Taking the Konopelchenko-Dubrovsky system as a simple example, some familles of rational formal hyperbolic function solutions, rational formal triangular periodic solutions, and rational solutions are constructed by u...Taking the Konopelchenko-Dubrovsky system as a simple example, some familles of rational formal hyperbolic function solutions, rational formal triangular periodic solutions, and rational solutions are constructed by using the extended Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.展开更多
Nonlinear interactions among incident wave, tank-sloshing and floating body coupling motion are investigated. The fully nonlinear sloshing and body-surface nonlinear free surface hydrodynamics is simulated using a Non...Nonlinear interactions among incident wave, tank-sloshing and floating body coupling motion are investigated. The fully nonlinear sloshing and body-surface nonlinear free surface hydrodynamics is simulated using a Non-Uniform Rational B-Spline （NURBS） higher-order panel method in time domain based on the potential theory. A robust and stable improved iterative procedure （Yan and Ma, 2007） for floating bodies is used for calculating the time derivative of velocity potential and floating body motion. An energy dissipation condition based on linear theory adopted by Huang （2011） is developed to consider flow viscosity effects of sloshing flow in nonlinear model. A two-dimensional tank model test was performed to identify its validity. The present nonlinear coupling sway motion results are subsequently compared with the corresponding Rognebakke and Faltinsen （2003）＇s experimental results, showing fair agreement. Thus, the numerical approach presented in this paper is expected to be very efficient and realistic in evaluating the coupling effects of nonlinear sloshing and body motion.展开更多
In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons ＆ Fractals 25 （2005） 1019] to uniformly const...In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons ＆ Fractals 25 （2005） 1019] to uniformly construct a series of stochastic nontravelling wave solutions for nonlinear stochastic evolution equation. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions including a series of rational formal nontraveling wave and coefficient functions＇ soliton-like solution.s and trigonometric-like function solutions. The method can also be applied to solve other nonlinear stochastic evolution equation or equations.展开更多
The stability of dams and their foundations is an important problem to which dam engineers have paid close attention over the years. This paper presented two methods to analyze the stability of a gravity dam and its f...The stability of dams and their foundations is an important problem to which dam engineers have paid close attention over the years. This paper presented two methods to analyze the stability of a gravity dam and its foundation. The direct analysis method was based on a rigid limit equilibrium method which regarded both dam and the rock foundation as undeformable rigid bodies. In this method, the safety factor of potential sliding surfaces was computed directly. The second method, the indirect analysis method, was based on elasto-plastic theory and employs nonlinear finite element method (FEM) in the analysis of stresses and deformation in the dam and its foundation. The determination of the safety degree of the structure was based on the convergence and abrupt the change criterion. The results obtained showed that structures' constituent material behavior played an active role in the failure of engineered structures in addition to the imposed load.展开更多
As a solution to the breaking of pipeline under high axial force,carbon fiber composite pipe with low density and high intensity is applied to deep-sea mining transporting system.Based on the fact that the transportin...As a solution to the breaking of pipeline under high axial force,carbon fiber composite pipe with low density and high intensity is applied to deep-sea mining transporting system.Based on the fact that the transporting pipe is under the forces of gravity,inner liquid,buoyancy as well as hydrodynamic force,geometric nonlinear finite element theory has been applied to analyzing the transporting system.Conclusions can be drawn as follows.Under the interaction of waves and currents,node forces FX and FZ acted by the transporting pipe on the mining vehicle are less than 2 kN,which indicates that waves and currents have little influence on the spatial shape of the transporting pipe and the mining vehicle movement.On the other hand,the horizontal force acting on the mining ship could be as large as 106 830 N,which has great influence on the mining system.展开更多
The rational solutions for the discrete Painlevé Ⅱ equation are constructed based on the bilinear formalism. It is shown that they are expressed by a determinant whose entries are given by the Laguerre Polynomials.
