We investigate a sufficient condition,in terms of the azimuthal componentω^(θ)ofω=curl u in cylindrical coordinates,for the regularity of axisymmetric weak solutions to the 3D incompressible Navier-Stokes equations...We investigate a sufficient condition,in terms of the azimuthal componentω^(θ)ofω=curl u in cylindrical coordinates,for the regularity of axisymmetric weak solutions to the 3D incompressible Navier-Stokes equations.More precisely,we prove that if■,then the weak solution u is actually a regular solution.Similar regularity criterion still holds in the homogeneous Triebel-Lizorkin spaces.展开更多
The cavitation tunnel with controlled background pressure is a pivotal experimental setup for studying the mechanisms of cavitating flows and hydrodynamic loads on cavitating bodies.Existing recirculating cavitation t...The cavitation tunnel with controlled background pressure is a pivotal experimental setup for studying the mechanisms of cavitating flows and hydrodynamic loads on cavitating bodies.Existing recirculating cavitation tunnels predominantly feature horizontal test sections for modeling cavity flows in horizontal incoming flow and vertical gravitational acceleration and fail to meet the requirements for long-duration experiments on ventilated cavity flows.This paper introduces the unique gravitydriven vertical water tunnel(GVWT),facilitating hydrodynamic experiments on axisymmetric slender bodies with ventilated cavities in the streamwise gravitational acceleration.It elaborates high-throughput data processing method for synchronously measured high-speed camera images of cavity forms and pressure distribution from sensor arrays on model surfaces in unsteady long-duration ventilation conditions.For the ventilated cavity flow against an axisymmetric slender body with 60°cone headform at zero angle of attack,the developed partial cavity can be divided into four regimes:The sheet cavity,the combined sheet and cloud cavity,the entire cloud cavity,and the shedding cloud cavity.The mean cavity length and thickness are well-defined by the high-speed images.For the unsteady ventilated cavity due to the re-entrant jet,the Strouhal number based on cavity length and pulsation frequency of the cloud cavity equals 0.276.The mean pressure distribution in the ventilated cavity reveals a difference between the pressure within the sheet cavity and the maximum pressure in the cavity closure,which is influenced by the streamwise gravitational effect.The experimental results demonstrate that GVWT provides a novel experimental approach for understanding the physics of ventilated cavity evolution and bubbly flows under the effect of the streamwise gravitational acceleration.展开更多
Multiphase flows widely exist in various scientific and engineering fields,and strongly compressible multiphase flows commonly occur in practical applications,which makes them an important part of computational fluid ...Multiphase flows widely exist in various scientific and engineering fields,and strongly compressible multiphase flows commonly occur in practical applications,which makes them an important part of computational fluid dynamics.In this study,an axisymmetric adaptive multiresolution smooth particle hydrodynamics(SPH)model is proposed to solve various strongly compressible multiphase flow problems.In the present model,the governing equations are discretized in cylindrical polar coordinates,and an improved volume adaptive scheme is developed to better solve the problem of excessive volume change in strongly compressible multiphase flows.On this basis,combined with the adaptive particle refinement technique,an adaptive multiresolution scheme is proposed in this study.In addition,the high-order differential operator and diffusion correction term are utilized to improve the accuracy and stability.The effectiveness of the model is verified by testing four typical strongly compressible multiphase flow problems.By comparing the results of adaptive multiresolution SPH with other numerical results or experimental data,we can conclude that the present SPH method effectively models strongly compressible multiphase flows.展开更多
New developments have been made on the applications of the differential quadrature(DQ)method to analysis of structural problems recently.The method is used to obtain solutions of large deflections, membrane and bendin...New developments have been made on the applications of the differential quadrature(DQ)method to analysis of structural problems recently.The method is used to obtain solutions of large deflections, membrane and bending stresses of circular plates with movable and immovable edges under uniform pressures or a central point load.The shortcomings existing in the earlier analysis by the DQ method have been overcome by a new approach in applying the boundary conditions. The accuracy and the efficiency of the newly developed method for solving nonlinear problems are demonstrated.展开更多
