The stress gradient of surrounding rock and reasonable prestress of support are the keys to ensuring the stability of roadways.The elastic-plastic analytical solution for surrounding rock was derived based on unified ...The stress gradient of surrounding rock and reasonable prestress of support are the keys to ensuring the stability of roadways.The elastic-plastic analytical solution for surrounding rock was derived based on unified strength theory.A model for solving the stress gradient of the surrounding rock with the intermediate principal stress parameter b was established.The correctness and applicability of the solution for the stress gradient in the roadway surrounding rock was verified via multiple methods.Furthermore,the laws of stress,displacement,and the plastic zone of the surrounding rock with different b values and prestresses were revealed.As b increases,the stress gradient in the plastic zone increases,and the displacement and plastic zone radius decrease.As the prestress increases,the peak stress shifts toward the sidewalls,and the stress and stress gradient increments decrease.In addition,the displacement increment and plastic zone increment were proposed to characterize the support effect.The balance point of the plastic zone area appears before that of the displacement zone.The relationship between the stress gradient compensation coefficient and the prestress is obtained.This study provides a research method and idea for determining the reasonable prestress of support in roadways.展开更多
Waterproof performance of gaskets between segments is the focus of shield tunnels.This paper proposed an analytical method for determining seepage characteristics at tunnel-gasketed joints based on the hydraulic fract...Waterproof performance of gaskets between segments is the focus of shield tunnels.This paper proposed an analytical method for determining seepage characteristics at tunnel-gasketed joints based on the hydraulic fracturing theories.First,the mathematical model was established,and the seepage governing equation and boundary conditions were obtained.Second,three dimensionless parameters were introduced for simplifying the expressions,and the seepage governing equations were normalized.Third,analytical expressions were derived for the interface opening and liquid pressure.Moreover,the influencing factors of seepage process at the gasketed interface were analyzed.Parametric analyses revealed that,in the normalized criterion of liquid viscosity,the liquid tip coordinate was influenced by the degree of negative pressure in the liquid lag region,which was related to the initial contact stress.The coordinate of the liquid tip affected the liquid pressure distribution and the interface opening,which were analyzed under different liquid tip coordinate conditions.Finally,under two limit states,comparative analysis showed that the results of the variation trend of the proposed method agree well with those of previous research.Overall,the proposed analytical method provides a novel solution for the design of the waterproof in shield tunnels.展开更多
For the longitudinal midcourse guidance problem of a cruise-glide integrated hypersonic vehicle(CGHV),an analytical method based on optimal control theory is proposed.This method constructs a guidance dynamics model f...For the longitudinal midcourse guidance problem of a cruise-glide integrated hypersonic vehicle(CGHV),an analytical method based on optimal control theory is proposed.This method constructs a guidance dynamics model for such vehicles,using aerodynamic load as the control variable,and introduces a framework for solving the guidance laws.This framework unifies the design process of guidance laws for both the glide and cruise phases.By decomposing the longitudinal guidance task into position control and velocity control,and minimizing energy consumption as the objective function,the method provides an analytical solution for velocity control load through the calculation of costate variables.This approach requires only the current state and terminal state parameters to determine the guidance law solution.Furthermore,by transforming path constraints into aerodynamic load constraints and solving backwards to obtain the angle of attack,bank angle,and throttle setting,this method ensures a smooth transition from the glide phase to the cruise phase,guaranteeing the successful completion of the guidance task.Finally,the effectiveness and practicality of the proposed method are validated through case simulations and analysis.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 stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common...The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common cases.Stress analytical method for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and uniform radial pressure on the inner surface is given.The power series method of complex function is used.The stress analytical solution is obtained with the assumption that two layers of a cylinder are fully contacted.The distributions of normal and tangential contact stress along the interface,tangential stress on the inner boundary and stresses in the radial direction at θ=0°,45° and 90°,are obtained.An example indicates that,when the elastic modulus of the inner layer of a double-layered thick-walled cylinder is smaller than that of the outer layer,the tangential stress is smaller than that in the corresponding point for a traditional cylinder composed of homogeneous materials.In that way,stress concentration at the inner surface can be alleviated and the stress distribution is more uniform.This is a capable way to enhance the elastic ultimate bearing capacity of thick-walled cylinder.展开更多
An analytical solution was presented to the unsaturated soil with a finite thickness under confinement in the lateral direction and sinusoidal cyclic loading in the vertical direction based on Fredlund's one-dimen...An analytical solution was presented to the unsaturated soil with a finite thickness under confinement in the lateral direction and sinusoidal cyclic loading in the vertical direction based on Fredlund's one-dimensional consolidation equation for unsaturated soil. The transfer relationship between the state vectors at the top surface and any depth was gained by applying the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy's law and Fick's law. The excess pore-air and pore-water pressures and settlement in the Laplace-transformed domain were obtained by using the Laplace transform with the initial and boundary conditions. The analytical solutions of the excess pore-air and pore-water pressures at any depth and settlement were obtained in the time domain by performing the inverse Laplace transforms. A typical example illustrates the consolidation characteristics of unsaturated soil under sinusoidal loading from analytical results. Finally, comparisons between the analytical solutions and results of the numerical method indicate that the analytical solution is correct.展开更多
