Underhand cut-and-fill mining has been widely used in underground mining operations,especially when the rock mass or orebody is of poor quality or prone to rockburst due to high stress.In such cases,mining workers sho...Underhand cut-and-fill mining has been widely used in underground mining operations,especially when the rock mass or orebody is of poor quality or prone to rockburst due to high stress.In such cases,mining workers should carry out all production activities under the cemented backfill roof or sill mat instead of a highly fractured and unstable rock roof or a strong rock roof with a high potential of rockburst.Therefore,the stability and required strength of the sill mat are critical issues for mining engineers.In 1991,Mitchell considered that sill mat could fail by caving,sliding,rotation,and flexure.Mitchell also proposed an analytical solution to determine the minimum required strength of the sill mat for each type of failure based on two stiff or immobile rock walls.However,recent publications using numerical modeling and field measurements indicate that the compressive stresses in the sill mat induced by rock wall closure due to a stope excavation beneath the sill mat can be significant.It is thus highly necessary to investigate the required strength of the sill mat by considering rock wall closure.In this study,the crushing failure of sill mat due to rock wall closure generated by underground excavation and a new failure mode called"crushing and caving”is revealed by numerical modeling.An analytical solution corresponding to each failure mode is then developed to estimate the minimum required cohesion(cmin)of the sill mat.A criterion is also proposed to determine if the sill mat fails by crushing or crushing-and-caving failure.The proposed analytical solution does not involve any correction coefficients.The validity of the proposed analytical solution is demonstrated by numerical modeling.The proposed analytical solution can thus be employed to predict the cmin of sill mat subjected to wall closure generated by underlying stope excavation.展开更多
In the underhand cut-and-fill mining method,a sill mat(i.e.an artificial horizontal pillar)constructed by cemented backfill is essential to prevent mine workers from being directly exposed under problematic rock roofs...In the underhand cut-and-fill mining method,a sill mat(i.e.an artificial horizontal pillar)constructed by cemented backfill is essential to prevent mine workers from being directly exposed under problematic rock roofs.A critical issue is to determine the minimum required strength of the sill mat to ensure a safe and cost-effective design.Until now,Mitchell’s analytical solution is the only available option,considering two stiff and immobile rock walls.Unavoidable rock wall closure associated with stope excavation below the sill mat was neglected.This,along with other undefined parameters,explains why Mitchell’s solution is rarely used in sill mat design.A new analytical solution for determining the minimum required strength of the sill mat accounting for wall closure is necessary.In this study,a closed-form analytical solution for estimating rock wall closure generated by stope excavation below a sill mat is developed by using Salamon’s and Flamant’s models.The proposed analytical solution does not contain any coefficients of correction or calibration.Despite several assumptions(or somewhat of oversimplifications)necessary to render a simple analytical solution possible,good agreements are obtained between the rock wall closures predicted by applying the proposed analytical solution and those obtained numerically with FLAC3D for many cases with arbitrarily chosen geometrical and material parameters.The proposed analytical solution is therefore validated and can be used to evaluate the rock wall closure generated by stope excavation below a sill mat.展开更多
Progressive modifications in submarine topography and shorelines drastically affect tidal dynamics in bays.This study examines the influence of topographic slope,bay length,and driving forces on tidal currents followi...Progressive modifications in submarine topography and shorelines drastically affect tidal dynamics in bays.This study examines the influence of topographic slope,bay length,and driving forces on tidal currents following land reclamation.Tidal equa-tions are analytically solved using infinite series,deriving expressions for tidal levels and currents in narrow bays with varying topog-raphy.Tidal levels,influenced by topographic variations,are characterized by amplitude and phase lag of their complex amplitude.These levels demonstrate high sensitivity to longitudinal slope variations but remain relatively stable under lateral slope changes.Un-der constant topographic slopes,even minor changes in bay length can drastically modify amplitude and phase lag,highlighting the sensitivity of tidal dynamics to geometric alterations.Tidal velocity notably increases with steeper longitudinal slopes and modestly rises with elevated lateral slopes.However,changes in longitudinal and lateral slopes do not considerably alter flow patterns.While external forces predominantly regulate tidal velocity with negligible effects on flow patterns,endogenous resistance influences veloci-ty but minimally impacts flow structure.These findings enhance the understanding of tidal responses to geometric and topographic changes,providing valuable guidance for land reclamation projects and coastal management strategies.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