The absorber is known to be vertical axisymmetric for a single-point wave energy converter （WEC）. The shape of the wetted surface usually has a great influence on the absorber＇s hydrodynamic characteristics which a...The absorber is known to be vertical axisymmetric for a single-point wave energy converter （WEC）. The shape of the wetted surface usually has a great influence on the absorber＇s hydrodynamic characteristics which are closely linked with the wave power conversion ability. For complex wetted surface, the hydrodynamic coefficients have been predicted traditionally by hydrodynamic software based on the BEM. However, for a systematic study of various parameters and geometries, they are too multifarious to generate so many models and data grids. This paper examines a semi-analytical method of decomposing the complex axisyrnmetric boundary into several ring-shaped and stepped surfaces based on the boundary discretization method （BDM） which overcomes the previous difficulties. In such case, by using the linear wave theory based on eigenfunction expansion matching method, the expressions of velocity potential in each domain, the added mass, radiation damping and wave excitation forces of the oscillating absorbers are obtained. The good astringency of the hydrodynamic coefficients and wave forces are obtained for various geometries when the discrete number reaches a certain value. The captured wave power for a same given draught and displacement for various geometries are calculated and compared. Numerical results show that the geometrical shape has great effect on the wave conversion performance of the absorber. For absorbers with the same outer radius and draught or displacement, the cylindrical type shows fantastic wave energy conversion ability at some given frequencies, while in the random sea wave, the parabolic and conical ones have better stabilization and applicability in wave power conversion.展开更多
This paper investigates the effects of charge parameters of the underwater contact explosion based on the axisymmetric smoothed particle hydrodynamics （SPH） method. The dynamic boundary particle is proposed to impro...This paper investigates the effects of charge parameters of the underwater contact explosion based on the axisymmetric smoothed particle hydrodynamics （SPH） method. The dynamic boundary particle is proposed to improve the pressure fluctuation and numerical accuracy near the symmetric axis. An in-depth study is carried out over the influence of charge shapes and detonation modes on the near-field loads in terms of the peak pressure and impulse of shock waves. For different charge shapes, the cylindrical charge with different length-diameter ratios may cause strong directivity of peak pressure and impulse in the near field. Compared with spherical charge, the peak pressure of cylindrical charge may be either weakened or enhanced in different directions. Within a certain range, the greater the length-diameter ratio is, the more obvious the effect will be. The weakened ratio near the detonation end may reach 25% approximately, while the enhanced ratio may reach around 20% in the opposite direction. However, the impulse in different directions seems to be uniform. For different detonation modes, compared with point-source explosion, the peak pressure of plane-source explosion is enhanced by about 5%. Besides, the impulse of plane-source explosion is enhanced by around 5% near the detonation end, but close to those of the point-source explosion in other directions. Based on the material constitutive relation in the axisymmetric coordinates, a simple case of underwater contact explosion is simulated to verify the above conclusions, showing that the charge parameters of underwater contact explosion should not be ignored.展开更多
Based on the three dimensional elastic theory, the state equationfo the axisymmetric free vibration of transversely isotropic circularplates is established. Taking the advantage of finite Hankeltransform, tow exact so...Based on the three dimensional elastic theory, the state equationfo the axisymmetric free vibration of transversely isotropic circularplates is established. Taking the advantage of finite Hankeltransform, tow exact solutions are derived for two boundaryconditions, i.e. the rigid-slipping boundary and elastic simplysupported boundary. Finally, numerical results are presented and com-pared with those of FEM.展开更多
The analytical layer-elements for a single poroelastic soil layer and the underlying half-space are established using an algebraic manipulation and Hankel trans- form. According to the boundary conditions and adjacent...The analytical layer-elements for a single poroelastic soil layer and the underlying half-space are established using an algebraic manipulation and Hankel trans- form. According to the boundary conditions and adjacent continuity conditions of general stresses and displacements, a global matrix equation in the transform domain for multi- layered saturated soil media is assembled and solved. Solutions in the frequency domain can be further obtained with an inverse Hankel transform. Numerical examples are used to examine accuracy of the present method and demonstrate effects of soil parameters and load conditions on dynamic responses of the multilayered poroelastic saturated soils.展开更多