An exact solution for simply-supported laminated beams with material properties variable with temperature under a combination of uniform thermo-load and mechanical loads was investigated,based on the two-dimensional(2...An exact solution for simply-supported laminated beams with material properties variable with temperature under a combination of uniform thermo-load and mechanical loads was investigated,based on the two-dimensional(2-D)thermo-elasticity theory.Firstly,the beam was divided into a series of layers with uniform material properties along the interfaces of the beam.The uniform thermo-load acted on each layer was transformed into a combination of the normal surface forces acted at the two ends and the transverse thermo-load.Secondly,the state space method was employed to obtain the general solutions of displacements and stresses in an arbitrary layer.Thirdly,based on the interfacial continuity conditions between adjacent layers,the relations of displacement and stress components between the top and bottom layers of the beam were recursively derived by use of the transfer-matrix method.The unknowns in the solutions can be solved by the mechanical loads acted on the top and bottom surfaces.The convergence of the present solutions was checked.The comparative study of the present solutions with the Timoshenko’s solutions and the finite element(FE)solutions was carried out.The effects of material properties variable with temperature on the thermo-elastic behavior of laminated beams were discussed in detail.展开更多
The present study deals with analytical investigation of temperature of a single burning iron particle.Three mathematical methods including AGM(Akbari-Ganji’s method),CM(Collocation method)and GM(Galerkin Method)are ...The present study deals with analytical investigation of temperature of a single burning iron particle.Three mathematical methods including AGM(Akbari-Ganji’s method),CM(Collocation method)and GM(Galerkin Method)are applied to solving non-linear differential governing equation and effectiveness of these methods is examined as well.For further investigation,forth order Runge-Kutta approach,a numerical method,is used to validate the obtained analytical results.In the present study,the developed mathematical model takes into account the effects of thermal radiation,convective heat transfer and particle density variations during combustion process.Due to particles’small size and high thermal conductivity,the system is assumed to be lumped in which the particle temperature does not change within the body and all of its regions are at the same temperature.The temperature distributions obtained by analytical methods have satisfactory agreement with numerical outputs.Finally,the results indicate that AGM is a more appropriate method than GM and CM due to its lower mean relative error and less run time.展开更多
This paper proposes a time-varying sliding mode control method to address nonlinear missile body kinematics based on the suboptimal control theory.The analytical solution of suboptimal time-varying sliding surface and...This paper proposes a time-varying sliding mode control method to address nonlinear missile body kinematics based on the suboptimal control theory.The analytical solution of suboptimal time-varying sliding surface and the corresponding suboptimal control law are obtained by solving the state-dependent Riccati equation analytically.Then,the Lyapunov method is used to analyze the motion trend in sliding surface and the asymptotic stability of the closed-loop system is validated.The suboptimal control law is transformed to the form of pseudo-angle-of-attack feedback.The simulation results indicate that the satisfactory performance can be obtained and the control law can overcome the influence of parameter errors.展开更多
Shield tunneling inevitably passes through a large number of pile foundations in urban areas.Thus,an accurate assessment of tunneling-induced pile displacement and potential damage becomes a critical part of shield co...Shield tunneling inevitably passes through a large number of pile foundations in urban areas.Thus,an accurate assessment of tunneling-induced pile displacement and potential damage becomes a critical part of shield construction.This study presents a mechanism research of pile-soil-tunnel interaction through Pasternak-based two-stage analysis method.In the first stage,based on Mindlin’s solution,the soil displacement fields induced by shield thrust force,cutterhead frictions,shield shell frictions and grouting pressure are derived.The analytical solution of threedimensional soil displacement field is established by introducing Pinto’s three-dimensional volume loss formula,which solves the problems that shield construction factors are not taken into account in Loganathan’s formula and only twodimensional soil displacement field can be obtained.In the second stage,based on Pasternak’s two-parameter foundation model,the analytical solution of pile displacement induced by shield tunneling in layered soil is derived.A case was found in the project of interval tunnels from Wanjiali Square to Furong District Government of Changsha Metro Line 5,where the shield tunnels were constructed near viaduct piles.The reliability of the analytical solution proposed in this study is verified by comparing with the field measured data and the results of finite element method(FEM).In addition,the comparisons of longitudinal,horizontal and vertical displacements of soil and pile foundation analyzed by the analytical solution and FEM provide corresponding theoretical basis,which has significant engineering guidance for similar projects.展开更多
The main objective of this work is to investigate analytically the steady nanofluid flow and heat transfer characteristics between nonparallel plane walls. Using appropriate transformations for the velocity and temper...The main objective of this work is to investigate analytically the steady nanofluid flow and heat transfer characteristics between nonparallel plane walls. Using appropriate transformations for the velocity and temperature, the basic nonlinear partial differential equations are reduced to the ordinary differential equations. Then, these equations have been solved analytically and numerically for some values of the governing parameters, Reynolds number, Re, channel half angle, α, Prandtl number, Pr, and Eckert number, Ec, using Adomian decomposition method and the Runge-Kutta method with mathematic package. Analytical and numerical results are searched for the skin friction coefficient, Nusselt number and the velocity and temperature profiles. It is found on one hand that the Nusselt number increases as Eckert number or channel half-angle increases, but it decreases as Reynolds number increases. On the other hand, it is also found that the presence of Cu nanoparticles in a water base fluid enhances heat transfer between nonparallel plane walls and in consequence the Nusselt number increases with the increase of nanoparticles volume fraction. Finally, an excellent agreement between analytical results and those obtained by numerical Runge-Kutta method is highly noticed.展开更多
