Based on the extended homogeneous capacity high precision integration method and the spectrum method of virtual boundary with a complex radius vector, a novel semi-analytical method, which has satisfactory computation...Based on the extended homogeneous capacity high precision integration method and the spectrum method of virtual boundary with a complex radius vector, a novel semi-analytical method, which has satisfactory computation efectiveness and precision, is presented for solving the acoustic radiation from a submerged infnite non-circular cylindrical shell stifened by longitudinal ribs by means of the Fourier integral transformation and stationary phase method. In this work, besides the normal interacting force, which is commonly adopted by some researchers, the other interacting forces and moments between the longitudinal ribs and the non-circular cylindrical shell are considered at the same time. The efects of the number and the size of the cross-section of longitudinal ribs on the characteristics of acoustic radiation are investigated. Numerical results show that the method proposed is more efcient than the existing mixed FE-BE method.展开更多
The effect of axial shallow groove on the nonlinear dynamic response and buckling of laminated cylindrical shells subjected to radial compression loading was investigated. Based on the first-order shear deformation th...The effect of axial shallow groove on the nonlinear dynamic response and buckling of laminated cylindrical shells subjected to radial compression loading was investigated. Based on the first-order shear deformation theory （FSDT）, the nonlinear dynamic equations involving the transverse shear deformation and initial geometric imperfections were derived with the Hamilton philosophy. The axial shallow groove of the laminated composite cylindrical shell was treated as the initial geometric imperfections in the dynamic equations. A semi-analytical method of expanding displacements and loads along the circumferential direction and employing the finite difference method along the axial direction and in the time domain is used to solve the governing equations and obtain the dynamic response of the laminated shell. The B-R criterion was employed to determine the critical loads of dynamic buckling of the shell. The effects of the parameters of the shallow groove on the dynamic response and buckling were discussed in this paper and the results show that the axial shallow grooves greatly affect the dynamic response and buckling.展开更多
In this paper,a semi-analytical method was proposed to evaluate the acoustic nonlinearity parameter for single crystals of Cu,Ag and Au.The acoustic nonlinearity parameter can be derived analytically by general expres...In this paper,a semi-analytical method was proposed to evaluate the acoustic nonlinearity parameter for single crystals of Cu,Ag and Au.The acoustic nonlinearity parameter can be derived analytically by general expressions in terms of the interatomic potentials with the distances between each pair of atoms in these transition metals.To evaluate the acoustic nonlinearity parameter,one needs to conduct one step molecular static simulation and obtain the equilibrium positions of all the atoms.Further,based on this method,numerical experiments with molecular dynamic code LAMMPS were given to compute the acoustic nonlinearity parameter of Cu,Ag and Au.To illustrate the validity of these expressions,comparison was made between calculation results and data in the literature.Reasonable agreement is observed.Because of the analytical nature of this method,it provides a fundamental understanding of the nonlinear elastic behavior of these transition metals.展开更多
The PDFs(probability density functions) and probability of a ship rolling under the random parametric and forced excitations were studied by a semi-analytical method. The rolling motion equation of the ship in random ...The PDFs(probability density functions) and probability of a ship rolling under the random parametric and forced excitations were studied by a semi-analytical method. The rolling motion equation of the ship in random oblique waves was established. The righting arm obtained by the numerical simulation was approximately fitted by an analytical function. The irregular waves were decomposed into two Gauss stationary random processes, and the CARMA(2, 1) model was used to fit the spectral density function of parametric and forced excitations. The stochastic energy envelope averaging method was used to solve the PDFs and the probability. The validity of the semi-analytical method was verified by the Monte Carlo method. The C11 ship was taken as an example, and the influences of the system parameters on the PDFs and probability were analyzed. The results show that the probability of ship rolling is affected by the characteristic wave height, wave length, and the heading angle. In order to provide proper advice for the ship’s manoeuvring, the parametric excitations should be considered appropriately when the ship navigates in the oblique seas.展开更多
In this paper,a semi-analytical method is presented for free vibration and buckling analysis of functionally graded(FG)size-dependent nanobeams based on the physical neutral axis position.It is the first time that a s...In this paper,a semi-analytical method is presented for free vibration and buckling analysis of functionally graded(FG)size-dependent nanobeams based on the physical neutral axis position.It is the first time that a semi-analytical differential transform method(DTM)solution is developed for the FG nanobeams vibration and buckling analysis.Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form.The physical neutral axis position for mentioned FG nanobeams is determined.The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen.The nonlocal equations of motion are derived through Hamilton’s principle and they are solved applying DTM.It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of FG nanobeams.The good agreement between the results of this article and those available in literature validated the presented approach.The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as neutral axis position,small scale effects,the material distribution profile,mode number,thickness ratio and boundary conditions on the normalized natural frequencies and dimensionless buckling load of the FG nanobeams in detail.It is explicitly shown that the vibration and buckling behaviour of a FG nanobeams is significantly influenced by these effects.展开更多