A new analytical method is presented to study the axisymmetric Biot＇s consolidation of a finite soil layer. Starting from the governing equations of axisymmetric Blot＇s consolidation, and based on the property of La...A new analytical method is presented to study the axisymmetric Biot＇s consolidation of a finite soil layer. Starting from the governing equations of axisymmetric Blot＇s consolidation, and based on the property of Laplace transform, the relation of basic variables for a point of a finite soil layer is established between the ground surface （z= 0） and the depth z in the Laplace and Hankel transform domains. Combined with the boundary conditions of the finite soil layer, the analytical solution of any point in the transform domain can be obtained. The actual solution in the physical domain can be obtained by inverse Laplace and Hankel transforms. A numerical analysis for the axisymmetric consolidation of a finite soil layer is carried out.展开更多
In this article, we study the axisymmetric torsional contact problem of a half-space coated with functionally graded piezoelectric material (FGPM) and subjected to a rigid circular punch. It is found that, along the t...In this article, we study the axisymmetric torsional contact problem of a half-space coated with functionally graded piezoelectric material (FGPM) and subjected to a rigid circular punch. It is found that, along the thickness direction, the electromechanical properties of FGPMs change exponentially. We apply the Hankel integral transform technique and reduce the problem to a singular integral equation, and then numerically determine the unknown contact stress and electric displacement at the contact surface. The results show that the surface contact stress, surface azimuthal displacement, surface electric displacement, and inner electromechanical field are obviously dependent on the gradient index of the FGPM coating. It is found that we can adjust the gradient index of the FGPM coating to modify the distributions of the electric displacement and contact stress.展开更多
In this paper, a three-parameter family of self-similar and weak solutions are constructed rigorously in two space dimensions for all positive time to the Euler equations with axisymmetric and radial negative initial ...In this paper, a three-parameter family of self-similar and weak solutions are constructed rigorously in two space dimensions for all positive time to the Euler equations with axisymmetric and radial negative initial velocity for the Chaplygin gas. Under the axisymmetry and self-similar assumptions, the equations are reduced to a system of three ordinary differential equations, from which we obtain structures of solutions besides their existence. The solutions exhibit some phenomena, such as formation and evolution of black hole, expansion and explosive expansion, in the evolution of universe.展开更多
Weak axisymmetrical fountains resulting from the injection of a dense fluid upwards into a large container of homogeneous fluid of lower density has been studied numerically in this paper using a time-accurate finite ...Weak axisymmetrical fountains resulting from the injection of a dense fluid upwards into a large container of homogeneous fluid of lower density has been studied numerically in this paper using a time-accurate finite volume scheme. The behaviour of fountains for both the uniform and parabolic profiles of the discharge velocity at the fountain source has been investigated. The evolution of transient fountain flow has been analysed and two distinct stages of evolution have been identified. The time trace of the position of the fountain front has been presented and the initial, temporary and final fountain height and fountain width have been determined.展开更多
A highly efficient "hybrid integral-equation method" for computing hydrodynamic added-mass, wave-damping, and wave-exciting force of general body geometries with a vertical axis of symmetry is presented. The...A highly efficient "hybrid integral-equation method" for computing hydrodynamic added-mass, wave-damping, and wave-exciting force of general body geometries with a vertical axis of symmetry is presented. The hybrid method utilizes a numerical inner domain and a semi-infinite analytical outer domain separated by a vertical cylindrical matching boundary.Eigenfunction representation of velocity potential is used in the outer domain;the three-dimensional potential in the inner domain is solved using a "two-dimensional" boundary element method with ring sources and ring dipoles to exploit the body symmetry for efficiency. With proper solution matching at the common boundary, both radiation and diffraction potentials can be solved efficiently while satisfying the far-field radiation condition exactly. This method is applied to compute the hydrodynamic properties of two different body geometries: a vertical-walled moonpool with a bottom plate that restricts the opening and a spar-like structure with a diverging bottom opening inspired by designs of floating Oscillating Water Columns. The effects of the size of the bottom opening on the hydrodynamic properties of the body are investigated for both geometries. The heave motion of the floater as well as the motion of the internal free surface under incident wave excitation are computed and studied for the spar-like structure.展开更多