Corrugated steel web is folded along the longitudinal direction and has the mechanical properties such as axial compression stiffness corrugation effect, shear modulus corrugation effect, similar to that of an accordi...Corrugated steel web is folded along the longitudinal direction and has the mechanical properties such as axial compression stiffness corrugation effect, shear modulus corrugation effect, similar to that of an accordion. In order to study the lateral-torsional buckling of box beams with corrugated steel webs (BBCSW) under the action of bending moment load, the neutral equilibrium equation of BBCSW under the action of bending moment load is derived through the stationary value theory of total potential energy and further, along with taking Kollbrunner-Hajdin correction method and the mechanical properties of the corrugated web into consideration. The analytical calculation formula of lateral-torsional buckling critical bending moment of BBCSW is then obtained. The lateral-torsional buckling critical bending moment of 96 BBCSW test specimens with different geometry dimensions are then calculated using both the analytical calculation method and ANSYS finite element method. The results show that the analytical calculation results agree well with the numerical calculation results using ANSYS, thus proving the accuracy of the analytical calculation method and model simplification hypothesis proposed in this paper. Also, compared with the box beams with flat steel webs (BBFSW) with the same geometry dimensions as BBCSW, within the common range of web space-depth ratio and web span-depth ratio, BBCSW’s lateral-torsional buckling critical bending moment is larger than that of BBFSW. Moreover, the advantages of BBCSW’s stability are even more significant with the increase of web space-depth ratio and web depth-thickness ratio.展开更多
In order to avoid the curing effects of paraffin on the transport process and reduce the transport difficulty,usually high temperature and high pressure are used in the transportation of oil and gas.The differences of...In order to avoid the curing effects of paraffin on the transport process and reduce the transport difficulty,usually high temperature and high pressure are used in the transportation of oil and gas.The differences of temperature and pressure cause additional stress along the pipeline,due to the constraint of the foundation soil,the additional stress can not release freely,when the additional stress is large enough to motivate the submarine pipelines buckle.In this work,the energy method is introduced to deduce the analytical solution which is suitable for the global buckling modes of idealized subsea pipeline and analyze the relationship between the critical buckling temperature,buckling length and amplitude under different high-order global lateral buckling modes.To obtain a consistent formulation of the problem,the principles of virtual displacements and the variation calculus for variable matching points are applied.The finite element method based on elasto-plastic theory is used to simulate the lateral global buckling of the pipelines under high temperature and pressure.The factors influencing the lateral buckling of pipelines are further studied.Based upon some actual engineering projects,the finite element results are compared with the analytical ones,and then the influence of thermal stress,the section rigidity of pipeline,the soil properties and the trigging force to the high order lateral buckling are discussed.The method of applying the small trigging force on pipeline is reliable in global buckling numerical analysis.In practice,increasing the section rigidity of a pipeline is an effective measure to improve the ability to resist the global buckling.展开更多
Buckling of submarine pipelines under thermal stress is one of the most important problems to be considered in pipeline design. And pipeline with initial imperfections will easily undergo failure due to global bucklin...Buckling of submarine pipelines under thermal stress is one of the most important problems to be considered in pipeline design. And pipeline with initial imperfections will easily undergo failure due to global buckling under thermal stress and internal pressure. Therefore, it is vitally important to study the global buckling of the submarine pipeline with initial imperfections. On the basis of the characteristics of the initial imperfections, the global lateral buckling of submarine pipelines was analyzed. Based on the deduced analytical solutions for the global lateral buckling, effects of temperature difference and properties of foundation soil on pipeline buckling were analyzed. The results show that the snap buckling is predominantly governed by the amplitude value of initial imperfection; the triggering temperature difference of Mode I for pipelines with initial imperfections is higher than that of Mode I1; a pipeline with a larger friction coefficient is safer than that with a smaller one; pipelines with larger initial imperfections are safer than those with smaller ones.展开更多
A simplified method is presented for predicting consolidation settlement of soft ground improved by floating soil-cement column on the basis of double soil-layer consolidation theory. Combining the axisymmetric consol...A simplified method is presented for predicting consolidation settlement of soft ground improved by floating soil-cement column on the basis of double soil-layer consolidation theory. Combining the axisymmetric consolidation model and equal strain assumption, the governing equation was derived for the consolidation of clayey subsoil reinforced by soil-cement column. By modifying the boundary condition of the interface between the improved layer and underlying layer on seepage and pore-water pressure, the analytical solution of consolidation of soft ground improved by floating soil-cement column was developed under depth-dependent ramp load. The results of the parameter analysis of consolidation behavior show that the consolidation rate is closely related with the depth replacement ratio by the column and the permeability of upper layer. The influence of column-soil constrained modulus ratio and radius ratio of the influence zone to the column on consolidation is also affected by depth replacement ratio. The column-soil total stress ratio increases with time and approaches the final value accompanied with the dissipation of excess pore water pressure.展开更多
A new analytical study on stresses around a post-tensioned anchor in rocks with two perpendicular joint sets is presented. The assumptions of orthotropic elastic rock with plane strain conditions are made in derivatio...A new analytical study on stresses around a post-tensioned anchor in rocks with two perpendicular joint sets is presented. The assumptions of orthotropic elastic rock with plane strain conditions are made in derivation of the formulations. A tri-linear bond-slip constitutive law is used for modeling the tendon-grout interface behavior and debonding of this interface. The bearing plate width is also considered in the analysis. The obtained solutions are in the integral forms and numerical techniques that have been used for evaluation. In the illustrative example given, the major principal stress is compressive in the anchor free zone and compressive stress concentrations of 815 k Pa and 727 k Pa(for the anchor load of 300 k N) are observed under the bearing plate and the bond length proximal end, respectively. However, large values of tensile stresses with the maximum of-434 k Pa are formed at the bond length distal end. The results obtained using the proposed solution are compared very those of numerical method(FEM).展开更多