In this paper, two (3+1)-dimensional equations are investigated.Auto-Baecklund transformation is obtained, which is used with some ansatze to seek new types ofexact solutions including some arbitrary functions. When t...In this paper, two (3+1)-dimensional equations are investigated.Auto-Baecklund transformation is obtained, which is used with some ansatze to seek new types ofexact solutions including some arbitrary functions. When these arbitrary functions are taken assome special functions, these solutions possess abundant structures. These solutions containsoliton-like solutions and rational solutions.展开更多
In this paper, based on a new more general ansitz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution eq...In this paper, based on a new more general ansitz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution equations with nonlinear terms of any order. Compared with most existing tanh methods for finding travelling wave solutions, the proposed method not only recovers the results by most known algebraic methods, but also provides new and more general solutions. We choose the generalized Burgers-Fisher equation with nonlinear terms of any order to illustrate our method. As a result, we obtain several new kinds of exact solutions for the equation. This approach can also be applied to other nonlinear evolution equations with nonlinear terms of any order.展开更多
The new rational form solutions to the elliptic equation are shown, and then these solutions to the elliptic equation are taken as a transformation and applied to solve nonlinear coupled wave equations. It is shown th...The new rational form solutions to the elliptic equation are shown, and then these solutions to the elliptic equation are taken as a transformation and applied to solve nonlinear coupled wave equations. It is shown that more novel kinds of solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form,and so on.展开更多
In this paper, a further extended Jacobi elliptic function rationM expansion method is proposed for constructing new forms of exact solutions to nonlinear partial differential equations by making a more general transf...In this paper, a further extended Jacobi elliptic function rationM expansion method is proposed for constructing new forms of exact solutions to nonlinear partial differential equations by making a more general transformation. For illustration, we apply the method to （2＋1）-dimensionM dispersive long wave equation and successfully obtain many new doubly periodic solutions. When the modulus m→1, these sohitions degenerate as soliton solutions. The method can be also applied to other nonlinear partial differential equations.展开更多
Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous.Although a considerable amount of research has been carried ...Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous.Although a considerable amount of research has been carried out in the field of nonlinear differential-difference equations,the majority of the results deal with polynomial types.Limited research has been reported regarding such equations of rational type.In this paper we present an adaptation of the(G /G)-expansion method to solve nonlinear rational differential-difference equations.The procedure is demonstrated using two distinct equations.Our approach allows one to construct three types of exact traveling wave solutions(hyperbolic,trigonometric,and rational) by means of the simplified form of the auxiliary equation method with reduced parameters.Our analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well.展开更多
The aim of this paper is to study 6-canonical system of a nonsingular minimal 3-fold X. If|2Kx|is not composed of pencils, it is shown that is birational with possible exceptionsfor:
In this paper, the failure mechanisms of full-size concrete filled steel tubes(CFST) under uniaxial compression were investigated with nonlinear finite element method. Existing experimental results were employed to ve...In this paper, the failure mechanisms of full-size concrete filled steel tubes(CFST) under uniaxial compression were investigated with nonlinear finite element method. Existing experimental results were employed to verify the validity of the finite element models of CFST specimens. Then, the numerical analysis was further conducted to study the mechanical behaviors of full-size CFST columns with circular and square cross sections under uniaxial compression. The simulation results indicate that the distribution of the contact pressure between circular steel tube and core concrete is much more uniform than that between square steel tube and concrete, resulting in much higher confinement and more efficient interaction between steel tube and core concrete in circular CFST columns, as well as ultimate load capacity and ultimate displacement. Extensive parametric analysis was also conducted to examine the effect of various parameters on the uniaxial compression behaviors of circular and square CFST columns.展开更多
In this paper, the authors are concerned with the forced isochronous oscillators with a repulsive singularity and a bounded nonlinearity x'' + V'(x) + g(x) = e(t, x, x'),where the assumptions on V, g a...In this paper, the authors are concerned with the forced isochronous oscillators with a repulsive singularity and a bounded nonlinearity x'' + V'(x) + g(x) = e(t, x, x'),where the assumptions on V, g and e are regular, described precisely in the introduction.Using a variant of Moser's twist theorem of invariant curves, the authors show the existence of quasi-periodic solutions and boundedness of all solutions. This extends the result of Liu to the case of the above system where e depends on the velocity.展开更多
Considering a spherical planet with a liquid core surrounded by a solid shell,we developed a quasi-static model to investigate the deformation of the double-layered planet with self-gravity and obtained the boundary v...Considering a spherical planet with a liquid core surrounded by a solid shell,we developed a quasi-static model to investigate the deformation of the double-layered planet with self-gravity and obtained the boundary value problem about radial equilibrium,which is solved by the numerical methods.The effects of governing parameters about geometry,density and bulk modulus on the deformation of the planet with self-gravity were discussed.In addition,we also developed the incremental equation theory to investigate the stability of the double-layered planet under its own gravity.It is concluded that instability is more likely to occur on the planet with smaller liquid cores when the outer radius and density of the planets are constant.Although we only study special double-layered planets,these methods can be conveniently extended to complex multi-layered planets.展开更多
基金The project partially supported by the State Key Basic Research Program of China under Grant No. 2004CB318000
文摘Taking the Konopelchenko-Dubrovsky system as a simple example, some familles of rational formal hyperbolic function solutions, rational formal triangular periodic solutions, and rational solutions are constructed by using the extended Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.