A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special Junction was introduced to transform the inhomogeneous bound...A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special Junction was introduced to transform the inhomogeneous boundary conditions into the homogeneous ones. Secondly, using the method of separation of variables, the quantity that the displacement subtracts the special function was expanded as the multiplication series of Bassel functions and time functions. Then by virtue of the orthogonal properties of Bessel Junctions, the equation With respect to the time variable was derived, of which the solution is easily obtained. The displacement solution was finally obtained by adding the two parts mentioned above. The present method can avoid the integral transform and is fit for arbitrary loads. Numerical results are presented for internally shocked isotropic and cylindrically isotropic cylindrical shells and externally shocked cylinders, as well as for an externally shocked, cylindrically isotropic cylindrical shell that is fixed at the internal surface.展开更多
This paper presents an analytical layer-element method used to analyze the displacement of a multi-layered transversely isotropic elastic medium of arbitrary depth subjected to axisymmetric loading.Based on the basic ...This paper presents an analytical layer-element method used to analyze the displacement of a multi-layered transversely isotropic elastic medium of arbitrary depth subjected to axisymmetric loading.Based on the basic constitutive equations and the HU Hai-chang's solutions for transversely isotropic elastic media,the state vectors of a multi-layered transversely isotropic medium were deduced.From the state vectors,an analytical layer element for a single layer(i.e.,a symmetric and exact stiffness matrix) was acquired in the Hankel transformed domain,which not only simplified the calculation but also improved the numerical efficiency and stability due to the absence of positive exponential functions.The global stiffness matrix was obtained by assembling the interrelated layer elements based on the principle of the finite layer method.By solving the algebraic equations of the global stiffness matrix which satisfy the boundary conditions,the solutions for multi-layered transversely isotropic media in the Hankel transformed domain were obtained.The actual solutions of this problem in the physical domain were acquired by inverting the Hankel transform.This paper presents numerical examples to verify the proposed solutions and investigate the influence of the properties of the multi-layered medium on the load-displacement response.展开更多
A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry ...A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional （2D） problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method （FEM） shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.展开更多
The coherent structures and the chaotic phenomena in the transition of the axisymmetric countercurrent mixing shear flow were investigated experimentally. Two kinds of self-excited oscillation modes could exist in the...The coherent structures and the chaotic phenomena in the transition of the axisymmetric countercurrent mixing shear flow were investigated experimentally. Two kinds of self-excited oscillation modes could exist in the axisymmetric countercurrent mixing shear flow. One is the shear layer self-excited oscillation mode corresponding to the high Reynolds number regime and the other is the jet column self-excited oscillation mode corresponding to the low Reynolds number regime in the case of the velocity ratio ranging from I to 1.5. Analyzing the auto-power spectrum, self-correlation-function and three dimensional reconstructed phase trajectory, the route to chaos through three Hopf bifurcations intercepted by an intermittence of the dynamical system corresponding to the axisymmetric countercurrent mixing shear flow was discovered when the velocity ratio is equal to 1.32.展开更多
The effects of axisymmetric flow of a Powell-Eyring fluid over an impermeable radially stretching surface are presented. Characteristics of the heat transfer process are analyzed with a more realistic condition named ...The effects of axisymmetric flow of a Powell-Eyring fluid over an impermeable radially stretching surface are presented. Characteristics of the heat transfer process are analyzed with a more realistic condition named the convective boundary condition. Governing equations for the flow problem are derived by the boundary layer approximations. The modeled highly coupled partial differential system is converted into a system of ordinary differential equations with acceptable similarity transformations. The convergent series solutions for the resulting system are constructed and analyzed. Optimal values are obtained and presented in a numerical form using an optimal homotopy analysis method （OHAM）. The rheological characteristics of different parameters of the velocity and temperature profiles are presented graphically. Tabular variations of the skin friction coefficient and the Nusselt number are also calculated. It is observed that the temperature distribution shows opposite behavior for Prandtl and Biot numbers. Furthermore, the rate of heating/cooling is higher for both the Prandtl and Biot numbers.展开更多