随着市场竞争愈发激烈、全球环境日益恶化以及公众环保意识的提高,绿色采购问题受到了广泛关注。现有研究绝大多数聚焦于考虑绿色准则的供应商选择问题,以实现可持续经营。然而,在综合考虑时间、价格和成本等因素的前提下,从适应性强的...随着市场竞争愈发激烈、全球环境日益恶化以及公众环保意识的提高,绿色采购问题受到了广泛关注。现有研究绝大多数聚焦于考虑绿色准则的供应商选择问题,以实现可持续经营。然而,在综合考虑时间、价格和成本等因素的前提下,从适应性强的供应商处获得适当的产品,对于企业来说更为可行和经济,即供应商选择和订单分配。为了解决上述关键问题,提出了一种模糊环境下的多准则群体决策方法。提出了一种基于理想解相似性偏好排序和层次分析法(technique for order of preference by similarity to ideal solution and analytic hierarchy process,TOPSIS-AHP)的模糊排序方法,该方法可根据企业战略灵活调整传统准则和绿色准则的权重。在双目标优化模型中引入供应商排名进行订货,在实现采购绩效最大化的同时,最大限度地降低采购成本。结果表明:所提方法能够有效评价供应商绩效,并优化候选供应商之间的订单分配。展开更多
In this study,the effect of influencing parameters on the stress distribution around a polygonal cutout within a laminated composite under uniform heat flux was analytically examined.The analytical method was develope...In this study,the effect of influencing parameters on the stress distribution around a polygonal cutout within a laminated composite under uniform heat flux was analytically examined.The analytical method was developed based on the classical laminated plate theory and two-dimensional thermo-elastic method.A mapping function was employed to extend the solution of a perforated symmetric laminate with a circular cutout to the solution of polygonal cutouts.The effect of significant parameters such as the cutout angular position,bluntness and aspect ratio,the heat flux angle and the laminate stacking sequence in symmetric composite laminate containing triangular,square and pentagonal cutouts was studied.The Neumann boundary condition was used at the edges of the thermally insulated polygonal cutout.The laminate was made of graphite/epoxy(AS/3501) material with two different stacking sequences of [30/45]sand[30/0/-30]_(s).The analytical solutions were well validated against finite element results.展开更多
Failure of pipe networks due to blast loads resulting from terrorist attacks or construction facilities, may cause economic loss, environmental pollution, source of firing or even it may lead to a disaster. The presen...Failure of pipe networks due to blast loads resulting from terrorist attacks or construction facilities, may cause economic loss, environmental pollution, source of firing or even it may lead to a disaster. The present work develops a closed-form solution of buried pipe with barrier system subjected to subsurface detonation. The solution is derived based on the concept of double-beam system. Euler Bernoulli's beams are used to simulate the buried pipe and the barrier system. Soil is idealized as viscoelastic foundation along with shear interaction between discrete Winkler springs(advanced soil model). The finite SineFourier transform is employed to solve the coupled partial differential equations. The solution is validated with past studies. A parametric study is conducted to investigate the influence of TNT charge weight, pipe material, damping ratio and TNT offset on the response of buried pipe with and without barrier system. Further a statistical analysis is carried out to get the significant soil and pipe input parameters. It is perceived that peak pipe displacements for both the cases(with and without barrier) are increases with increasing the weight of TNT charge and decreases with increasing the damping ratio and TNT offset. The deformation of pipe also varies with pipe material. Pipe safety against blast loads can be ensured by providing suitable barrier layer. The present study can be utilized in preliminary design stage as an alternative to expensive numerical analysis or field study.展开更多
In order to build the model of the drum level wave action and sloshing, based on the method of modularization modeling, the hydrodynamic model of drum level wave action and sloshing was developed, and dynamic simulati...In order to build the model of the drum level wave action and sloshing, based on the method of modularization modeling, the hydrodynamic model of drum level wave action and sloshing was developed, and dynamic simulation researches were carried out based on the model. The results indicate that both drum level and drum length have functional relations with period of drum level wave action and sloshing. When the drum level decreases or drum length increases, the period of drum level wave action and sloshing increases, density of liquid and number of sub-module division have little influence on the period of drum level wave action and sloshing. The model was validated by the analytical solution theory of liquid’s wave action and sloshing in cuboid container, and the 3D graphics of drum level wave action and sloshing was also obtained. The model can dynamically reflect the rules of wave action and sloshing of water in the container exactly.展开更多
基金Project(52274130)supported by the National Natural Science Foundation of ChinaProject(ZR2024ZD22)supported by the Major Basic Research Project of the Shandong Provincial Natural Science Foundation,China+2 种基金Project(2023375)supported by the Guizhou University Research and Innovation Team,ChinaProject(Leading Fund(2023)09)supported by the Natural Science Research Fund of Guizhou University,ChinaProject(JYBSYS2021101)supported by the Open Fund of Key Laboratory of Safe and Effective Coal Mining,Ministry of Education,China。
文摘The stress gradient of surrounding rock and reasonable prestress of support are the keys to ensuring the stability of roadways.The elastic-plastic analytical solution for surrounding rock was derived based on unified strength theory.A model for solving the stress gradient of the surrounding rock with the intermediate principal stress parameter b was established.The correctness and applicability of the solution for the stress gradient in the roadway surrounding rock was verified via multiple methods.Furthermore,the laws of stress,displacement,and the plastic zone of the surrounding rock with different b values and prestresses were revealed.As b increases,the stress gradient in the plastic zone increases,and the displacement and plastic zone radius decrease.As the prestress increases,the peak stress shifts toward the sidewalls,and the stress and stress gradient increments decrease.In addition,the displacement increment and plastic zone increment were proposed to characterize the support effect.The balance point of the plastic zone area appears before that of the displacement zone.The relationship between the stress gradient compensation coefficient and the prestress is obtained.This study provides a research method and idea for determining the reasonable prestress of support in roadways.