The aim of this paper is to introduce a new semi-analytical method,namely PIMOL(precise integration method of lines,the parametric finite difference method of lines based on the precise integration method),which is de...The aim of this paper is to introduce a new semi-analytical method,namely PIMOL(precise integration method of lines,the parametric finite difference method of lines based on the precise integration method),which is developed and used to solve the ordinary differential equation(ODEs)systems based on the finite difference method of lines and the precise integration method(PIM).Two examples of Poisson^equation problems are given:a boundary value problem and an ODE eigenvalue problem.The PIMOL can effectively reduce a semi-discrete ODE problem to a linear algebraic matrix equation.Numerical results show that the PIMOL is a powerful method.展开更多
Dual vectors are applied in Hamilton system of applied mechanics. Electric and magnetic field vectors are the dual vectors in electromagnetic field. The Hamilton system method is introduced into the analysis of electr...Dual vectors are applied in Hamilton system of applied mechanics. Electric and magnetic field vectors are the dual vectors in electromagnetic field. The Hamilton system method is introduced into the analysis of electromagnetism waveguide with inhomogeneous materials. The transverse electric and magnetic fields are regarded as the dual. The basic equations are solved in Hamilton system and symplectic geometry. With the Hamilton variational principle, the symplectic semi_analytical equations are derived and preserve their symplectic structures. The given numerical example demonstrates the solution of LSE (Longitudinal Section Electric) mode in a dielectric waveguide. (展开更多
Recently, pH-sensitive hydrogels have been utilized in the diverse applications including sensors, switches, and actuators. In order to have continuous stress and deformation ?elds, a new semi-analytical approach is d...Recently, pH-sensitive hydrogels have been utilized in the diverse applications including sensors, switches, and actuators. In order to have continuous stress and deformation ?elds, a new semi-analytical approach is developed to predict the swelling induced?nite bending for a functionally graded(FG) layer composed of a pH-sensitive hydrogel,in which the cross-link density is continuously distributed along the thickness direction under the plane strain condition. Without considering the intermediary virtual reference,the initial state is mapped into the deformed con?guration in a circular shape by utilizing a total deformation gradient tensor stemming from the inhomogeneous swelling of an FG layer in response to the variation of the pH value of the solvent. To enlighten the capability of the presented analytical method, the ?nite element method(FEM) is used to verify the accuracy of the analytical results in some case studies. The perfect agreement con-?rms the accuracy of the presented method. Due to the applicability of FG pH-sensitive hydrogels, some design factors such as the semi-angle, the bending curvature, the aspect ratio, and the distributions of deformation and stress ?elds are studied. Furthermore, the tangential free-stress axes are illustrated in deformed con?guration.展开更多
We present a semi-analytical method of calculating the electrostatic interaction of colloid solutions for confined and unconfined systems. We expand the electrostatic potential of the system in terms of some basis fun...We present a semi-analytical method of calculating the electrostatic interaction of colloid solutions for confined and unconfined systems. We expand the electrostatic potential of the system in terms of some basis functions such as spherical harmonic function and cylinder function. The expansion coefficients can be obtained by solving the equations of the boundary conditions, combining an analytical translation transform of the coordinates and a numerical multipoint collection method. The precise electrostatic potential and the interaction energy are then obtained automatically. The method is available not only for the uniformly charged colloids but also for nonuniformly charged ones. We have successfully applied it to unconfined diluted colloid system and some confined systems such as the long cylinder wall confinement, the air–water interfacial confinement and porous membrane confinement. The consistence checks of our calculations with some known analytical cases have been made for all our applications. In theory, the method is applicable to any dilute colloid solutions with an arbitrary distribution of the surface charge on the colloidal particle under a regular solid confinement, such as spherical cavity confinement and lamellar confinement.展开更多
This paper presents the theory and applications of a new computational technique referred to as Differential Transform Method (DTM) for solving second order linear ordinary differential equations, for both homogeneous...This paper presents the theory and applications of a new computational technique referred to as Differential Transform Method (DTM) for solving second order linear ordinary differential equations, for both homogeneous and nonhomogeneous cases. For the robustness and efficiency of the method, four examples are considered. The results indicate that the DTM is reliable and accurate when compared to the exact solutions of the solved problems.展开更多