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 analyzing the complex interaction between the wellbore and the reservoir formation,the hydromechanical properties of the region proximal to the wellbore,referred to as the“wellbore skin zone”,play a pivotal role ...In analyzing the complex interaction between the wellbore and the reservoir formation,the hydromechanical properties of the region proximal to the wellbore,referred to as the“wellbore skin zone”,play a pivotal role in determining flow dynamics and the resulting formation deformation.Existing models of the wellbore skin zone generally assume a constant permeability throughout,resulting in a sharp permeability discontinuity at the skin-reservoir interface.This paper introduces a model for a wellbore with a continuously graded skin zone of finite thickness within a poroelastic medium.Analytical solutions are derived using the Laplace transform method,addressing both positive and negative skin zones.Numerical results are presented to illustrate the effects of graded permeability/skin zone thickness on pore pressures and stresses around a wellbore.The results highlight a distinct divergence in stress and pore pressure fields when comparing wellbores with negative skin zones to those with positive skin zones or no skin at all.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
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
The problem of shield tunnel uplift is a common issue in tunnel construction.Due to the decrease in shear stiffness at the joints between the rings,uplift is typically observed as bending and dislocation deformation a...The problem of shield tunnel uplift is a common issue in tunnel construction.Due to the decrease in shear stiffness at the joints between the rings,uplift is typically observed as bending and dislocation deformation at these joints.Existing modeling methods typically rely on the Euler-Bernoulli beam theory,only considering the bending effect while disregarding shear deformation.Furthermore,the constraints on the shield tail are often neglected in existing models.In this study,an improved theoretical model of tunnel floating is proposed.The constraint effect of the shield machine shell on the tunnel structure is considered using the structural forms of two finite long beams and one semi-infinite long beam.Furthermore,the Timoshenko beam theory is adopted,providing a more accurate description of tunnel deformation,including both the bending effect and shear deformation,than existing models.Meanwhile,the buoyancy force and stratum resistance are calculated in a nonlinear manner.A reliable method for calculating the shear stiffness correction factor is proposed to better determination of the calculation parameters.The proposed theoretical model is validated through five cases using sitemonitored data.Its applicability and effectiveness are demonstrated.Furthermore,the influences of soil type,buried depth,and buoyancy force on the three key indicators of tunnel floating(i.e.the maximum uplift magnitude,the ring position with the fastest uplift race,and the ring position with the maximum uplift magnitude)are analyzed.The results indicate that the proposed model can provide a better understanding of the floating characteristics of the tunnel structure during construction.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
This article describes the solution procedure of the fractional Pade-Ⅱ equation and generalized Zakharov equation(GSEs)using the sine-cosine method.Pade-Ⅱ is an important nonlinear wave equation modeling unidirectio...This article describes the solution procedure of the fractional Pade-Ⅱ equation and generalized Zakharov equation(GSEs)using the sine-cosine method.Pade-Ⅱ is an important nonlinear wave equation modeling unidirectional propagation of long-wave in dispersive media and GSEs are used to model the interaction between one-dimensional high,and low-frequency waves.Classes of trigonometric and hyperbolic function solutions in fractional calculus are discussed.Graphical simulations of the numerical solutions are flaunted by MATLAB.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
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
To find analytical solutions of nonlinear systems for locating the acoustic emission/microseismic（AE/MS） source without knowing the wave velocity of structures, the sensor location coordinates were simplified as a c...To find analytical solutions of nonlinear systems for locating the acoustic emission/microseismic（AE/MS） source without knowing the wave velocity of structures, the sensor location coordinates were simplified as a cuboid monitoring network. Different locations of sensors on upper and lower surfaces were considered and used to establish nonlinear equations. Based on the proposed functions of time difference of arrivals, the analytical solutions were obtained using five sensors under three networks. The proposed analytical solutions were validated using authentic data of numerical tests and experiments. The results show that located results are consistent with authentic data, and the outstanding characteristics of the new solution are that the solved process is not influenced by the wave velocity knowledge and iterated algorithms.展开更多
To find the analytical solution of the acoustic emission/microseismic(AE/MS) source location coordinates, the sensor location coordinates were optimized and simplified. A cube monitoring network of sensor location was...To find the analytical solution of the acoustic emission/microseismic(AE/MS) source location coordinates, the sensor location coordinates were optimized and simplified. A cube monitoring network of sensor location was selected, and the AE/MS source localization equations were established. A location method with P-wave velocity by analytical solutions (P-VAS) was obtained with these equations. The virtual location tests show that the relocation results of analytical method are fully consistent with the actual coordinates for events both inside and outside the monitoring network; whereas the location error of traditional time difference method is between 0.01 and 0.03 m for events inside the sensor array, and the location errors are larger, which is up to 1080986 m for events outside the sensor array. The broken pencil location tests were carried out in the cross section of 100 mm×98 mm, 350 mm-length granite rock specimen using five AE sensors. Five AE sources were relocated with the conventional method and the P-VAS method. For the four events outside monitoring network, the positioning accuracy by P-VAS method is higher than that by the traditional method, and the location accuracy of the larger one can be increased by 17.61 mm. The results of both virtual and broken pencil location tests show that the proposed analytical solution is effective to improve the positioning accuracy. It can locate the coordinates of AE/MS source only using simple four arithmetic operations, without determining the fitting initial value and iterative calculation, which can be solved by a conventional calculator or Microsoft Excel.展开更多