基金Foundation item： Supported by the National Natural Science Foundation of China （Grant No. 51079032） and the ＂111 project＂ （Grant No. B07019）.
文摘Nonlinear interactions among incident wave, tank-sloshing and floating body coupling motion are investigated. The fully nonlinear sloshing and body-surface nonlinear free surface hydrodynamics is simulated using a Non-Uniform Rational B-Spline （NURBS） higher-order panel method in time domain based on the potential theory. A robust and stable improved iterative procedure （Yan and Ma, 2007） for floating bodies is used for calculating the time derivative of velocity potential and floating body motion. An energy dissipation condition based on linear theory adopted by Huang （2011） is developed to consider flow viscosity effects of sloshing flow in nonlinear model. A two-dimensional tank model test was performed to identify its validity. The present nonlinear coupling sway motion results are subsequently compared with the corresponding Rognebakke and Faltinsen （2003）＇s experimental results, showing fair agreement. Thus, the numerical approach presented in this paper is expected to be very efficient and realistic in evaluating the coupling effects of nonlinear sloshing and body motion.
基金The author would like to thank the referees very much for their careful reading of the manuscript and many valuable suggestions.
文摘In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons ＆ Fractals 25 （2005） 1019] to uniformly construct a series of stochastic nontravelling wave solutions for nonlinear stochastic evolution equation. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions including a series of rational formal nontraveling wave and coefficient functions＇ soliton-like solution.s and trigonometric-like function solutions. The method can also be applied to solve other nonlinear stochastic evolution equation or equations.
文摘The stability of dams and their foundations is an important problem to which dam engineers have paid close attention over the years. This paper presented two methods to analyze the stability of a gravity dam and its foundation. The direct analysis method was based on a rigid limit equilibrium method which regarded both dam and the rock foundation as undeformable rigid bodies. In this method, the safety factor of potential sliding surfaces was computed directly. The second method, the indirect analysis method, was based on elasto-plastic theory and employs nonlinear finite element method (FEM) in the analysis of stresses and deformation in the dam and its foundation. The determination of the safety degree of the structure was based on the convergence and abrupt the change criterion. The results obtained showed that structures' constituent material behavior played an active role in the failure of engineered structures in addition to the imposed load.
基金Project(50975290) supported by the National Natural Science Foundation of ChinaProject(2011QNZT057) supported by the Basic Operational Cost of Special Research Funding of Central Universities in ChinaProject(11JJ5028) supported by Hunan Provincial Natural Science Foundation,China
文摘As a solution to the breaking of pipeline under high axial force,carbon fiber composite pipe with low density and high intensity is applied to deep-sea mining transporting system.Based on the fact that the transporting pipe is under the forces of gravity,inner liquid,buoyancy as well as hydrodynamic force,geometric nonlinear finite element theory has been applied to analyzing the transporting system.Conclusions can be drawn as follows.Under the interaction of waves and currents,node forces FX and FZ acted by the transporting pipe on the mining vehicle are less than 2 kN,which indicates that waves and currents have little influence on the spatial shape of the transporting pipe and the mining vehicle movement.On the other hand,the horizontal force acting on the mining ship could be as large as 106 830 N,which has great influence on the mining system.
文摘The rational solutions for the discrete Painlevé Ⅱ equation are constructed based on the bilinear formalism. It is shown that they are expressed by a determinant whose entries are given by the Laguerre Polynomials.