基金Project(52278421)supported by the National Natural Science Foundation of ChinaProject(2024ZZTS0754)supported by the Fundamental Research Funds for the Central Universities of Central South University,China+2 种基金Project(2023CXQD067)supported by the Central South University Innovation-Driven Research Programme,ChinaProject(2022QNRC001)supported by Young Elite Scientists Sponsorship Program by CASTProject(2023TJ-N24)supported by the Youth Talent Program by China Railway Society and the Hunan Provincial Science and Technology Promotion Talent Project。
文摘Waterproof performance of gaskets between segments is the focus of shield tunnels.This paper proposed an analytical method for determining seepage characteristics at tunnel-gasketed joints based on the hydraulic fracturing theories.First,the mathematical model was established,and the seepage governing equation and boundary conditions were obtained.Second,three dimensionless parameters were introduced for simplifying the expressions,and the seepage governing equations were normalized.Third,analytical expressions were derived for the interface opening and liquid pressure.Moreover,the influencing factors of seepage process at the gasketed interface were analyzed.Parametric analyses revealed that,in the normalized criterion of liquid viscosity,the liquid tip coordinate was influenced by the degree of negative pressure in the liquid lag region,which was related to the initial contact stress.The coordinate of the liquid tip affected the liquid pressure distribution and the interface opening,which were analyzed under different liquid tip coordinate conditions.Finally,under two limit states,comparative analysis showed that the results of the variation trend of the proposed method agree well with those of previous research.Overall,the proposed analytical method provides a novel solution for the design of the waterproof in shield tunnels.
基金supported by the National Natural Science Foundation of China(Grant Nos.62473374,62403487 and U2441243).
文摘For the longitudinal midcourse guidance problem of a cruise-glide integrated hypersonic vehicle(CGHV),an analytical method based on optimal control theory is proposed.This method constructs a guidance dynamics model for such vehicles,using aerodynamic load as the control variable,and introduces a framework for solving the guidance laws.This framework unifies the design process of guidance laws for both the glide and cruise phases.By decomposing the longitudinal guidance task into position control and velocity control,and minimizing energy consumption as the objective function,the method provides an analytical solution for velocity control load through the calculation of costate variables.This approach requires only the current state and terminal state parameters to determine the guidance law solution.Furthermore,by transforming path constraints into aerodynamic load constraints and solving backwards to obtain the angle of attack,bank angle,and throttle setting,this method ensures a smooth transition from the glide phase to the cruise phase,guaranteeing the successful completion of the guidance task.Finally,the effectiveness and practicality of the proposed method are validated through case simulations and analysis.
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Projects(50874047,51074014,51174014)supported by the National Natural Science Foundation of China
文摘The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common cases.Stress analytical method for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and uniform radial pressure on the inner surface is given.The power series method of complex function is used.The stress analytical solution is obtained with the assumption that two layers of a cylinder are fully contacted.The distributions of normal and tangential contact stress along the interface,tangential stress on the inner boundary and stresses in the radial direction at θ=0°,45° and 90°,are obtained.An example indicates that,when the elastic modulus of the inner layer of a double-layered thick-walled cylinder is smaller than that of the outer layer,the tangential stress is smaller than that in the corresponding point for a traditional cylinder composed of homogeneous materials.In that way,stress concentration at the inner surface can be alleviated and the stress distribution is more uniform.This is a capable way to enhance the elastic ultimate bearing capacity of thick-walled cylinder.