Using the variable transformation method,the formulae of the axial symmetrical wall temperature distribution during steady heat conduction of a hollow cylinder are derived in this paper.The wall temperature distributi...Using the variable transformation method,the formulae of the axial symmetrical wall temperature distribution during steady heat conduction of a hollow cylinder are derived in this paper.The wall temperature distribution and the wall heat flux distribution in both axial and radial direction can be calculated by the temperature distribution of the liquid medium both inside and outside the cylinder with temperature changing in axial direction.The calculation results are almost consistent with the experience results.The applicative condition of the formulae in this paper consists with most of practice.They can be applied to the engineering calculation of the steady heat conduction.The calculation is simple and accurate.展开更多
Unified analytical solutions are presented for the predictions of the stresses and displacements around a circular opening based on nonqinear unified failure criterion and the elastic-brittle-plastic softening model. ...Unified analytical solutions are presented for the predictions of the stresses and displacements around a circular opening based on nonqinear unified failure criterion and the elastic-brittle-plastic softening model. Unified analytical solutions not only involve generally traditional solutions which are based on the Hock-Brown （H-B） failure criterion or the non-linear twin-shear failure criterion, but also involve other new results. The results of the radius of plastic zone, radial displacements and stresses are obviously different using three rock masses when different values of the unified failure criterion parameter or different material behavior models are used. For a given condition, the radius of plastic zone and radial displacements are reduced by increasing the unified failure criterion parameter. The latent potentialities of rock mass result from considering the effect of intermediate principal stress. It is shown that proper choices of the failure criterion and the material behavior model for rock mass are significant in the tunnel design.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
The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordin...The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.展开更多
基金financial support from the Young Scientist Project of the National Key Research and Development Program of China(Grant No.2021YFC2900600)Beijing Nova Program(Grant No.20220484057)+1 种基金The authors acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada(Grant No.RGPIN-2018-06902)industrial partners of the Research Institute on Mines and the Environment(RIME UQAT-Polytechnique:https://irme.ca/en/).
文摘Underhand cut-and-fill mining has been widely used in underground mining operations,especially when the rock mass or orebody is of poor quality or prone to rockburst due to high stress.In such cases,mining workers should carry out all production activities under the cemented backfill roof or sill mat instead of a highly fractured and unstable rock roof or a strong rock roof with a high potential of rockburst.Therefore,the stability and required strength of the sill mat are critical issues for mining engineers.In 1991,Mitchell considered that sill mat could fail by caving,sliding,rotation,and flexure.Mitchell also proposed an analytical solution to determine the minimum required strength of the sill mat for each type of failure based on two stiff or immobile rock walls.However,recent publications using numerical modeling and field measurements indicate that the compressive stresses in the sill mat induced by rock wall closure due to a stope excavation beneath the sill mat can be significant.It is thus highly necessary to investigate the required strength of the sill mat by considering rock wall closure.In this study,the crushing failure of sill mat due to rock wall closure generated by underground excavation and a new failure mode called"crushing and caving”is revealed by numerical modeling.An analytical solution corresponding to each failure mode is then developed to estimate the minimum required cohesion(cmin)of the sill mat.A criterion is also proposed to determine if the sill mat fails by crushing or crushing-and-caving failure.The proposed analytical solution does not involve any correction coefficients.The validity of the proposed analytical solution is demonstrated by numerical modeling.The proposed analytical solution can thus be employed to predict the cmin of sill mat subjected to wall closure generated by underlying stope excavation.
基金financial support from the Young Scientist Project of the National Key Research and Development Program of China(Grant No.2021YFC2900600)the Beijing Nova Program(Grant No.20220484057)+1 种基金The authors acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada(Grant No.RGPIN-2018-06902)industrial partners of the Research Institute on Mines and the Environment(RIME UQAT-Polytechnique:https://irme.ca/en/).
