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
A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions o...A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.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
Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with th...Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.展开更多
We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh–Nagumo model with truncated M-fractional derivative, in which the expafunction and extended sinh-Gor...We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh–Nagumo model with truncated M-fractional derivative, in which the expafunction and extended sinh-Gordon equation expansion(ESh GEE) schemes are utilized. The solutions obtained include dark, bright, dark-bright, periodic and other kinds of solitons. These analytical wave solutions are gained and verified with the use of Mathematica software. These solutions do not exist in literature. Some of the solutions are demonstrated by 2D, 3D and contour graphs. This model is mostly used in circuit theory, transmission of nerve impulses, and population genetics. Finally, both the schemes are more applicable, reliable and significant to deal with the fractional nonlinear partial differential equations.展开更多
Multiple objectives to be optimized simultaneously are prevalent in real-life problems. This paper develops a new Pareto Method for bi-objective optimization which yields analytical solutions. The Pareto optimal front...Multiple objectives to be optimized simultaneously are prevalent in real-life problems. This paper develops a new Pareto Method for bi-objective optimization which yields analytical solutions. The Pareto optimal front is obtained in closed-form, enabling the derivation of various solutions in a convenient and efficient way. The advantage of analytical solution is the possibility of deriving accurate, exact and well-understood solutions, which is especially useful for policy analysis. An extension of the method to include multiple objectives is provided with the objectives being classified into two types. Such an extension expands the applicability of the developed techniques.展开更多
This paper investigates the validity and shortcomings of the existing analytical solution for the ultimate bearing capacity of a pile embedded in a rock mass using the modified HoekeBrown failure criterion.Although th...This paper investigates the validity and shortcomings of the existing analytical solution for the ultimate bearing capacity of a pile embedded in a rock mass using the modified HoekeBrown failure criterion.Although this criterion is considered a reference value for empirical and numerical calculations,some limitations of its basic simplifications have not been clarified yet.This research compares the analytical results obtained from the novel discontinuity layout optimization(DLO)method and the numerical solutions from the finite difference method(FDM).The limitations of the analytical solution are considered by comparing different DLO failure modes,thus allowing for the first time a critical evaluation of its scope and conditioning for implementation.Errors of up to 40%in the bearing capacity and unrealistic failure modes are the main issues in the analytical solution.The main aspects of the DLO method are also analyzed with an emphasis on the linearization of the rock failure criterion and the accuracy resulting from the discretization size.The analysis demonstrates DLO as a very efficient and accurate tool to address the pile tip bearing capacity,presenting considerable advantages over other methods.展开更多
The near crack line analysis method was used to investigate a centric crack loaded by two pairs of point shear forces in a finite plate, and the analytical solution was obtained. The solution includes the unit normal ...The near crack line analysis method was used to investigate a centric crack loaded by two pairs of point shear forces in a finite plate, and the analytical solution was obtained. The solution includes the unit normal vector of the elastic-plastic boundary near the crack line, the elastic-plastic stress fields near the crack line, the variations of the length of the plastic zone along the crack line with an external load, and the bearing capacity of a finite plate with a centric crack loaded by two pairs of point shear forces. The results are sufficiently precise near the crack line because the assumptions of small scale yielding theory have not been made and no other assumptions are taken.展开更多
In regard to unconventional oil reservoirs,the transient dual-porosity and triple-porosity models have been adopted to describe the fluid flow in the complex fracture network.It has been proven to cause inaccurate pro...In regard to unconventional oil reservoirs,the transient dual-porosity and triple-porosity models have been adopted to describe the fluid flow in the complex fracture network.It has been proven to cause inaccurate production evaluations because of the absence of matrix-macrofracture communication.In addition,most of the existing models are solved analytically based on Laplace transform and numerical inversion.Hence,an approximate analytical solution is derived directly in real-time space considering variable matrix blocks and simultaneous matrix depletion.To simplify the derivation,the simultaneous matrix depletion is divided into two parts:one part feeding the macrofractures and the other part feeding the microfractures.Then,a series of partial differential equations(PDEs)describing the transient flow and boundary conditions are constructed and solved analytically by integration.Finally,a relationship between oil rate and production time in real-time space is obtained.The new model is verified against classical analytical models.When the microfracture system and matrix-macrofracture communication is neglected,the result of the new model agrees with those obtained with the dual-porosity and triple-porosity model,respectively.Certainly,the new model also has an excellent agreement with the numerical model.The model is then applied to two actual tight oil wells completed in western Canada sedimentary basin.After identifying the flow regime,the solution suitably matches the field production data,and the model parameters are determined.Through these output parameters,we can accurately forecast the production and even estimate the petrophysical properties.展开更多