The electromagnetic(EM)telemetry systems,employed for real-time data transmission from the borehole and the earth surface during drilling,are widely used in measurement-while-drilling(MWD)and logging-while-drilling(LW...The electromagnetic(EM)telemetry systems,employed for real-time data transmission from the borehole and the earth surface during drilling,are widely used in measurement-while-drilling(MWD)and logging-while-drilling(LWD).Several numerical methods,including the method of moments(MoM),the electric field integral equation(EFIE)method,and the finite-element(FE)method have been developed for the simulation of EM telemetry systems.The computational process of these methods is complicated and time-consuming.To solve this problem,we introduce an axisymmetric semi-analytical FE method(SAFEM)in the cylindrical coordinate system with the virtual layering technique for rapid simulation of EM telemetry in a layered earth.The proposed method divides the computational domain into a series of homogeneous layers.For each layer,only its cross-section is discretized,and a high-precision integration method based on Riccati equations is employed for the calculation of longitudinally homogeneous sections.The block-tridiagonal structure of the global coefficient matrix enables the use of the block Thomas algorithm,facilitating the efficient simulation of EM telemetry problems in layered media.After the theoretical development,we validate the accuracy and efficiency of our algorithm through a series of numerical experiments and comparisons with the Multiphysics modeling software COMSOL.We also discussed the impact of system parameters on EM telemetry signal and demonstrated the applicability of our method by testing it on a field dataset acquired from Dezhou,Shandong Province,China.展开更多
The three-dimensional natural vibration characteristics of water inside a moon pool of an ocean structures are studied. The governing equations are derived based on the linear potential flow theory, and the boundary c...The three-dimensional natural vibration characteristics of water inside a moon pool of an ocean structures are studied. The governing equations are derived based on the linear potential flow theory, and the boundary condition of the total opening bottom suggested by Molin is adopted. A semi-analytical method is used to solve the governing equations, and the natural frequencies and the motion modes are obtained. Two types of motions are studied： （1） the piston motion in the vertical direction, and （2） the sloshing motion of the free surface. The influences of moon pool＇s structural parameters on the natural frequencies, and the modal shapes are analyzed.展开更多
In this paper,a semi-analytical method for the forced vibration analysis of cracked laminated composite beam(CLCB)is investigated.One computational model is formulated by Timoshenko beam theory and its dynamic solutio...In this paper,a semi-analytical method for the forced vibration analysis of cracked laminated composite beam(CLCB)is investigated.One computational model is formulated by Timoshenko beam theory and its dynamic solution is solved using the Jacobi-Ritz method.The boundary conditions(BCs)at both ends of the CLCB are generalized by the application of artificial elastic springs,the CLCB is separated into two elements along the crack,the flexibility coefficient of fracture theory is used to model the essential continuous condition of the connective interface.All the allowable displacement functions used to analyze dynamic characteristics of CLCB are expressed by classical Jacobi orthogonal polynomials in a more general form.The accuracy of the proposed method is verified through the compare with results of the finite element method(software ABAQUS is used in this paper).On this basis,the parametric study for dynamic analysis characteristics of CLCB is performed to provide reference datum for engineers.展开更多
A semi-analytical and semi-numerical method is proposed for the dynamic analysis of foundations. The Lamb＇s solution and the approximate formulae were used to establish the relation of the contact force and deflectio...A semi-analytical and semi-numerical method is proposed for the dynamic analysis of foundations. The Lamb＇s solution and the approximate formulae were used to establish the relation of the contact force and deflection between the foundation and soil. Therefore, the foundation can be separated from soil and analyzed by FEM as for the static cases. The plate can be treated as that the known forces are acting on the upper surface, and the contact pressure from soil can be represented as the deflection. So that only the plate needs to be divided into elements in the analysis. By this method, a series of vibration problems, including various shapes and rigidities of foundations, different excitation frequencies, were analyzed. Furthermore, it can be used for the embedded foundation. The numerical examples show that this method has simplicity, highly accurate and versatile. It is an effective method for the dynamic analysis of foundations.展开更多
Butterfly wings are closely related to the premature failure of rolling element bearings.In this study,butterfly formation is investigated using the developed semi-analytical three-dimensional(3D)contact model incorpo...Butterfly wings are closely related to the premature failure of rolling element bearings.In this study,butterfly formation is investigated using the developed semi-analytical three-dimensional(3D)contact model incorporating inclusion and material property degradation.The 3D elastic field introduced by inhomogeneous inclusion is solved by using numerical approaches,which include the equivalent inclusion method(EIM)and the conjugate gradient method(CGM).The accumulation of fatigue damage surrounding inclusions is described using continuum damage mechanics.The coupling between the development of the damaged zone and the stress field is considered.The effects of the inclusion properties on the contact status and butterfly formation are discussed in detail.The model provides a potential method for quantifying material defects and fatigue behavior in terms of the deterioration of material properties.展开更多
Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harm...Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harmonic excitation.Within any integration segment, as long as its length is small enough,along the circumferential curvilinear coordinate,the non- homogeneous matrix differential equation of an elastic ring of complex geometrical shape can be rewritten in terms of the homogeneous one by the method of extended homogeneous capacity proposed in this paper.For the exterior fluid domain,the multi-circular virtual source simulation technique is adopted.The source density distributed on each virtual circular curve may be ex- panded as the Fourier's series.Combining with the inverse fast Fourier transformation,a higher accuracy and efficiency method for solving 2-D exterior Helmholtz's problems is presented in this paper.In the aspect of solution to the coupling equations,the state vectors of elastic ring induced by the given harmonic excitation and generalized forces of coefficients of the Fourier series can be obtained respectively by using a high precision integration scheme combined with the method of extended homogeneous capacity put forward in this paper.According to the superposition princi- ple and compatibility conditions at the interface between the elastic ring and fluid,the algebraic equation of system can be directly constructed by using the least square approximation.Examples of acoustic radiation from two typical fluid-loaded elastic rings under a harmonic concentrated force are presented.Numerical results show that the method proposed is more efficient than the mixed FE-BE method in common use.展开更多