In this work, a design procedure extending the B-spline based finite cell method into shape optimization is developed for axisymmetric solids involving the centrifugal force effect. We first replace the traditional co...In this work, a design procedure extending the B-spline based finite cell method into shape optimization is developed for axisymmetric solids involving the centrifugal force effect. We first replace the traditional conforming mesh in the finite element method with structured cells that are fixed during the whole design process with a view to avoid the sophisticated re-meshing and eventual mesh distortion.Then, B-spline shape functions are further implemented to yield a high-order continuity field along the cell boundary in stress analysis. By means of the implicit description of the shape boundary, stress sensitivity is analytically derived with respect to shape design variables. Finally, we illustrate the efficiency and accuracy of the proposed protocol by several numerical test cases as well as a whole design procedure carried out on an aeronautic turbine disk.展开更多
In this paper,we consider the 3D compressible isentropic Navier-Stokes equations when the shear viscosityμis a positive constant and the bulk viscosity is λ(ρ)=ρ^(β) with β>2,which is a situation that was fir...In this paper,we consider the 3D compressible isentropic Navier-Stokes equations when the shear viscosityμis a positive constant and the bulk viscosity is λ(ρ)=ρ^(β) with β>2,which is a situation that was first introduced by Vaigant and Kazhikhov in[1].The global axisymmetric classical solution with arbitrarily large initial data in a periodic domain Ω={(r,z)|r=√x^(2)+y^(2),(x,y,z)∈R^(3),r∈I⊂(0,+∞),-∞<z<+∞} is obtained.Here the initial density keeps a non-vacuum state ρ>0 when z→±∞.Our results also show that the solution will not develop the vacuum state in any finite time,provided that the initial density is uniformly away from the vacuum.展开更多
基金Supported by the National Natural Science Foundation of China(12361034)the Natural Science Foundation of Shaanxi Province(2022JM-034)。
文摘We investigate a sufficient condition,in terms of the azimuthal componentω^(θ)ofω=curl u in cylindrical coordinates,for the regularity of axisymmetric weak solutions to the 3D incompressible Navier-Stokes equations.More precisely,we prove that if■,then the weak solution u is actually a regular solution.Similar regularity criterion still holds in the homogeneous Triebel-Lizorkin spaces.
基金supported by the National Natural Science Foundation of China(Grant No.12102262)CST Foundation of China Academy of Launch Vehicle Technology.
文摘The cavitation tunnel with controlled background pressure is a pivotal experimental setup for studying the mechanisms of cavitating flows and hydrodynamic loads on cavitating bodies.Existing recirculating cavitation tunnels predominantly feature horizontal test sections for modeling cavity flows in horizontal incoming flow and vertical gravitational acceleration and fail to meet the requirements for long-duration experiments on ventilated cavity flows.This paper introduces the unique gravitydriven vertical water tunnel(GVWT),facilitating hydrodynamic experiments on axisymmetric slender bodies with ventilated cavities in the streamwise gravitational acceleration.It elaborates high-throughput data processing method for synchronously measured high-speed camera images of cavity forms and pressure distribution from sensor arrays on model surfaces in unsteady long-duration ventilation conditions.For the ventilated cavity flow against an axisymmetric slender body with 60°cone headform at zero angle of attack,the developed partial cavity can be divided into four regimes:The sheet cavity,the combined sheet and cloud cavity,the entire cloud cavity,and the shedding cloud cavity.The mean cavity length and thickness are well-defined by the high-speed images.For the unsteady ventilated cavity due to the re-entrant jet,the Strouhal number based on cavity length and pulsation frequency of the cloud cavity equals 0.276.The mean pressure distribution in the ventilated cavity reveals a difference between the pressure within the sheet cavity and the maximum pressure in the cavity closure,which is influenced by the streamwise gravitational effect.The experimental results demonstrate that GVWT provides a novel experimental approach for understanding the physics of ventilated cavity evolution and bubbly flows under the effect of the streamwise gravitational acceleration.
基金Supported by the Guangxi Natural Science Foundation(Grant No.2021GXNSFBA196008)the Guangxi Science and Technology Development Program(Grant No.GuikeAD22035189).
文摘Multiphase flows widely exist in various scientific and engineering fields,and strongly compressible multiphase flows commonly occur in practical applications,which makes them an important part of computational fluid dynamics.In this study,an axisymmetric adaptive multiresolution smooth particle hydrodynamics(SPH)model is proposed to solve various strongly compressible multiphase flow problems.In the present model,the governing equations are discretized in cylindrical polar coordinates,and an improved volume adaptive scheme is developed to better solve the problem of excessive volume change in strongly compressible multiphase flows.On this basis,combined with the adaptive particle refinement technique,an adaptive multiresolution scheme is proposed in this study.In addition,the high-order differential operator and diffusion correction term are utilized to improve the accuracy and stability.The effectiveness of the model is verified by testing four typical strongly compressible multiphase flow problems.By comparing the results of adaptive multiresolution SPH with other numerical results or experimental data,we can conclude that the present SPH method effectively models strongly compressible multiphase flows.
