a systematic understanding of the mechanical performance of binary nanotubes consisting of III-V and II-VI group elements.
文摘This paper first gives the general solution of two-dimensional orthotropic media expressed with two harmonic displacement functions by using the governing equations. Then, based on the general solution in the case of distinct eigenvalues, a series of beam problems, including the problem of cantilever beam under uniform loads, cantilever beam with axial load and bending moment at the free end, cantilever beam under the first, second, third and fourth power ofx tangential loads, is solved by the superposition principle and the trial-and-error methods.
基金Project (Nos. 10432030 and 10472102) supported by the NationalNatural Science Foundation of China
文摘In this paper, the specific solutions of orthotropic plane problems with body forces are derived. Then, based on the general solution in the case of distinct eigenvalues and the specific solution for density functionally graded orthotropic media, a series of beam problem, including the problems of cantilever beam with body forces depending only on z or on x coordinate and expressed by z or x polynomial is solved by the principle of superposition and the trial-and-error method.
基金supported by the National Natural Science Foundation of China (No.62273119).
文摘To efficiently and accurately design satellite constellations equipped with Reentry Glide Vehicles(RGVs),new analytical solutions are developed for calculating their coverage perfor-mance.Specifically,a new coverage model is established by approximating the Reentry Reachable Domain(RRD).However,the computation of real-time relative distances between satellites and targets,which is essential for coverage analysis based on this model,imposes a significant compu-tational burden.To address this challenge,a coverage analysis method based on two-dimensional map theory is proposed.This method represents the coverage conditions of a target as a fixed area on a two-dimensional map and transforms the satellite trajectory into a series of parallel lines.By determining the intersection points between these lines and the area boundaries,the coverage ana-lytical solutions for a target point are derived.On this basis,coverage theorems are presented for rapid calculation of the constellation coverage performance for an area.Simulation results demon-strate the effectiveness and high precision of the proposed analytical solutions.
基金Foundation item： Supported by the National Natural Science Foundation of China （51109034）.
文摘In recent years, as the composite laminated plates are widely used in engineering practice such as aerospace, marine and building engineering, the vibration problem of the composite laminated plates is becoming more and more important. Frequency, especially the fundamental frequency, has been considered as an important factor in vibration problem. In this paper, a calculation method of the fundamental frequency of arbitrary laminated plates under various boundary conditions is proposed. The vibration differential equation of the laminated plates is established at the beginning of this paper and the frequency formulae of specialty orthotropic laminated plates under various boundary conditions and antisymmetric angle-ply laminated plates with simply-supported edges are investigated. They are proved to be correct. Simple algorithm of the fundamental frequency for multilayer antisymmetric and arbitrary laminated plates under various boundary conditions is studied by a series of typical examples. From the perspective of coupling, when the number of laminated plates layers N〉8-10, some coupling influence on the fundamental frequency can be neglected. It is reasonable to use specialty orthotropic laminated plates with the same thickness but less layers to calculate the corresponding fundamental frequency of laminated plates. Several examples are conducted to prove correctness of this conclusion. At the end of this paper, the influence of the selected number of layers of specialty orthotropic laminates on the fundamental frequency is investigated. The accuracy and complexity are determined by the number of layers. It is necessary to use proper number of layers of special orthotropic laminates with the same thickness to simulate the fundamental frequency in different boundary conditions.
基金＊Supported by the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2010291, the Professor and Doctor Foundation of Yancheng Teachers University under Grant No. 07YSYJB0203
文摘Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie functions of scattering states on the ＂k/2π scale＂ and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.
基金supported by the National Natural Science Foundation of China(12272126,12272127)the Doctoral Fund of HPU(B2015-64).
文摘Within the context of Gurtin-Murdoch surface elasticity theory,closed-form analytical solutions are derived for an isotropic elastic half-plane subjected to a concentrated/uniform surface load.Both the effects of residual surface stress and surface elasticity are included.Airy stress function method and Fourier integral transform technique are used.The solutions are provided in a compact manner that can easily reduce to special situations that take into account either one surface effect or none at all.Numerical results indicate that surface effects generally lower the stress levels and smooth the deformation profiles in the half-plane.Surface elasticity plays a dominant role in the in-plane elastic fields for a tangentially loaded half-plane,while the effect of residual surface stress is fundamentally crucial for the out-of-plane stress and displacement when the half-plane is normally loaded.In the remaining situations,combined effects of surface elasticity and residual surface stress should be considered.The results for a concentrated surface force serve essentially as fundamental solutions of the Flamant and the half-plane Cerruti problems with surface effects.The solutions presented in this work may be helpful for understanding the contact behaviors between solids at the nanoscale.
文摘The improved near crack line analysis method was used to investigate an eccentric cracked plate loaded by two pairs of anti_plane point forces at the crack surface in an elastic_perfectly plastic solid. The analytical solutions of the elastic_plastic stress fields and displacements near the crack line have been found without the assumptions of the small scale yielding. The law that the length of the plastic zone along the crack line is varied with an external loads and the bearing capacity of an eccentric cracked plate are obtained.
文摘The present study has obtained the new model of the reservoir filtration problem by taking into account the effect of wellbore storage and skin and by making use of the coupled equations of doubled porous media filtration and consequently has got, through various forms of limits, the exact analytical solutions of the three common reservoirs (fissure, homogeneous and the two-layered) pressure distribution under the conditions of three boundaries, i.e., infinite boundary, sealed finite boundary and the finite boundary at constant pressures.