The impact-sliding wear behavior of steam generator tubes in nuclear power plants is complex owing to the dynamic nature of the mechanical response and self-induced tribological changes.In this study,the effects of im...The impact-sliding wear behavior of steam generator tubes in nuclear power plants is complex owing to the dynamic nature of the mechanical response and self-induced tribological changes.In this study,the effects of impact and sliding velocity on the impact-sliding wear behavior of a 2.25Cr1Mo steel tube are investigated experimentally and numerically.In the experimental study,a wear test rig that can measure changes in the impact and friction forces as well as the compressive displacement over different wear cycles,both in real time,is designed.A semi-analytical model based on the Archard wear law and Hertz contact theory is used to predict wear.The results indicate that the impact dynamic effect by the impact velocity is more significant than that of the sliding velocity,and that both velocities affect the friction force and wear degree.The experimental results for the wear depth evolution agree well with the corresponding simulation predictions.展开更多
Motion responses of two ships advancing parallel in waves with hydrodynamic interactions are investigated in this paper. Within the framework of the frequency-domain potential flow theory, a semi-analytical higher-ord...Motion responses of two ships advancing parallel in waves with hydrodynamic interactions are investigated in this paper. Within the framework of the frequency-domain potential flow theory, a semi-analytical higher-order translating-pulsating source(HOTP) method is presented to solve the problems of coupled radiation and diffraction potential. The method employs nine-node bi-quadratic curvilinear elements to discretize the boundary integral equations(BIEs) constructed over the mean wetted surface of the two ship hulls. In order to eliminate the numerical oscillation, analytical quadrature formulas are derived and adopted to evaluate the integrals related to the Froudedependent part of the Green’s function along the horizontal direction in the BIEs. Based on the method, a numerical program is originally coded. Through the calculations of hydrodynamic responses of single ships, the numerical implementation is proved successful. Then the validated program is applied in the investigations on the hydrodynamic interactions of two identical Wigley Ⅲ hulls and the underway replenishment of a frigate and a supply ship in waves with and without stagger, respectively. The comparison between the present computed results with experimental data and numerical solutions of other methods shows that the semi-analytical HOTP method is of higher accuracy than the pulsating source Green’s function method with speed correction and better stability than the traditional HOTP method based on Gauss quadrature. In addition, for two ships with obviously different dimensions,the influence of hydrodynamic interactions on the smaller ship is found to be more noticeable than that on the larger ship, which leads to the differences between the motions of frigate with and without the presence of supply ship.展开更多
Based on the Hamiltonian governing equations of plane elasticity for sectorial domain, the variable separation and eigenfunction expansion techniques were employed to develop a novel analytical finite element for the ...Based on the Hamiltonian governing equations of plane elasticity for sectorial domain, the variable separation and eigenfunction expansion techniques were employed to develop a novel analytical finite element for the fictitious crack model in fracture mechanics of concrete. The new analytical element can be implemented into FEM program systems to solve fictitious crack propagation problems for concrete cracked plates with arbitrary shapes and loads. Numerical results indicate that the method is more efficient and accurate than ordinary finite element method.展开更多
This work focuses on the fluid-rigid interaction dynamics in the presence of a magnetic field.A rigid thin rectangular column immersed inside stationary metal liquid vibrates with a fixed small amplitude.The magneto-f...This work focuses on the fluid-rigid interaction dynamics in the presence of a magnetic field.A rigid thin rectangular column immersed inside stationary metal liquid vibrates with a fixed small amplitude.The magneto-fluid-solid interaction(MFSI)dynamics issue is studied based on the complex Green’s function method.Considering either the normal or tangential vibration of a column,two types of semi-analytical solutions expressed by stream function integral equations of magnetic corrections,describing the time-displacement history of the column,flow field and electrical potential field of metal fluid and representing transient coupling effects of multi-physics field,are derived,respectively.Nonuniform discretization schemes and an iterative plan are applied to evaluate added damping and inertial loads.The results show that the main factor affecting normal vibration is pressure load,and the main factor affecting tangential vibration is vorticity load.The nonlinear effects of magnetic fields on the dynamics of fluid-rigid thin columns are revealed.The normal vibration exhibits better stability than the tangential vibration under the magnetic field.The induced electrical potential field and current intensity excited by normal vibration are significantly stronger than that of tangential vibration.These semi-analytical solutions can be applied as benchmarks in future validation and verification works for MFSI numerical algorithms for magnetic confinement nuclear fusion science.展开更多
基金Project supported by the National Natural Science Foundation of China(No.10172038),the Doctoral Foundation ofthe National Education Ministry(No.20040487013)and the Natural Science Foundation of Guangxi(No.0339019).