We report on the magnetohydrodynamic impact on the axisymmetric flow of Al_(2)O_(3)/Cu nanoparticles suspended in H_(2)O past a stretched/shrinked sheet.With the use of partial differential equations and the correspon...We report on the magnetohydrodynamic impact on the axisymmetric flow of Al_(2)O_(3)/Cu nanoparticles suspended in H_(2)O past a stretched/shrinked sheet.With the use of partial differential equations and the corresponding thermophysical characteristics of nanoparticles,the physical flow process is illustrated.The resultant nonlinear system of partial differential equations is converted into a system of ordinary differential equations using the suitable similarity transformations.The transformed differential equations are solved analytically.Impacts of the magnetic parameter,solid volume fraction and stretching/shrinking parameter on momentum and temperature distribution have been analyzed and interpreted graphically.The skin friction and Nusselt number were also evaluated.In addition,existence of dual solution was deduced for the shrinking sheet and unique solution for the stretching one.Further,Al_(2)O_(3)/H_(2)O nanofluid flow has better thermal conductivity on comparing with Cu/H_(2)O nanofluid.Furthermore,it was found that the first solutions of the stream are stable and physically realizable,whereas those of the second ones are unstable.展开更多
In the non-uniform stress field, the surrounding rock plastic zone of the circular roadway shows different shapes under the different confining pressure conditions. Based on the boundary shape characteristics of the p...In the non-uniform stress field, the surrounding rock plastic zone of the circular roadway shows different shapes under the different confining pressure conditions. Based on the boundary shape characteristics of the plastic zone, the characteristic radii of the plastic zone were proposed, namely the horizontal,longitudinal and medial axis radii, which could reflect the plastic zone shapes characteristics and classify the sizes of the key parts. On the theoretical basis of elastic-plastic mechanics, analytical solutions for the characteristic radii were obtained by theoretical deduction, and the relationships between the characteristic radii and key influencing factors were analyzed. Finally, the evaluation criterion of the circular roadway surrounding rock plastic zone shapes, evaluation criterion of the location of potential hazards caused by the roadway surrounding rock and evaluation critical points of roadway dynamic disasters based on characteristic radii were proposed. This work could provide a theoretical basis for stability analysis of the surrounding rock, support design, and guide the prevention and control of dynamic roadway disasters.展开更多
The stress concentration problem in structures with a circular or elliptic hole can be investigated by analytical methods. For the problem with a rectangular hole, only approximate results are derived. This paper dedu...The stress concentration problem in structures with a circular or elliptic hole can be investigated by analytical methods. For the problem with a rectangular hole, only approximate results are derived. This paper deduces the analytical solutions to the stress concentration problem in plates with a rectangular hole under biaxial tensions. By using the U-transformation technique and the finite element method, the analytical displacement solutions of the finite element equations are derived in the series form. Therefore, the stress concentration can then be discussed easily and conveniently. For plate problem the bilinear rectangular element with four nodes is taken as an example to demonstrate the applicability of the proposed method. The stress concentration factors for various ratios of height to width of the hole are obtained.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
The electromagnetic concentrative coils are indispensable in the functional magnetic stimulation and have potential applications in nondestructive testing. In this paper, we propose a figure-8-shaped coil being compos...The electromagnetic concentrative coils are indispensable in the functional magnetic stimulation and have potential applications in nondestructive testing. In this paper, we propose a figure-8-shaped coil being composed of two arbitrary oblique elliptical coils, which can change the electromagnetic concentrative region and the magnitude of eddy current density by changing the elliptical shape and/or spread angle between two elliptical coils. Pulsed current is usually the excitation source in the functional magnetic stimulation, so in this paper we derive the analytical solutions of transient pulsed eddy current field in the time domain due to the elliptical concentrative coil placed in an arbitrary position over a half-infinite plane conductor by making use of the scale-transformation, the Laplace transform and the Fourier transform are used in our derivation. Calculation results of field distributions produced by the figure-8-shaped elliptical coil show some behaviours as follows: 1) the eddy currents are focused on the conductor under the geometric symmetric centre of figure-8-shaped coil; 2) the greater the scale factor of ellipse is, the higher the eddy current density is and the wider the concentrative area of eddy current along y axis is; 3) the maximum magnitude of eddy current density increases with the increase of spread angle. When spread angle is 180°, there are two additional reverse concentrative areas on both sides of x axis.展开更多