基金Supported by the National Natural Science Foundation of China under Grant No 14101020155the Fundamental Research Funds for the Central Universities under Grant No GK201402012
文摘The analytical solutions to the Schrodinger equation with the Eckart potential in arbitrary dimension D is investigated by using the Nikiforov-Uvarov method, and the centrifugal term is treated approximatively with the scheme of Greene and Aldrich. The discrete spectrum is obtained and the wavefunetion is expressed in terms of the Jacobi polynomial or the hypergeometric function. Some special cases of the Eckart potential are discussed for D=3, and the resulting energy equation agrees well with that obtained by other methods.
基金Project supported by the National Key Basic Research and Development Project of China(No.2004CB418300)the National Natural Science Foundation of China (No.40375023)
文摘Using the Boussinesq approximation, the vortex in the boundary layer is assumed to be axisymmetrical and thermal-wind balanced system forced by diabatic heating and friction, and is solved as an initial-value problem of linearized vortex equation set in cylindrical coordinates. The impacts of thermal forcing on the flow field structure of vortex are analyzed. It is found that thermal forcing has significant impacts on the flow field structure, and the material representative forms of these impacts are closely related to the radial distribution of heating. The discussion for the analytical solutions for the vortex in the boundary layer can explain some main structures of the vortex over the Tibetan Plateau.
基金Supported in part by National Natural Science Foundation of China(No.62003012)in part by the Young Tulents Support Program funded by Bcihang Univer-sity,China(No.YWF-23-L-702).
文摘In the scenario that a solid-fuel launch vehicle maneuvers in outer space at high angles of attack and sideslip for energy management,Approximate Analytical Solutions(AAS)for the threedimensional(3D)ascent flight states are derived,which are the only solutions capable of considering time-varying Mass Flow Rate(MFR)at present.The uneven MFR makes the thrust vary nonlinearly and thus increases the difficulty of the problem greatly.The AAS are derived based on a 3D Generalized Ascent Dynamics Model(GADM)with a normalized mass as the independent variable.To simplify some highly nonlinear terms in the GADM,several approximate functions are introduced carefully,while the errors of the approximations relative to the original terms are regarded as minor perturbations.Notably,a finite series with positive and negative exponents,called Exponent-Symmetry Series(ESS),is proposed for function approximation to decrease the highest exponent in the AAS so as to reduce computer round-off errors.To calculate the ESS coefficients,a method of seeking the Optimal Interpolation Points(OIP)is proposed using the leastsquares-approximation theory.Due to the artful design of the approximations,the GADM can be decomposed into two analytically solvable subsystems by a perturbation method,and thus the AAS are obtained successfully.Finally,to help implement the AAS,two indirect methods for measuring the remaining mass and predicting the burnout time in flight are put forward using information from accelerometers.Simulation results verify the superiority of the AAS under the condition of time-varying MFR.
基金Project supported by the National Key R&D Program of China (Grant No.2021YFB3501300)the National Natural Science Foundation of China (Grant Nos.91963201 and 12174163)the 111 Project (Grant No.B20063)。
文摘Based on the Landau-Lifshitz-Gilbert(LLG)equation,the precession relaxation of magnetization is studied when the external field H is parallel to the uniaxial anisotropic field H_(k).The evolution of three-component magnetization is solved analytically under the condition of H=nH_(k)(n=3,1 and 0).It is found that with an increase of H or a decrease of the initial polar angle of magnetization,the relaxation time decreases and the angular frequency of magnetization increases.For comparison,the analytical solution for H_(k)=0 is also given.When the magnetization becomes stable,the angular frequency is proportional to the total effective field acting on the magnetization.The analytical solutions are not only conducive to the understanding of the precession relaxation of magnetization,but also can be used as a standard model to test the numerical calculation of LLG equation.
基金Project supported in part by the Natural Science Foundation of China (Grant Nos. 10575040,90503010,10634060 and 10874050)by National Basic Research Program of China (Grant No. 2005CB724508)+1 种基金the Foundation from the ministry of the National Education of China (Grant No. 200804870051)the Science Innovation Foundation of Huazhong University of Science and Technology (Grant No. HF-06-010-08-012)
文摘By using a two-mode mean-field approximation, we study the dynamics of the microcavities containing semiconductor quantum wells. The exact analytical solutions are obtained in this study. Based on these solutions, we show that the emission from the microcavity manifests periodic oscillation behaviour and the oscillation can be suppressed under a certain condition.
文摘This paper presents analytieal solutions to the partial differential equations for unsteady flow of the second-order fluid and Maxwell fluid in tube by using the integral transform method. It can be used to analyse the behaviour of axial velocity and shear stress for unsteady flow of nun-Newtonian visco-elastie fluids in tube, and to provide a theoretical base for the projection of pipe-line engineering.
文摘On the basis of the concept of finite element methods, the rigorous analytical solutions of structural response in terms of the design variables are researched in this paper. The spatial trusses are taken as an example for the solution of the analytical expressions of the explicit displacements which are proved mathematically; then some conclusions are reached that are useful to structural sensitivity analysis and optimization. In the third part of the paper, a generalized geometric programming method is sugviped for the optimal model with the explicit displacement. Finally, the analytical solutions of the displacements of three trusses are given as examples.
文摘It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analytical solutions. In this paper, exact solutions for the periodic forcing by surface heat flux and wind stress are given by solving the linearized equations of motion neglecting the rotation, advection and horizontal diffusion terms. The temperature at the bottom is set to a prescribed periodic value and a slip condition on flow is enforced at the bottom. The geometry of the quarter annulus, which has been extensively studied for two- and three-dimensional analytical solutions of unstratified water bodies, is used with a general power law variation of the bottom slope in the radial direction and is constant in the azimuthal direction. The analytical solutions are derived in a cylindrical coordinate system, which describes the three-dimensional fluid field in a Cartesian coordinate system. The results presented in this paper should provide a foundation for studying and verifying the baroclinic term over a varied topography in a three-dimensional numerical model.