文摘New developments have been made on the applications of the differential quadrature(DQ)method to analysis of structural problems recently.The method is used to obtain solutions of large deflections, membrane and bending stresses of circular plates with movable and immovable edges under uniform pressures or a central point load.The shortcomings existing in the earlier analysis by the DQ method have been overcome by a new approach in applying the boundary conditions. The accuracy and the efficiency of the newly developed method for solving nonlinear problems are demonstrated.
基金supported by the National Natural Science Foundation of China(Grant Nos.11572094,51579055 and 51509048)
文摘The absorber is known to be vertical axisymmetric for a single-point wave energy converter （WEC）. The shape of the wetted surface usually has a great influence on the absorber＇s hydrodynamic characteristics which are closely linked with the wave power conversion ability. For complex wetted surface, the hydrodynamic coefficients have been predicted traditionally by hydrodynamic software based on the BEM. However, for a systematic study of various parameters and geometries, they are too multifarious to generate so many models and data grids. This paper examines a semi-analytical method of decomposing the complex axisyrnmetric boundary into several ring-shaped and stepped surfaces based on the boundary discretization method （BDM） which overcomes the previous difficulties. In such case, by using the linear wave theory based on eigenfunction expansion matching method, the expressions of velocity potential in each domain, the added mass, radiation damping and wave excitation forces of the oscillating absorbers are obtained. The good astringency of the hydrodynamic coefficients and wave forces are obtained for various geometries when the discrete number reaches a certain value. The captured wave power for a same given draught and displacement for various geometries are calculated and compared. Numerical results show that the geometrical shape has great effect on the wave conversion performance of the absorber. For absorbers with the same outer radius and draught or displacement, the cylindrical type shows fantastic wave energy conversion ability at some given frequencies, while in the random sea wave, the parabolic and conical ones have better stabilization and applicability in wave power conversion.
基金supported by the National Natural Science Foundation of China(No.51379039)the Excellent Young Scientists Fund(No.51222904)
文摘This paper investigates the effects of charge parameters of the underwater contact explosion based on the axisymmetric smoothed particle hydrodynamics （SPH） method. The dynamic boundary particle is proposed to improve the pressure fluctuation and numerical accuracy near the symmetric axis. An in-depth study is carried out over the influence of charge shapes and detonation modes on the near-field loads in terms of the peak pressure and impulse of shock waves. For different charge shapes, the cylindrical charge with different length-diameter ratios may cause strong directivity of peak pressure and impulse in the near field. Compared with spherical charge, the peak pressure of cylindrical charge may be either weakened or enhanced in different directions. Within a certain range, the greater the length-diameter ratio is, the more obvious the effect will be. The weakened ratio near the detonation end may reach 25% approximately, while the enhanced ratio may reach around 20% in the opposite direction. However, the impulse in different directions seems to be uniform. For different detonation modes, compared with point-source explosion, the peak pressure of plane-source explosion is enhanced by about 5%. Besides, the impulse of plane-source explosion is enhanced by around 5% near the detonation end, but close to those of the point-source explosion in other directions. Based on the material constitutive relation in the axisymmetric coordinates, a simple case of underwater contact explosion is simulated to verify the above conclusions, showing that the charge parameters of underwater contact explosion should not be ignored.
基金the National Natural Science Foundation of Chinathe Zhejiang Provincial Natural Science Foundation
文摘Based on the three dimensional elastic theory, the state equationfo the axisymmetric free vibration of transversely isotropic circularplates is established. Taking the advantage of finite Hankeltransform, tow exact solutions are derived for two boundaryconditions, i.e. the rigid-slipping boundary and elastic simplysupported boundary. Finally, numerical results are presented and com-pared with those of FEM.
文摘The analytical layer-elements for a single poroelastic soil layer and the underlying half-space are established using an algebraic manipulation and Hankel trans- form. According to the boundary conditions and adjacent continuity conditions of general stresses and displacements, a global matrix equation in the transform domain for multi- layered saturated soil media is assembled and solved. Solutions in the frequency domain can be further obtained with an inverse Hankel transform. Numerical examples are used to examine accuracy of the present method and demonstrate effects of soil parameters and load conditions on dynamic responses of the multilayered poroelastic saturated soils.