基金Project(2010G016-B)supported by Science and Technology Research and Development of China
文摘An analytical solution was presented to the unsaturated soil with a finite thickness under confinement in the lateral direction and sinusoidal cyclic loading in the vertical direction based on Fredlund's one-dimensional consolidation equation for unsaturated soil. The transfer relationship between the state vectors at the top surface and any depth was gained by applying the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy's law and Fick's law. The excess pore-air and pore-water pressures and settlement in the Laplace-transformed domain were obtained by using the Laplace transform with the initial and boundary conditions. The analytical solutions of the excess pore-air and pore-water pressures at any depth and settlement were obtained in the time domain by performing the inverse Laplace transforms. A typical example illustrates the consolidation characteristics of unsaturated soil under sinusoidal loading from analytical results. Finally, comparisons between the analytical solutions and results of the numerical method indicate that the analytical solution is correct.
基金Project(2012CB026205)supported by the National Basic Research Program of ChinaProjects(51608264,51778289)supported by the National Natural Science Foundation of ChinaProject(2014Y01)supported by the Transportation Science and Technology Project of Jiangsu Province,China
文摘An exact solution for simply-supported laminated beams with material properties variable with temperature under a combination of uniform thermo-load and mechanical loads was investigated,based on the two-dimensional(2-D)thermo-elasticity theory.Firstly,the beam was divided into a series of layers with uniform material properties along the interfaces of the beam.The uniform thermo-load acted on each layer was transformed into a combination of the normal surface forces acted at the two ends and the transverse thermo-load.Secondly,the state space method was employed to obtain the general solutions of displacements and stresses in an arbitrary layer.Thirdly,based on the interfacial continuity conditions between adjacent layers,the relations of displacement and stress components between the top and bottom layers of the beam were recursively derived by use of the transfer-matrix method.The unknowns in the solutions can be solved by the mechanical loads acted on the top and bottom surfaces.The convergence of the present solutions was checked.The comparative study of the present solutions with the Timoshenko’s solutions and the finite element(FE)solutions was carried out.The effects of material properties variable with temperature on the thermo-elastic behavior of laminated beams were discussed in detail.
文摘The present study deals with analytical investigation of temperature of a single burning iron particle.Three mathematical methods including AGM(Akbari-Ganji’s method),CM(Collocation method)and GM(Galerkin Method)are applied to solving non-linear differential governing equation and effectiveness of these methods is examined as well.For further investigation,forth order Runge-Kutta approach,a numerical method,is used to validate the obtained analytical results.In the present study,the developed mathematical model takes into account the effects of thermal radiation,convective heat transfer and particle density variations during combustion process.Due to particles’small size and high thermal conductivity,the system is assumed to be lumped in which the particle temperature does not change within the body and all of its regions are at the same temperature.The temperature distributions obtained by analytical methods have satisfactory agreement with numerical outputs.Finally,the results indicate that AGM is a more appropriate method than GM and CM due to its lower mean relative error and less run time.
基金supported by the China Postdoctoral Science Foundation(2017M620863).
文摘This paper proposes a time-varying sliding mode control method to address nonlinear missile body kinematics based on the suboptimal control theory.The analytical solution of suboptimal time-varying sliding surface and the corresponding suboptimal control law are obtained by solving the state-dependent Riccati equation analytically.Then,the Lyapunov method is used to analyze the motion trend in sliding surface and the asymptotic stability of the closed-loop system is validated.The suboptimal control law is transformed to the form of pseudo-angle-of-attack feedback.The simulation results indicate that the satisfactory performance can be obtained and the control law can overcome the influence of parameter errors.
基金Project(52078060) supported by the National Natural Science Foundation of ChinaProject(2020JJ4606)supported by the Natural Science Foundation of Hunan Province,China+1 种基金Project(2018IC19) supported by the International Cooperation and Development Project of Double-First-Class Scientific Research in Changsha University of Science&Technology,ChinaProject(18ZDXK05) supported by Innovative Program of Key Disciplines with Advantages and Characteristics of Civil Engineering of Changsha University of Science&Technology,China。
文摘Shield tunneling inevitably passes through a large number of pile foundations in urban areas.Thus,an accurate assessment of tunneling-induced pile displacement and potential damage becomes a critical part of shield construction.This study presents a mechanism research of pile-soil-tunnel interaction through Pasternak-based two-stage analysis method.In the first stage,based on Mindlin’s solution,the soil displacement fields induced by shield thrust force,cutterhead frictions,shield shell frictions and grouting pressure are derived.The analytical solution of threedimensional soil displacement field is established by introducing Pinto’s three-dimensional volume loss formula,which solves the problems that shield construction factors are not taken into account in Loganathan’s formula and only twodimensional soil displacement field can be obtained.In the second stage,based on Pasternak’s two-parameter foundation model,the analytical solution of pile displacement induced by shield tunneling in layered soil is derived.A case was found in the project of interval tunnels from Wanjiali Square to Furong District Government of Changsha Metro Line 5,where the shield tunnels were constructed near viaduct piles.The reliability of the analytical solution proposed in this study is verified by comparing with the field measured data and the results of finite element method(FEM).In addition,the comparisons of longitudinal,horizontal and vertical displacements of soil and pile foundation analyzed by the analytical solution and FEM provide corresponding theoretical basis,which has significant engineering guidance for similar projects.