文摘In the underhand cut-and-fill mining method,a sill mat(i.e.an artificial horizontal pillar)constructed by cemented backfill is essential to prevent mine workers from being directly exposed under problematic rock roofs.A critical issue is to determine the minimum required strength of the sill mat to ensure a safe and cost-effective design.Until now,Mitchell’s analytical solution is the only available option,considering two stiff and immobile rock walls.Unavoidable rock wall closure associated with stope excavation below the sill mat was neglected.This,along with other undefined parameters,explains why Mitchell’s solution is rarely used in sill mat design.A new analytical solution for determining the minimum required strength of the sill mat accounting for wall closure is necessary.In this study,a closed-form analytical solution for estimating rock wall closure generated by stope excavation below a sill mat is developed by using Salamon’s and Flamant’s models.The proposed analytical solution does not contain any coefficients of correction or calibration.Despite several assumptions(or somewhat of oversimplifications)necessary to render a simple analytical solution possible,good agreements are obtained between the rock wall closures predicted by applying the proposed analytical solution and those obtained numerically with FLAC3D for many cases with arbitrarily chosen geometrical and material parameters.The proposed analytical solution is therefore validated and can be used to evaluate the rock wall closure generated by stope excavation below a sill mat.
基金supported by the National Natural Sci-ence Foundation of China(No.U2106204)the Shanxi Water Conservancy Science and Technology Re-search and Extension Project(No.2023ZF19).
文摘Progressive modifications in submarine topography and shorelines drastically affect tidal dynamics in bays.This study examines the influence of topographic slope,bay length,and driving forces on tidal currents following land reclamation.Tidal equa-tions are analytically solved using infinite series,deriving expressions for tidal levels and currents in narrow bays with varying topog-raphy.Tidal levels,influenced by topographic variations,are characterized by amplitude and phase lag of their complex amplitude.These levels demonstrate high sensitivity to longitudinal slope variations but remain relatively stable under lateral slope changes.Un-der constant topographic slopes,even minor changes in bay length can drastically modify amplitude and phase lag,highlighting the sensitivity of tidal dynamics to geometric alterations.Tidal velocity notably increases with steeper longitudinal slopes and modestly rises with elevated lateral slopes.However,changes in longitudinal and lateral slopes do not considerably alter flow patterns.While external forces predominantly regulate tidal velocity with negligible effects on flow patterns,endogenous resistance influences veloci-ty but minimally impacts flow structure.These findings enhance the understanding of tidal responses to geometric and topographic changes,providing valuable guidance for land reclamation projects and coastal management strategies.
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the financial support from Shaanxi Key Research and Development Program under Grant No.2023-YBGY-058the Fundamental Research Funds for the Central Universities under Grant No.G2020KY05312.
文摘In analyzing the complex interaction between the wellbore and the reservoir formation,the hydromechanical properties of the region proximal to the wellbore,referred to as the“wellbore skin zone”,play a pivotal role in determining flow dynamics and the resulting formation deformation.Existing models of the wellbore skin zone generally assume a constant permeability throughout,resulting in a sharp permeability discontinuity at the skin-reservoir interface.This paper introduces a model for a wellbore with a continuously graded skin zone of finite thickness within a poroelastic medium.Analytical solutions are derived using the Laplace transform method,addressing both positive and negative skin zones.Numerical results are presented to illustrate the effects of graded permeability/skin zone thickness on pore pressures and stresses around a wellbore.The results highlight a distinct divergence in stress and pore pressure fields when comparing wellbores with negative skin zones to those with positive skin zones or no skin at all.
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.
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.
基金the National Natural Science Foundation of China (Grant Nos.52379111,51979270 and 52208380).
文摘The problem of shield tunnel uplift is a common issue in tunnel construction.Due to the decrease in shear stiffness at the joints between the rings,uplift is typically observed as bending and dislocation deformation at these joints.Existing modeling methods typically rely on the Euler-Bernoulli beam theory,only considering the bending effect while disregarding shear deformation.Furthermore,the constraints on the shield tail are often neglected in existing models.In this study,an improved theoretical model of tunnel floating is proposed.The constraint effect of the shield machine shell on the tunnel structure is considered using the structural forms of two finite long beams and one semi-infinite long beam.Furthermore,the Timoshenko beam theory is adopted,providing a more accurate description of tunnel deformation,including both the bending effect and shear deformation,than existing models.Meanwhile,the buoyancy force and stratum resistance are calculated in a nonlinear manner.A reliable method for calculating the shear stiffness correction factor is proposed to better determination of the calculation parameters.The proposed theoretical model is validated through five cases using sitemonitored data.Its applicability and effectiveness are demonstrated.Furthermore,the influences of soil type,buried depth,and buoyancy force on the three key indicators of tunnel floating(i.e.the maximum uplift magnitude,the ring position with the fastest uplift race,and the ring position with the maximum uplift magnitude)are analyzed.The results indicate that the proposed model can provide a better understanding of the floating characteristics of the tunnel structure during construction.