基金supported by the National Natural Science Foundation of China (No. 50578121)
文摘A new analytical method is presented to study the axisymmetric Biot＇s consolidation of a finite soil layer. Starting from the governing equations of axisymmetric Blot＇s consolidation, and based on the property of Laplace transform, the relation of basic variables for a point of a finite soil layer is established between the ground surface （z= 0） and the depth z in the Laplace and Hankel transform domains. Combined with the boundary conditions of the finite soil layer, the analytical solution of any point in the transform domain can be obtained. The actual solution in the physical domain can be obtained by inverse Laplace and Hankel transforms. A numerical analysis for the axisymmetric consolidation of a finite soil layer is carried out.
基金supported by the National Natural Science Foundation of China (Grants 11272040, 11322218)the Fundamental Research Funds for the Central Universities (Grant 2016YJS113)
文摘In this article, we study the axisymmetric torsional contact problem of a half-space coated with functionally graded piezoelectric material (FGPM) and subjected to a rigid circular punch. It is found that, along the thickness direction, the electromechanical properties of FGPMs change exponentially. We apply the Hankel integral transform technique and reduce the problem to a singular integral equation, and then numerically determine the unknown contact stress and electric displacement at the contact surface. The results show that the surface contact stress, surface azimuthal displacement, surface electric displacement, and inner electromechanical field are obviously dependent on the gradient index of the FGPM coating. It is found that we can adjust the gradient index of the FGPM coating to modify the distributions of the electric displacement and contact stress.
基金Project supported by the Natural Science Foundation of China (Grant No.10671120)the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘In this paper, a three-parameter family of self-similar and weak solutions are constructed rigorously in two space dimensions for all positive time to the Euler equations with axisymmetric and radial negative initial velocity for the Chaplygin gas. Under the axisymmetry and self-similar assumptions, the equations are reduced to a system of three ordinary differential equations, from which we obtain structures of solutions besides their existence. The solutions exhibit some phenomena, such as formation and evolution of black hole, expansion and explosive expansion, in the evolution of universe.
文摘Weak axisymmetrical fountains resulting from the injection of a dense fluid upwards into a large container of homogeneous fluid of lower density has been studied numerically in this paper using a time-accurate finite volume scheme. The behaviour of fountains for both the uniform and parabolic profiles of the discharge velocity at the fountain source has been investigated. The evolution of transient fountain flow has been analysed and two distinct stages of evolution have been identified. The time trace of the position of the fountain front has been presented and the initial, temporary and final fountain height and fountain width have been determined.
文摘A highly efficient "hybrid integral-equation method" for computing hydrodynamic added-mass, wave-damping, and wave-exciting force of general body geometries with a vertical axis of symmetry is presented. The hybrid method utilizes a numerical inner domain and a semi-infinite analytical outer domain separated by a vertical cylindrical matching boundary.Eigenfunction representation of velocity potential is used in the outer domain;the three-dimensional potential in the inner domain is solved using a "two-dimensional" boundary element method with ring sources and ring dipoles to exploit the body symmetry for efficiency. With proper solution matching at the common boundary, both radiation and diffraction potentials can be solved efficiently while satisfying the far-field radiation condition exactly. This method is applied to compute the hydrodynamic properties of two different body geometries: a vertical-walled moonpool with a bottom plate that restricts the opening and a spar-like structure with a diverging bottom opening inspired by designs of floating Oscillating Water Columns. The effects of the size of the bottom opening on the hydrodynamic properties of the body are investigated for both geometries. The heave motion of the floater as well as the motion of the internal free surface under incident wave excitation are computed and studied for the spar-like structure.
文摘A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special Junction was introduced to transform the inhomogeneous boundary conditions into the homogeneous ones. Secondly, using the method of separation of variables, the quantity that the displacement subtracts the special function was expanded as the multiplication series of Bassel functions and time functions. Then by virtue of the orthogonal properties of Bessel Junctions, the equation With respect to the time variable was derived, of which the solution is easily obtained. The displacement solution was finally obtained by adding the two parts mentioned above. The present method can avoid the integral transform and is fit for arbitrary loads. Numerical results are presented for internally shocked isotropic and cylindrically isotropic cylindrical shells and externally shocked cylinders, as well as for an externally shocked, cylindrically isotropic cylindrical shell that is fixed at the internal surface.