文摘The main objective of this work is to investigate analytically the steady nanofluid flow and heat transfer characteristics between nonparallel plane walls. Using appropriate transformations for the velocity and temperature, the basic nonlinear partial differential equations are reduced to the ordinary differential equations. Then, these equations have been solved analytically and numerically for some values of the governing parameters, Reynolds number, Re, channel half angle, α, Prandtl number, Pr, and Eckert number, Ec, using Adomian decomposition method and the Runge-Kutta method with mathematic package. Analytical and numerical results are searched for the skin friction coefficient, Nusselt number and the velocity and temperature profiles. It is found on one hand that the Nusselt number increases as Eckert number or channel half-angle increases, but it decreases as Reynolds number increases. On the other hand, it is also found that the presence of Cu nanoparticles in a water base fluid enhances heat transfer between nonparallel plane walls and in consequence the Nusselt number increases with the increase of nanoparticles volume fraction. Finally, an excellent agreement between analytical results and those obtained by numerical Runge-Kutta method is highly noticed.
基金Projects(51408449,51778630)supported by the National Natural Science Foundation of ChinaProject(2018zzts189)supported by the Fundamental Research Funds for the Central Universities,China
文摘Corrugated steel web is folded along the longitudinal direction and has the mechanical properties such as axial compression stiffness corrugation effect, shear modulus corrugation effect, similar to that of an accordion. In order to study the lateral-torsional buckling of box beams with corrugated steel webs (BBCSW) under the action of bending moment load, the neutral equilibrium equation of BBCSW under the action of bending moment load is derived through the stationary value theory of total potential energy and further, along with taking Kollbrunner-Hajdin correction method and the mechanical properties of the corrugated web into consideration. The analytical calculation formula of lateral-torsional buckling critical bending moment of BBCSW is then obtained. The lateral-torsional buckling critical bending moment of 96 BBCSW test specimens with different geometry dimensions are then calculated using both the analytical calculation method and ANSYS finite element method. The results show that the analytical calculation results agree well with the numerical calculation results using ANSYS, thus proving the accuracy of the analytical calculation method and model simplification hypothesis proposed in this paper. Also, compared with the box beams with flat steel webs (BBFSW) with the same geometry dimensions as BBCSW, within the common range of web space-depth ratio and web span-depth ratio, BBCSW’s lateral-torsional buckling critical bending moment is larger than that of BBFSW. Moreover, the advantages of BBCSW’s stability are even more significant with the increase of web space-depth ratio and web depth-thickness ratio.
基金Project(51021004)supported by Innovative Research Groups of the National Natural Science Foundation of ChinaProject(NCET-11-0370)supported by Program for New Century Excellent Talents in Universities of China+1 种基金Project(40776055)supported by the National Natural Science Foundation of ChinaProject(1002)supported by State Key Laboratory of Ocean Engineering Foundation,China
文摘In order to avoid the curing effects of paraffin on the transport process and reduce the transport difficulty,usually high temperature and high pressure are used in the transportation of oil and gas.The differences of temperature and pressure cause additional stress along the pipeline,due to the constraint of the foundation soil,the additional stress can not release freely,when the additional stress is large enough to motivate the submarine pipelines buckle.In this work,the energy method is introduced to deduce the analytical solution which is suitable for the global buckling modes of idealized subsea pipeline and analyze the relationship between the critical buckling temperature,buckling length and amplitude under different high-order global lateral buckling modes.To obtain a consistent formulation of the problem,the principles of virtual displacements and the variation calculus for variable matching points are applied.The finite element method based on elasto-plastic theory is used to simulate the lateral global buckling of the pipelines under high temperature and pressure.The factors influencing the lateral buckling of pipelines are further studied.Based upon some actual engineering projects,the finite element results are compared with the analytical ones,and then the influence of thermal stress,the section rigidity of pipeline,the soil properties and the trigging force to the high order lateral buckling are discussed.The method of applying the small trigging force on pipeline is reliable in global buckling numerical analysis.In practice,increasing the section rigidity of a pipeline is an effective measure to improve the ability to resist the global buckling.
基金Project(51021004)supported by Innovative Research Groups of the National Natural Science Foundation of ChinaProject(NCET-11-0370)supported by Program for New Century Excellent Talents in Universities of China+1 种基金Project(40776055)supported by the National Natural Science Foundation of ChinaProject(1002)supported by State Key Laboratory of Ocean Engineering Foundation,China
文摘Buckling of submarine pipelines under thermal stress is one of the most important problems to be considered in pipeline design. And pipeline with initial imperfections will easily undergo failure due to global buckling under thermal stress and internal pressure. Therefore, it is vitally important to study the global buckling of the submarine pipeline with initial imperfections. On the basis of the characteristics of the initial imperfections, the global lateral buckling of submarine pipelines was analyzed. Based on the deduced analytical solutions for the global lateral buckling, effects of temperature difference and properties of foundation soil on pipeline buckling were analyzed. The results show that the snap buckling is predominantly governed by the amplitude value of initial imperfection; the triggering temperature difference of Mode I for pipelines with initial imperfections is higher than that of Mode I1; a pipeline with a larger friction coefficient is safer than that with a smaller one; pipelines with larger initial imperfections are safer than those with smaller ones.