A closed form of an analytical expression of concentration in the single-enzyme, single-substrate system for the full range of enzyme activities has been derived. The time dependent analytical solution for substrate, ...A closed form of an analytical expression of concentration in the single-enzyme, single-substrate system for the full range of enzyme activities has been derived. The time dependent analytical solution for substrate, enzyme-substrate complex and product concentrations are presented by solving system of non-linear differential equation. We employ He’s Homotopy perturbation method to solve the coupled non-linear differential equations containing a non-linear term related to basic enzymatic reaction. The time dependent simple analytical expressions for substrate, enzyme-substrate and free enzyme concentrations have been derived in terms of dimensionless reaction diffusion parameters ε, λ1, λ2 and λ3 using perturbation method. The numerical solution of the problem is also reported using SCILAB software program. The analytical results are compared with our numerical results. An excellent agreement with simulation data is noted. The obtained results are valid for the whole solution domain.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
Practical resolution of consolidation problems that we often face requires an extensive and solid knowledge of the different parameters highlighted by the Terzaghi one-dimensional consolidation theory. This theory, wi...Practical resolution of consolidation problems that we often face requires an extensive and solid knowledge of the different parameters highlighted by the Terzaghi one-dimensional consolidation theory. This theory, with its assumptions, leads to a partial differential equation of second order in space and first order in time of pore water pressure. Analytical and numerical resolutions of this equation allow determining the water pressure variation before and after the application of a charge. Numerical modeling has enabled the simulation of the whole results obtained by the two methods of resolution (pressure, degree of consolidation, time factor, among others) to have a physical analysis and a lawful observation that lead to a suitable understanding of the phenomenon of Terzaghi one-dimensional consolidation.展开更多
The problem of momentum and heat transfer in a compressible boundary layerbehind a thin expansion wave was solved by the application of the similarity transformation and theshooting technique. Utilizing the analytical...The problem of momentum and heat transfer in a compressible boundary layerbehind a thin expansion wave was solved by the application of the similarity transformation and theshooting technique. Utilizing the analytical expression of a two-point boundary value problem formomentum transfer, the energy boundary layer solution was represented as a function of thedimensionless velocity, and as the parameters of the Prandtl number, the velocity ratio, and thetemperature ratio.展开更多
This paper proposes a simplified analytical solution considering non-Darcian and wellbore storage effect to investigate the pumping flow in a confined aquifer with barrier and recharge boundaries.The mathematical mode...This paper proposes a simplified analytical solution considering non-Darcian and wellbore storage effect to investigate the pumping flow in a confined aquifer with barrier and recharge boundaries.The mathematical modelling for the pumping-induced flow in aquifers with different boundaries is developed by employing image-well theory with the superposition principle,of which the non-Darcian effect is characterized by Izbash’s equation.The solutions are derived by Boltzmann and dimensionless transformations.Then,the non-Darcian effect and wellbore storage are especially investigated according to the proposed solution.The results show that the aquifer boundaries have non-negligible effects on pumping,and ignoring the wellbore storage can lead to an over-estimation of the drawdown in the first 10 minutes of pumping.The higher the degree of non-Darcian,the smaller the drawdown.展开更多
Based on the Duhamel integral, a couple of analytical solutions are derived to predict the strain rates of concrete and steel reinforcement in reinforced concrete slabs under blast loads and to estimate their variatio...Based on the Duhamel integral, a couple of analytical solutions are derived to predict the strain rates of concrete and steel reinforcement in reinforced concrete slabs under blast loads and to estimate their variation over depth of a cross-section along the entire length of the member. The analytical approach utilizes the single-degree-of-freedom mode for the analysis of reinforced concrete simply supported one-way panels subjected to blast loads. These analytical solutions can give the strain rate profile for any cross-section at any time and permit variations of strain rate in each time step of numerical iteration method, thus making it possible to directly incorporate strain rate effects into non-linear dynamic response analysis of structural members subjected to blast loads.展开更多
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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12261064 and 11861048)the Natural Science Foundation of Inner Mongolia,China (Grant Nos.2021MS01004 and 2022QN01008)the High-level Talents Scientific Research Start-up Foundation of Inner Mongolia University (Grant No.10000-21311201/165)。
文摘A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.