基金Project (No.50578121) supported by the National Natural Science Foundation of China
文摘This paper presents an analytical layer-element method used to analyze the displacement of a multi-layered transversely isotropic elastic medium of arbitrary depth subjected to axisymmetric loading.Based on the basic constitutive equations and the HU Hai-chang's solutions for transversely isotropic elastic media,the state vectors of a multi-layered transversely isotropic medium were deduced.From the state vectors,an analytical layer element for a single layer(i.e.,a symmetric and exact stiffness matrix) was acquired in the Hankel transformed domain,which not only simplified the calculation but also improved the numerical efficiency and stability due to the absence of positive exponential functions.The global stiffness matrix was obtained by assembling the interrelated layer elements based on the principle of the finite layer method.By solving the algebraic equations of the global stiffness matrix which satisfy the boundary conditions,the solutions for multi-layered transversely isotropic media in the Hankel transformed domain were obtained.The actual solutions of this problem in the physical domain were acquired by inverting the Hankel transform.This paper presents numerical examples to verify the proposed solutions and investigate the influence of the properties of the multi-layered medium on the load-displacement response.
基金Project supported by the National Natural Science Foundation of China(Grant No.11002054)the Foundation of Hunan Educational Committee(Grant No.12C0059).
文摘A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional （2D） problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method （FEM） shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.
文摘The coherent structures and the chaotic phenomena in the transition of the axisymmetric countercurrent mixing shear flow were investigated experimentally. Two kinds of self-excited oscillation modes could exist in the axisymmetric countercurrent mixing shear flow. One is the shear layer self-excited oscillation mode corresponding to the high Reynolds number regime and the other is the jet column self-excited oscillation mode corresponding to the low Reynolds number regime in the case of the velocity ratio ranging from I to 1.5. Analyzing the auto-power spectrum, self-correlation-function and three dimensional reconstructed phase trajectory, the route to chaos through three Hopf bifurcations intercepted by an intermittence of the dynamical system corresponding to the axisymmetric countercurrent mixing shear flow was discovered when the velocity ratio is equal to 1.32.
文摘The effects of axisymmetric flow of a Powell-Eyring fluid over an impermeable radially stretching surface are presented. Characteristics of the heat transfer process are analyzed with a more realistic condition named the convective boundary condition. Governing equations for the flow problem are derived by the boundary layer approximations. The modeled highly coupled partial differential system is converted into a system of ordinary differential equations with acceptable similarity transformations. The convergent series solutions for the resulting system are constructed and analyzed. Optimal values are obtained and presented in a numerical form using an optimal homotopy analysis method （OHAM）. The rheological characteristics of different parameters of the velocity and temperature profiles are presented graphically. Tabular variations of the skin friction coefficient and the Nusselt number are also calculated. It is observed that the temperature distribution shows opposite behavior for Prandtl and Biot numbers. Furthermore, the rate of heating/cooling is higher for both the Prandtl and Biot numbers.
基金supported by the National Natura Science Foundation of China (Grant 51275424)973 Program (Gran2011CB610304)+1 种基金Research Fund for the Doctoral Program of Higher Education of China (Grant 20126102130003)the opening project (Grant KFJJ13-6M) of the State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology)
文摘In this work, a design procedure extending the B-spline based finite cell method into shape optimization is developed for axisymmetric solids involving the centrifugal force effect. We first replace the traditional conforming mesh in the finite element method with structured cells that are fixed during the whole design process with a view to avoid the sophisticated re-meshing and eventual mesh distortion.Then, B-spline shape functions are further implemented to yield a high-order continuity field along the cell boundary in stress analysis. By means of the implicit description of the shape boundary, stress sensitivity is analytically derived with respect to shape design variables. Finally, we illustrate the efficiency and accuracy of the proposed protocol by several numerical test cases as well as a whole design procedure carried out on an aeronautic turbine disk.
基金supported by NNSFC(11701443,11901444,11931013)Natural Science Basic Research Plan in Shaanxi Province of China(2019JQ-870)。
文摘In this paper,we consider the 3D compressible isentropic Navier-Stokes equations when the shear viscosityμis a positive constant and the bulk viscosity is λ(ρ)=ρ^(β) with β>2,which is a situation that was first introduced by Vaigant and Kazhikhov in[1].The global axisymmetric classical solution with arbitrarily large initial data in a periodic domain Ω={(r,z)|r=√x^(2)+y^(2),(x,y,z)∈R^(3),r∈I⊂(0,+∞),-∞<z<+∞} is obtained.Here the initial density keeps a non-vacuum state ρ>0 when z→±∞.Our results also show that the solution will not develop the vacuum state in any finite time,provided that the initial density is uniformly away from the vacuum.