文摘Based on the extended homogeneous capacity high precision integration method and the spectrum method of virtual boundary with a complex radius vector, a novel semi-analytical method, which has satisfactory computation efectiveness and precision, is presented for solving the acoustic radiation from a submerged infnite non-circular cylindrical shell stifened by longitudinal ribs by means of the Fourier integral transformation and stationary phase method. In this work, besides the normal interacting force, which is commonly adopted by some researchers, the other interacting forces and moments between the longitudinal ribs and the non-circular cylindrical shell are considered at the same time. The efects of the number and the size of the cross-section of longitudinal ribs on the characteristics of acoustic radiation are investigated. Numerical results show that the method proposed is more efcient than the existing mixed FE-BE method.
基金Project supported by the National Natural Science Foundation of China （Grant No. 10202013）
文摘The effect of axial shallow groove on the nonlinear dynamic response and buckling of laminated cylindrical shells subjected to radial compression loading was investigated. Based on the first-order shear deformation theory （FSDT）, the nonlinear dynamic equations involving the transverse shear deformation and initial geometric imperfections were derived with the Hamilton philosophy. The axial shallow groove of the laminated composite cylindrical shell was treated as the initial geometric imperfections in the dynamic equations. A semi-analytical method of expanding displacements and loads along the circumferential direction and employing the finite difference method along the axial direction and in the time domain is used to solve the governing equations and obtain the dynamic response of the laminated shell. The B-R criterion was employed to determine the critical loads of dynamic buckling of the shell. The effects of the parameters of the shallow groove on the dynamic response and buckling were discussed in this paper and the results show that the axial shallow grooves greatly affect the dynamic response and buckling.
基金financially supported by the National Sci-Tech Support Plan(No.2015BAF06B01)。
文摘In this paper,a semi-analytical method was proposed to evaluate the acoustic nonlinearity parameter for single crystals of Cu,Ag and Au.The acoustic nonlinearity parameter can be derived analytically by general expressions in terms of the interatomic potentials with the distances between each pair of atoms in these transition metals.To evaluate the acoustic nonlinearity parameter,one needs to conduct one step molecular static simulation and obtain the equilibrium positions of all the atoms.Further,based on this method,numerical experiments with molecular dynamic code LAMMPS were given to compute the acoustic nonlinearity parameter of Cu,Ag and Au.To illustrate the validity of these expressions,comparison was made between calculation results and data in the literature.Reasonable agreement is observed.Because of the analytical nature of this method,it provides a fundamental understanding of the nonlinear elastic behavior of these transition metals.
基金financially supported by the Project of"Nonlinear Wave Excitation and Response of Surface Vehicle"(Grant No.B2420132001)the Natural Science Foundation of Tianjin(Grant No.15JCQNJC07700)
文摘The PDFs(probability density functions) and probability of a ship rolling under the random parametric and forced excitations were studied by a semi-analytical method. The rolling motion equation of the ship in random oblique waves was established. The righting arm obtained by the numerical simulation was approximately fitted by an analytical function. The irregular waves were decomposed into two Gauss stationary random processes, and the CARMA(2, 1) model was used to fit the spectral density function of parametric and forced excitations. The stochastic energy envelope averaging method was used to solve the PDFs and the probability. The validity of the semi-analytical method was verified by the Monte Carlo method. The C11 ship was taken as an example, and the influences of the system parameters on the PDFs and probability were analyzed. The results show that the probability of ship rolling is affected by the characteristic wave height, wave length, and the heading angle. In order to provide proper advice for the ship’s manoeuvring, the parametric excitations should be considered appropriately when the ship navigates in the oblique seas.