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We would like to acknowledge all the reviewers and editors and the sponsorship of National Natural Science Foundation of China(42030103)the Marine S&T Fund of Shandong Province for Pilot National Laboratory for Marine Science and Technology(Qingdao)(2021QNLM020001-6)the Laoshan National Laboratory of Science and Technology Foundation(LSKJ202203400).
文摘Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.
文摘We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh–Nagumo model with truncated M-fractional derivative, in which the expafunction and extended sinh-Gordon equation expansion(ESh GEE) schemes are utilized. The solutions obtained include dark, bright, dark-bright, periodic and other kinds of solitons. These analytical wave solutions are gained and verified with the use of Mathematica software. These solutions do not exist in literature. Some of the solutions are demonstrated by 2D, 3D and contour graphs. This model is mostly used in circuit theory, transmission of nerve impulses, and population genetics. Finally, both the schemes are more applicable, reliable and significant to deal with the fractional nonlinear partial differential equations.
文摘Multiple objectives to be optimized simultaneously are prevalent in real-life problems. This paper develops a new Pareto Method for bi-objective optimization which yields analytical solutions. The Pareto optimal front is obtained in closed-form, enabling the derivation of various solutions in a convenient and efficient way. The advantage of analytical solution is the possibility of deriving accurate, exact and well-understood solutions, which is especially useful for policy analysis. An extension of the method to include multiple objectives is provided with the objectives being classified into two types. Such an extension expands the applicability of the developed techniques.
文摘This paper investigates the validity and shortcomings of the existing analytical solution for the ultimate bearing capacity of a pile embedded in a rock mass using the modified HoekeBrown failure criterion.Although this criterion is considered a reference value for empirical and numerical calculations,some limitations of its basic simplifications have not been clarified yet.This research compares the analytical results obtained from the novel discontinuity layout optimization(DLO)method and the numerical solutions from the finite difference method(FDM).The limitations of the analytical solution are considered by comparing different DLO failure modes,thus allowing for the first time a critical evaluation of its scope and conditioning for implementation.Errors of up to 40%in the bearing capacity and unrealistic failure modes are the main issues in the analytical solution.The main aspects of the DLO method are also analyzed with an emphasis on the linearization of the rock failure criterion and the accuracy resulting from the discretization size.The analysis demonstrates DLO as a very efficient and accurate tool to address the pile tip bearing capacity,presenting considerable advantages over other methods.
基金Key Project(2004BA901A02) supported by the Ministry of Science and Technology of China
文摘The near crack line analysis method was used to investigate a centric crack loaded by two pairs of point shear forces in a finite plate, and the analytical solution was obtained. The solution includes the unit normal vector of the elastic-plastic boundary near the crack line, the elastic-plastic stress fields near the crack line, the variations of the length of the plastic zone along the crack line with an external load, and the bearing capacity of a finite plate with a centric crack loaded by two pairs of point shear forces. The results are sufficiently precise near the crack line because the assumptions of small scale yielding theory have not been made and no other assumptions are taken.
基金This study was supported by Basic Research Project from Jiangmen Science and Technology Bureau(Grant No.2220002000356)China University of Petroleum(Beijing)(Grand No.2462023BJRC007)The Guangdong Basic and Applied Basic Research Foundation(No.2022A1515110376).