基金Project(51278450)supported by the National Natural Science Foundation of China
文摘A simplified method is presented for predicting consolidation settlement of soft ground improved by floating soil-cement column on the basis of double soil-layer consolidation theory. Combining the axisymmetric consolidation model and equal strain assumption, the governing equation was derived for the consolidation of clayey subsoil reinforced by soil-cement column. By modifying the boundary condition of the interface between the improved layer and underlying layer on seepage and pore-water pressure, the analytical solution of consolidation of soft ground improved by floating soil-cement column was developed under depth-dependent ramp load. The results of the parameter analysis of consolidation behavior show that the consolidation rate is closely related with the depth replacement ratio by the column and the permeability of upper layer. The influence of column-soil constrained modulus ratio and radius ratio of the influence zone to the column on consolidation is also affected by depth replacement ratio. The column-soil total stress ratio increases with time and approaches the final value accompanied with the dissipation of excess pore water pressure.
文摘A new analytical study on stresses around a post-tensioned anchor in rocks with two perpendicular joint sets is presented. The assumptions of orthotropic elastic rock with plane strain conditions are made in derivation of the formulations. A tri-linear bond-slip constitutive law is used for modeling the tendon-grout interface behavior and debonding of this interface. The bearing plate width is also considered in the analysis. The obtained solutions are in the integral forms and numerical techniques that have been used for evaluation. In the illustrative example given, the major principal stress is compressive in the anchor free zone and compressive stress concentrations of 815 k Pa and 727 k Pa(for the anchor load of 300 k N) are observed under the bearing plate and the bond length proximal end, respectively. However, large values of tensile stresses with the maximum of-434 k Pa are formed at the bond length distal end. The results obtained using the proposed solution are compared very those of numerical method(FEM).
基金National Key Research and Development Program of China Under Grant(2020YFB1712203)。
文摘随着市场竞争愈发激烈、全球环境日益恶化以及公众环保意识的提高,绿色采购问题受到了广泛关注。现有研究绝大多数聚焦于考虑绿色准则的供应商选择问题,以实现可持续经营。然而,在综合考虑时间、价格和成本等因素的前提下,从适应性强的供应商处获得适当的产品,对于企业来说更为可行和经济,即供应商选择和订单分配。为了解决上述关键问题,提出了一种模糊环境下的多准则群体决策方法。提出了一种基于理想解相似性偏好排序和层次分析法(technique for order of preference by similarity to ideal solution and analytic hierarchy process,TOPSIS-AHP)的模糊排序方法,该方法可根据企业战略灵活调整传统准则和绿色准则的权重。在双目标优化模型中引入供应商排名进行订货,在实现采购绩效最大化的同时,最大限度地降低采购成本。结果表明:所提方法能够有效评价供应商绩效,并优化候选供应商之间的订单分配。
文摘In this study,the effect of influencing parameters on the stress distribution around a polygonal cutout within a laminated composite under uniform heat flux was analytically examined.The analytical method was developed based on the classical laminated plate theory and two-dimensional thermo-elastic method.A mapping function was employed to extend the solution of a perforated symmetric laminate with a circular cutout to the solution of polygonal cutouts.The effect of significant parameters such as the cutout angular position,bluntness and aspect ratio,the heat flux angle and the laminate stacking sequence in symmetric composite laminate containing triangular,square and pentagonal cutouts was studied.The Neumann boundary condition was used at the edges of the thermally insulated polygonal cutout.The laminate was made of graphite/epoxy(AS/3501) material with two different stacking sequences of [30/45]sand[30/0/-30]_(s).The analytical solutions were well validated against finite element results.
文摘Failure of pipe networks due to blast loads resulting from terrorist attacks or construction facilities, may cause economic loss, environmental pollution, source of firing or even it may lead to a disaster. The present work develops a closed-form solution of buried pipe with barrier system subjected to subsurface detonation. The solution is derived based on the concept of double-beam system. Euler Bernoulli's beams are used to simulate the buried pipe and the barrier system. Soil is idealized as viscoelastic foundation along with shear interaction between discrete Winkler springs(advanced soil model). The finite SineFourier transform is employed to solve the coupled partial differential equations. The solution is validated with past studies. A parametric study is conducted to investigate the influence of TNT charge weight, pipe material, damping ratio and TNT offset on the response of buried pipe with and without barrier system. Further a statistical analysis is carried out to get the significant soil and pipe input parameters. It is perceived that peak pipe displacements for both the cases(with and without barrier) are increases with increasing the weight of TNT charge and decreases with increasing the damping ratio and TNT offset. The deformation of pipe also varies with pipe material. Pipe safety against blast loads can be ensured by providing suitable barrier layer. The present study can be utilized in preliminary design stage as an alternative to expensive numerical analysis or field study.
基金Project(200310) supported by Edison Research Foundation from General Electric (GE) in USAProject(59976022) supported by the National Natural Science Foundation of China
文摘In order to build the model of the drum level wave action and sloshing, based on the method of modularization modeling, the hydrodynamic model of drum level wave action and sloshing was developed, and dynamic simulation researches were carried out based on the model. The results indicate that both drum level and drum length have functional relations with period of drum level wave action and sloshing. When the drum level decreases or drum length increases, the period of drum level wave action and sloshing increases, density of liquid and number of sub-module division have little influence on the period of drum level wave action and sloshing. The model was validated by the analytical solution theory of liquid’s wave action and sloshing in cuboid container, and the 3D graphics of drum level wave action and sloshing was also obtained. The model can dynamically reflect the rules of wave action and sloshing of water in the container exactly.