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.
文摘This article describes the solution procedure of the fractional Pade-Ⅱ equation and generalized Zakharov equation(GSEs)using the sine-cosine method.Pade-Ⅱ is an important nonlinear wave equation modeling unidirectional propagation of long-wave in dispersive media and GSEs are used to model the interaction between one-dimensional high,and low-frequency waves.Classes of trigonometric and hyperbolic function solutions in fractional calculus are discussed.Graphical simulations of the numerical solutions are flaunted by MATLAB.
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.
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Projects(11447242,41272304,51209236,51274254)supported by the National Natural Science Foundation of ChinaProject(2015CB060200)supported by the National Basic Research Program of China
文摘To find analytical solutions of nonlinear systems for locating the acoustic emission/microseismic（AE/MS） source without knowing the wave velocity of structures, the sensor location coordinates were simplified as a cuboid monitoring network. Different locations of sensors on upper and lower surfaces were considered and used to establish nonlinear equations. Based on the proposed functions of time difference of arrivals, the analytical solutions were obtained using five sensors under three networks. The proposed analytical solutions were validated using authentic data of numerical tests and experiments. The results show that located results are consistent with authentic data, and the outstanding characteristics of the new solution are that the solved process is not influenced by the wave velocity knowledge and iterated algorithms.
基金Project (10872218) supported by the National Natural Science Foundation of ChinaProject (2010CB732004) supported by the National Basic Research Program of China+1 种基金Project (kjdb2010-6) supported by Doctoral Candidate Innovation Research Support Program of Science & Technology ReviewProject (201105) supported by Scholarship Award for Excellent Doctoral Student of Ministry of Education of China
文摘To find the analytical solution of the acoustic emission/microseismic(AE/MS) source location coordinates, the sensor location coordinates were optimized and simplified. A cube monitoring network of sensor location was selected, and the AE/MS source localization equations were established. A location method with P-wave velocity by analytical solutions (P-VAS) was obtained with these equations. The virtual location tests show that the relocation results of analytical method are fully consistent with the actual coordinates for events both inside and outside the monitoring network; whereas the location error of traditional time difference method is between 0.01 and 0.03 m for events inside the sensor array, and the location errors are larger, which is up to 1080986 m for events outside the sensor array. The broken pencil location tests were carried out in the cross section of 100 mm×98 mm, 350 mm-length granite rock specimen using five AE sensors. Five AE sources were relocated with the conventional method and the P-VAS method. For the four events outside monitoring network, the positioning accuracy by P-VAS method is higher than that by the traditional method, and the location accuracy of the larger one can be increased by 17.61 mm. The results of both virtual and broken pencil location tests show that the proposed analytical solution is effective to improve the positioning accuracy. It can locate the coordinates of AE/MS source only using simple four arithmetic operations, without determining the fitting initial value and iterative calculation, which can be solved by a conventional calculator or Microsoft Excel.
文摘Using the variable transformation method,the formulae of the axial symmetrical wall temperature distribution during steady heat conduction of a hollow cylinder are derived in this paper.The wall temperature distribution and the wall heat flux distribution in both axial and radial direction can be calculated by the temperature distribution of the liquid medium both inside and outside the cylinder with temperature changing in axial direction.The calculation results are almost consistent with the experience results.The applicative condition of the formulae in this paper consists with most of practice.They can be applied to the engineering calculation of the steady heat conduction.The calculation is simple and accurate.
基金Project (No.SJ08E204) supported by the Natural Science Foundation of Shanxi Province,China
文摘Unified analytical solutions are presented for the predictions of the stresses and displacements around a circular opening based on nonqinear unified failure criterion and the elastic-brittle-plastic softening model. Unified analytical solutions not only involve generally traditional solutions which are based on the Hock-Brown （H-B） failure criterion or the non-linear twin-shear failure criterion, but also involve other new results. The results of the radius of plastic zone, radial displacements and stresses are obviously different using three rock masses when different values of the unified failure criterion parameter or different material behavior models are used. For a given condition, the radius of plastic zone and radial displacements are reduced by increasing the unified failure criterion parameter. The latent potentialities of rock mass result from considering the effect of intermediate principal stress. It is shown that proper choices of the failure criterion and the material behavior model for rock mass are significant in the tunnel design.
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Project supported by the National Natural Science Foundation of China (Nos. 10472102 and 1043203)the Foundation of Ningbo University (No. 2005014), China
文摘The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.