文摘In this paper,a semi-analytical method is presented for free vibration and buckling analysis of functionally graded(FG)size-dependent nanobeams based on the physical neutral axis position.It is the first time that a semi-analytical differential transform method(DTM)solution is developed for the FG nanobeams vibration and buckling analysis.Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form.The physical neutral axis position for mentioned FG nanobeams is determined.The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen.The nonlocal equations of motion are derived through Hamilton’s principle and they are solved applying DTM.It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of FG nanobeams.The good agreement between the results of this article and those available in literature validated the presented approach.The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as neutral axis position,small scale effects,the material distribution profile,mode number,thickness ratio and boundary conditions on the normalized natural frequencies and dimensionless buckling load of the FG nanobeams in detail.It is explicitly shown that the vibration and buckling behaviour of a FG nanobeams is significantly influenced by these effects.
文摘The aim of this paper is to introduce a new semi-analytical method,namely PIMOL(precise integration method of lines,the parametric finite difference method of lines based on the precise integration method),which is developed and used to solve the ordinary differential equation(ODEs)systems based on the finite difference method of lines and the precise integration method(PIM).Two examples of Poisson^equation problems are given:a boundary value problem and an ODE eigenvalue problem.The PIMOL can effectively reduce a semi-discrete ODE problem to a linear algebraic matrix equation.Numerical results show that the PIMOL is a powerful method.
文摘Dual vectors are applied in Hamilton system of applied mechanics. Electric and magnetic field vectors are the dual vectors in electromagnetic field. The Hamilton system method is introduced into the analysis of electromagnetism waveguide with inhomogeneous materials. The transverse electric and magnetic fields are regarded as the dual. The basic equations are solved in Hamilton system and symplectic geometry. With the Hamilton variational principle, the symplectic semi_analytical equations are derived and preserve their symplectic structures. The given numerical example demonstrates the solution of LSE (Longitudinal Section Electric) mode in a dielectric waveguide. (
文摘Recently, pH-sensitive hydrogels have been utilized in the diverse applications including sensors, switches, and actuators. In order to have continuous stress and deformation ?elds, a new semi-analytical approach is developed to predict the swelling induced?nite bending for a functionally graded(FG) layer composed of a pH-sensitive hydrogel,in which the cross-link density is continuously distributed along the thickness direction under the plane strain condition. Without considering the intermediary virtual reference,the initial state is mapped into the deformed con?guration in a circular shape by utilizing a total deformation gradient tensor stemming from the inhomogeneous swelling of an FG layer in response to the variation of the pH value of the solvent. To enlighten the capability of the presented analytical method, the ?nite element method(FEM) is used to verify the accuracy of the analytical results in some case studies. The perfect agreement con-?rms the accuracy of the presented method. Due to the applicability of FG pH-sensitive hydrogels, some design factors such as the semi-angle, the bending curvature, the aspect ratio, and the distributions of deformation and stress ?elds are studied. Furthermore, the tangential free-stress axes are illustrated in deformed con?guration.
基金supported by the National Natural Science Foundation of China(Grant No.11304169)the Natural Science Foundation of Ningbo City,China(Grant No.2012A610178)+1 种基金the Open Foundation of the Most Important Subjects of Zhejiang Province,China(Grant No.xkzwl1505)K.C.Wong Magna Fund in Ningbo University of China
文摘We present a semi-analytical method of calculating the electrostatic interaction of colloid solutions for confined and unconfined systems. We expand the electrostatic potential of the system in terms of some basis functions such as spherical harmonic function and cylinder function. The expansion coefficients can be obtained by solving the equations of the boundary conditions, combining an analytical translation transform of the coordinates and a numerical multipoint collection method. The precise electrostatic potential and the interaction energy are then obtained automatically. The method is available not only for the uniformly charged colloids but also for nonuniformly charged ones. We have successfully applied it to unconfined diluted colloid system and some confined systems such as the long cylinder wall confinement, the air–water interfacial confinement and porous membrane confinement. The consistence checks of our calculations with some known analytical cases have been made for all our applications. In theory, the method is applicable to any dilute colloid solutions with an arbitrary distribution of the surface charge on the colloidal particle under a regular solid confinement, such as spherical cavity confinement and lamellar confinement.
文摘This paper presents the theory and applications of a new computational technique referred to as Differential Transform Method (DTM) for solving second order linear ordinary differential equations, for both homogeneous and nonhomogeneous cases. For the robustness and efficiency of the method, four examples are considered. The results indicate that the DTM is reliable and accurate when compared to the exact solutions of the solved problems.
基金supported by the Major Research Project on Scientific Instrument Development of the National Natural Science Foundation of China(42327901)National Natural Science Foundation of China(42030806,42074120,41904104,423B2405).