文摘In regard to unconventional oil reservoirs,the transient dual-porosity and triple-porosity models have been adopted to describe the fluid flow in the complex fracture network.It has been proven to cause inaccurate production evaluations because of the absence of matrix-macrofracture communication.In addition,most of the existing models are solved analytically based on Laplace transform and numerical inversion.Hence,an approximate analytical solution is derived directly in real-time space considering variable matrix blocks and simultaneous matrix depletion.To simplify the derivation,the simultaneous matrix depletion is divided into two parts:one part feeding the macrofractures and the other part feeding the microfractures.Then,a series of partial differential equations(PDEs)describing the transient flow and boundary conditions are constructed and solved analytically by integration.Finally,a relationship between oil rate and production time in real-time space is obtained.The new model is verified against classical analytical models.When the microfracture system and matrix-macrofracture communication is neglected,the result of the new model agrees with those obtained with the dual-porosity and triple-porosity model,respectively.Certainly,the new model also has an excellent agreement with the numerical model.The model is then applied to two actual tight oil wells completed in western Canada sedimentary basin.After identifying the flow regime,the solution suitably matches the field production data,and the model parameters are determined.Through these output parameters,we can accurately forecast the production and even estimate the petrophysical properties.
基金LMP acknowledges financial support from ANID through Convocatoria Nacional Subvención a Instalación en la Academia Convocatoria Año 2021,Grant SA77210040。
文摘We report on the magnetohydrodynamic impact on the axisymmetric flow of Al_(2)O_(3)/Cu nanoparticles suspended in H_(2)O past a stretched/shrinked sheet.With the use of partial differential equations and the corresponding thermophysical characteristics of nanoparticles,the physical flow process is illustrated.The resultant nonlinear system of partial differential equations is converted into a system of ordinary differential equations using the suitable similarity transformations.The transformed differential equations are solved analytically.Impacts of the magnetic parameter,solid volume fraction and stretching/shrinking parameter on momentum and temperature distribution have been analyzed and interpreted graphically.The skin friction and Nusselt number were also evaluated.In addition,existence of dual solution was deduced for the shrinking sheet and unique solution for the stretching one.Further,Al_(2)O_(3)/H_(2)O nanofluid flow has better thermal conductivity on comparing with Cu/H_(2)O nanofluid.Furthermore,it was found that the first solutions of the stream are stable and physically realizable,whereas those of the second ones are unstable.
基金supported by the National Natural Science Foundation of China (Grant No. 51234006)the National Key Research and Development Program of China (Grant No. 2016YFC0600708)
文摘In the non-uniform stress field, the surrounding rock plastic zone of the circular roadway shows different shapes under the different confining pressure conditions. Based on the boundary shape characteristics of the plastic zone, the characteristic radii of the plastic zone were proposed, namely the horizontal,longitudinal and medial axis radii, which could reflect the plastic zone shapes characteristics and classify the sizes of the key parts. On the theoretical basis of elastic-plastic mechanics, analytical solutions for the characteristic radii were obtained by theoretical deduction, and the relationships between the characteristic radii and key influencing factors were analyzed. Finally, the evaluation criterion of the circular roadway surrounding rock plastic zone shapes, evaluation criterion of the location of potential hazards caused by the roadway surrounding rock and evaluation critical points of roadway dynamic disasters based on characteristic radii were proposed. This work could provide a theoretical basis for stability analysis of the surrounding rock, support design, and guide the prevention and control of dynamic roadway disasters.
基金supported by the National Natural Science Foundation of China (No.10772202)the Chinese PostdoctoralScience Foundation (No.20060400757).
文摘The stress concentration problem in structures with a circular or elliptic hole can be investigated by analytical methods. For the problem with a rectangular hole, only approximate results are derived. This paper deduces the analytical solutions to the stress concentration problem in plates with a rectangular hole under biaxial tensions. By using the U-transformation technique and the finite element method, the analytical displacement solutions of the finite element equations are derived in the series form. Therefore, the stress concentration can then be discussed easily and conveniently. For plate problem the bilinear rectangular element with four nodes is taken as an example to demonstrate the applicability of the proposed method. The stress concentration factors for various ratios of height to width of the hole are obtained.
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.