文摘The electromagnetic(EM)telemetry systems,employed for real-time data transmission from the borehole and the earth surface during drilling,are widely used in measurement-while-drilling(MWD)and logging-while-drilling(LWD).Several numerical methods,including the method of moments(MoM),the electric field integral equation(EFIE)method,and the finite-element(FE)method have been developed for the simulation of EM telemetry systems.The computational process of these methods is complicated and time-consuming.To solve this problem,we introduce an axisymmetric semi-analytical FE method(SAFEM)in the cylindrical coordinate system with the virtual layering technique for rapid simulation of EM telemetry in a layered earth.The proposed method divides the computational domain into a series of homogeneous layers.For each layer,only its cross-section is discretized,and a high-precision integration method based on Riccati equations is employed for the calculation of longitudinally homogeneous sections.The block-tridiagonal structure of the global coefficient matrix enables the use of the block Thomas algorithm,facilitating the efficient simulation of EM telemetry problems in layered media.After the theoretical development,we validate the accuracy and efficiency of our algorithm through a series of numerical experiments and comparisons with the Multiphysics modeling software COMSOL.We also discussed the impact of system parameters on EM telemetry signal and demonstrated the applicability of our method by testing it on a field dataset acquired from Dezhou,Shandong Province,China.
基金Project supported by the Natural Science Foundation of China(Grant No.51179125)the Greative Research Groups of the Natural Science Foundation of China(Grant No.51621092)the Natural Science Foundation of Tianjin(Grant No.16JCYBJC21200)
文摘The three-dimensional natural vibration characteristics of water inside a moon pool of an ocean structures are studied. The governing equations are derived based on the linear potential flow theory, and the boundary condition of the total opening bottom suggested by Molin is adopted. A semi-analytical method is used to solve the governing equations, and the natural frequencies and the motion modes are obtained. Two types of motions are studied： （1） the piston motion in the vertical direction, and （2） the sloshing motion of the free surface. The influences of moon pool＇s structural parameters on the natural frequencies, and the modal shapes are analyzed.
文摘In this paper,a semi-analytical method for the forced vibration analysis of cracked laminated composite beam(CLCB)is investigated.One computational model is formulated by Timoshenko beam theory and its dynamic solution is solved using the Jacobi-Ritz method.The boundary conditions(BCs)at both ends of the CLCB are generalized by the application of artificial elastic springs,the CLCB is separated into two elements along the crack,the flexibility coefficient of fracture theory is used to model the essential continuous condition of the connective interface.All the allowable displacement functions used to analyze dynamic characteristics of CLCB are expressed by classical Jacobi orthogonal polynomials in a more general form.The accuracy of the proposed method is verified through the compare with results of the finite element method(software ABAQUS is used in this paper).On this basis,the parametric study for dynamic analysis characteristics of CLCB is performed to provide reference datum for engineers.
文摘A semi-analytical and semi-numerical method is proposed for the dynamic analysis of foundations. The Lamb＇s solution and the approximate formulae were used to establish the relation of the contact force and deflection between the foundation and soil. Therefore, the foundation can be separated from soil and analyzed by FEM as for the static cases. The plate can be treated as that the known forces are acting on the upper surface, and the contact pressure from soil can be represented as the deflection. So that only the plate needs to be divided into elements in the analysis. By this method, a series of vibration problems, including various shapes and rigidities of foundations, different excitation frequencies, were analyzed. Furthermore, it can be used for the embedded foundation. The numerical examples show that this method has simplicity, highly accurate and versatile. It is an effective method for the dynamic analysis of foundations.
基金This project is supported by National Natural Science Foundation of China(Nos.52005057 and 51975063)the Fundamental Research Funds for the Central Universities(Nos.2020CDJQY-A069 and 2021CDJGXB 008).
文摘Butterfly wings are closely related to the premature failure of rolling element bearings.In this study,butterfly formation is investigated using the developed semi-analytical three-dimensional(3D)contact model incorporating inclusion and material property degradation.The 3D elastic field introduced by inhomogeneous inclusion is solved by using numerical approaches,which include the equivalent inclusion method(EIM)and the conjugate gradient method(CGM).The accumulation of fatigue damage surrounding inclusions is described using continuum damage mechanics.The coupling between the development of the damaged zone and the stress field is considered.The effects of the inclusion properties on the contact status and butterfly formation are discussed in detail.The model provides a potential method for quantifying material defects and fatigue behavior in terms of the deterioration of material properties.
基金Project supported by the National Natural Science Foundation of China (No.10172038)
文摘Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harmonic excitation.Within any integration segment, as long as its length is small enough,along the circumferential curvilinear coordinate,the non- homogeneous matrix differential equation of an elastic ring of complex geometrical shape can be rewritten in terms of the homogeneous one by the method of extended homogeneous capacity proposed in this paper.For the exterior fluid domain,the multi-circular virtual source simulation technique is adopted.The source density distributed on each virtual circular curve may be ex- panded as the Fourier's series.Combining with the inverse fast Fourier transformation,a higher accuracy and efficiency method for solving 2-D exterior Helmholtz's problems is presented in this paper.In the aspect of solution to the coupling equations,the state vectors of elastic ring induced by the given harmonic excitation and generalized forces of coefficients of the Fourier series can be obtained respectively by using a high precision integration scheme combined with the method of extended homogeneous capacity put forward in this paper.According to the superposition princi- ple and compatibility conditions at the interface between the elastic ring and fluid,the algebraic equation of system can be directly constructed by using the least square approximation.Examples of acoustic radiation from two typical fluid-loaded elastic rings under a harmonic concentrated force are presented.Numerical results show that the method proposed is more efficient than the mixed FE-BE method in common use.
基金This study is supported by the National Natural Science Foundation of China(No.U1530136)Young Scientific Innovation Team of Science and Technology of Sichuan(No.2017TD0017)The author Meigui YIN acknowledges the financial support from the China Scholarship Council(CSC No.201907000021).
文摘The impact-sliding wear behavior of steam generator tubes in nuclear power plants is complex owing to the dynamic nature of the mechanical response and self-induced tribological changes.In this study,the effects of impact and sliding velocity on the impact-sliding wear behavior of a 2.25Cr1Mo steel tube are investigated experimentally and numerically.In the experimental study,a wear test rig that can measure changes in the impact and friction forces as well as the compressive displacement over different wear cycles,both in real time,is designed.A semi-analytical model based on the Archard wear law and Hertz contact theory is used to predict wear.The results indicate that the impact dynamic effect by the impact velocity is more significant than that of the sliding velocity,and that both velocities affect the friction force and wear degree.The experimental results for the wear depth evolution agree well with the corresponding simulation predictions.
基金This work was financially supported by the National Natural Science Foundation of China(Grant No.52101357)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(Grant No.21KJB580012)the Scientific Research Start-up Fund of Jiangsu University of Science and Technology.
文摘Motion responses of two ships advancing parallel in waves with hydrodynamic interactions are investigated in this paper. Within the framework of the frequency-domain potential flow theory, a semi-analytical higher-order translating-pulsating source(HOTP) method is presented to solve the problems of coupled radiation and diffraction potential. The method employs nine-node bi-quadratic curvilinear elements to discretize the boundary integral equations(BIEs) constructed over the mean wetted surface of the two ship hulls. In order to eliminate the numerical oscillation, analytical quadrature formulas are derived and adopted to evaluate the integrals related to the Froudedependent part of the Green’s function along the horizontal direction in the BIEs. Based on the method, a numerical program is originally coded. Through the calculations of hydrodynamic responses of single ships, the numerical implementation is proved successful. Then the validated program is applied in the investigations on the hydrodynamic interactions of two identical Wigley Ⅲ hulls and the underway replenishment of a frigate and a supply ship in waves with and without stagger, respectively. The comparison between the present computed results with experimental data and numerical solutions of other methods shows that the semi-analytical HOTP method is of higher accuracy than the pulsating source Green’s function method with speed correction and better stability than the traditional HOTP method based on Gauss quadrature. In addition, for two ships with obviously different dimensions,the influence of hydrodynamic interactions on the smaller ship is found to be more noticeable than that on the larger ship, which leads to the differences between the motions of frigate with and without the presence of supply ship.
文摘Based on the Hamiltonian governing equations of plane elasticity for sectorial domain, the variable separation and eigenfunction expansion techniques were employed to develop a novel analytical finite element for the fictitious crack model in fracture mechanics of concrete. The new analytical element can be implemented into FEM program systems to solve fictitious crack propagation problems for concrete cracked plates with arbitrary shapes and loads. Numerical results indicate that the method is more efficient and accurate than ordinary finite element method.
基金supported by the National Natural Science Foundation of China(Grant Nos.52176089 and U23B20110).
文摘This work focuses on the fluid-rigid interaction dynamics in the presence of a magnetic field.A rigid thin rectangular column immersed inside stationary metal liquid vibrates with a fixed small amplitude.The magneto-fluid-solid interaction(MFSI)dynamics issue is studied based on the complex Green’s function method.Considering either the normal or tangential vibration of a column,two types of semi-analytical solutions expressed by stream function integral equations of magnetic corrections,describing the time-displacement history of the column,flow field and electrical potential field of metal fluid and representing transient coupling effects of multi-physics field,are derived,respectively.Nonuniform discretization schemes and an iterative plan are applied to evaluate added damping and inertial loads.The results show that the main factor affecting normal vibration is pressure load,and the main factor affecting tangential vibration is vorticity load.The nonlinear effects of magnetic fields on the dynamics of fluid-rigid thin columns are revealed.The normal vibration exhibits better stability than the tangential vibration under the magnetic field.The induced electrical potential field and current intensity excited by normal vibration are significantly stronger than that of tangential vibration.These semi-analytical solutions can be applied as benchmarks in future validation and verification works for MFSI numerical algorithms for magnetic confinement nuclear fusion science.