基金Project supported by the National Natural Science Foundation of China (Grant No. 50807001)
文摘The electromagnetic concentrative coils are indispensable in the functional magnetic stimulation and have potential applications in nondestructive testing. In this paper, we propose a figure-8-shaped coil being composed of two arbitrary oblique elliptical coils, which can change the electromagnetic concentrative region and the magnitude of eddy current density by changing the elliptical shape and/or spread angle between two elliptical coils. Pulsed current is usually the excitation source in the functional magnetic stimulation, so in this paper we derive the analytical solutions of transient pulsed eddy current field in the time domain due to the elliptical concentrative coil placed in an arbitrary position over a half-infinite plane conductor by making use of the scale-transformation, the Laplace transform and the Fourier transform are used in our derivation. Calculation results of field distributions produced by the figure-8-shaped elliptical coil show some behaviours as follows: 1) the eddy currents are focused on the conductor under the geometric symmetric centre of figure-8-shaped coil; 2) the greater the scale factor of ellipse is, the higher the eddy current density is and the wider the concentrative area of eddy current along y axis is; 3) the maximum magnitude of eddy current density increases with the increase of spread angle. When spread angle is 180°, there are two additional reverse concentrative areas on both sides of x axis.
文摘A closed form of an analytical expression of concentration in the single-enzyme, single-substrate system for the full range of enzyme activities has been derived. The time dependent analytical solution for substrate, enzyme-substrate complex and product concentrations are presented by solving system of non-linear differential equation. We employ He’s Homotopy perturbation method to solve the coupled non-linear differential equations containing a non-linear term related to basic enzymatic reaction. The time dependent simple analytical expressions for substrate, enzyme-substrate and free enzyme concentrations have been derived in terms of dimensionless reaction diffusion parameters ε, λ1, λ2 and λ3 using perturbation method. The numerical solution of the problem is also reported using SCILAB software program. The analytical results are compared with our numerical results. An excellent agreement with simulation data is noted. The obtained results are valid for the whole solution domain.
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.
文摘Practical resolution of consolidation problems that we often face requires an extensive and solid knowledge of the different parameters highlighted by the Terzaghi one-dimensional consolidation theory. This theory, with its assumptions, leads to a partial differential equation of second order in space and first order in time of pore water pressure. Analytical and numerical resolutions of this equation allow determining the water pressure variation before and after the application of a charge. Numerical modeling has enabled the simulation of the whole results obtained by the two methods of resolution (pressure, degree of consolidation, time factor, among others) to have a physical analysis and a lawful observation that lead to a suitable understanding of the phenomenon of Terzaghi one-dimensional consolidation.
基金This work was supported by the "Cross-Century Talents Projects of the Educational Ministry of China"the "Projects of Investigations of Post Graduate School, University of Science and Technology Beijing".
文摘The problem of momentum and heat transfer in a compressible boundary layerbehind a thin expansion wave was solved by the application of the similarity transformation and theshooting technique. Utilizing the analytical expression of a two-point boundary value problem formomentum transfer, the energy boundary layer solution was represented as a function of thedimensionless velocity, and as the parameters of the Prandtl number, the velocity ratio, and thetemperature ratio.
基金supported by the National Natural Science Foundation of China (Grant Numbers41807197, 2017YFC0405900, and 51469002)the Natural Science Foundation of Guangxi (Grant Numbers 2017GXNSFBA198087, 2018GXNSFAA138042, and GuiKeAB17195073)Hebei Highlevel Talent Funding Project (B2018003016)。
文摘This paper proposes a simplified analytical solution considering non-Darcian and wellbore storage effect to investigate the pumping flow in a confined aquifer with barrier and recharge boundaries.The mathematical modelling for the pumping-induced flow in aquifers with different boundaries is developed by employing image-well theory with the superposition principle,of which the non-Darcian effect is characterized by Izbash’s equation.The solutions are derived by Boltzmann and dimensionless transformations.Then,the non-Darcian effect and wellbore storage are especially investigated according to the proposed solution.The results show that the aquifer boundaries have non-negligible effects on pumping,and ignoring the wellbore storage can lead to an over-estimation of the drawdown in the first 10 minutes of pumping.The higher the degree of non-Darcian,the smaller the drawdown.
文摘Based on the Duhamel integral, a couple of analytical solutions are derived to predict the strain rates of concrete and steel reinforcement in reinforced concrete slabs under blast loads and to estimate their variation over depth of a cross-section along the entire length of the member. The analytical approach utilizes the single-degree-of-freedom mode for the analysis of reinforced concrete simply supported one-way panels subjected to blast loads. These analytical solutions can give the strain rate profile for any cross-section at any time and permit variations of strain rate in each time step of numerical iteration method, thus making it possible to directly incorporate strain rate effects into non-linear dynamic response analysis of structural members subjected to blast loads.