文摘In this paper, two (3+1)-dimensional equations are investigated.Auto-Baecklund transformation is obtained, which is used with some ansatze to seek new types ofexact solutions including some arbitrary functions. When these arbitrary functions are taken assome special functions, these solutions possess abundant structures. These solutions containsoliton-like solutions and rational solutions.
基金The project partially supported by the State Key Basic Research Program of China under Grant No. 2004CB318000
文摘In this paper, based on a new more general ansitz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution equations with nonlinear terms of any order. Compared with most existing tanh methods for finding travelling wave solutions, the proposed method not only recovers the results by most known algebraic methods, but also provides new and more general solutions. We choose the generalized Burgers-Fisher equation with nonlinear terms of any order to illustrate our method. As a result, we obtain several new kinds of exact solutions for the equation. This approach can also be applied to other nonlinear evolution equations with nonlinear terms of any order.
文摘The new rational form solutions to the elliptic equation are shown, and then these solutions to the elliptic equation are taken as a transformation and applied to solve nonlinear coupled wave equations. It is shown that more novel kinds of solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form,and so on.
基金The project partially supported by the State Key Basic Research Program of China under Grant No. 2004 CB 318000
文摘In this paper, a further extended Jacobi elliptic function rationM expansion method is proposed for constructing new forms of exact solutions to nonlinear partial differential equations by making a more general transformation. For illustration, we apply the method to （2＋1）-dimensionM dispersive long wave equation and successfully obtain many new doubly periodic solutions. When the modulus m→1, these sohitions degenerate as soliton solutions. The method can be also applied to other nonlinear partial differential equations.
文摘Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous.Although a considerable amount of research has been carried out in the field of nonlinear differential-difference equations,the majority of the results deal with polynomial types.Limited research has been reported regarding such equations of rational type.In this paper we present an adaptation of the(G /G)-expansion method to solve nonlinear rational differential-difference equations.The procedure is demonstrated using two distinct equations.Our approach allows one to construct three types of exact traveling wave solutions(hyperbolic,trigonometric,and rational) by means of the simplified form of the auxiliary equation method with reduced parameters.Our analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well.
文摘The aim of this paper is to study 6-canonical system of a nonsingular minimal 3-fold X. If|2Kx|is not composed of pencils, it is shown that is birational with possible exceptionsfor:
基金supported by the National Natural Science Foundation of China(Grant No.51278118)the Natural Science Foundation of Jiangsu Province(Grant No.BK2012756)the Scientific Research Project of Ministry of Education(Grant No.113029A)
文摘In this paper, the failure mechanisms of full-size concrete filled steel tubes(CFST) under uniaxial compression were investigated with nonlinear finite element method. Existing experimental results were employed to verify the validity of the finite element models of CFST specimens. Then, the numerical analysis was further conducted to study the mechanical behaviors of full-size CFST columns with circular and square cross sections under uniaxial compression. The simulation results indicate that the distribution of the contact pressure between circular steel tube and core concrete is much more uniform than that between square steel tube and concrete, resulting in much higher confinement and more efficient interaction between steel tube and core concrete in circular CFST columns, as well as ultimate load capacity and ultimate displacement. Extensive parametric analysis was also conducted to examine the effect of various parameters on the uniaxial compression behaviors of circular and square CFST columns.
基金supported by the National Natural Science Foundation of China(No.10325103)the Chinese Scholarship Council(No.201206010092)
文摘In this paper, the authors are concerned with the forced isochronous oscillators with a repulsive singularity and a bounded nonlinearity x'' + V'(x) + g(x) = e(t, x, x'),where the assumptions on V, g and e are regular, described precisely in the introduction.Using a variant of Moser's twist theorem of invariant curves, the authors show the existence of quasi-periodic solutions and boundedness of all solutions. This extends the result of Liu to the case of the above system where e depends on the velocity.
基金supported by the Science Foundation of National Key Laboratory of Science and Technology on advanced composites in special environments,and Heilongjiang Touyan Innovation Team Program.
文摘Considering a spherical planet with a liquid core surrounded by a solid shell,we developed a quasi-static model to investigate the deformation of the double-layered planet with self-gravity and obtained the boundary value problem about radial equilibrium,which is solved by the numerical methods.The effects of governing parameters about geometry,density and bulk modulus on the deformation of the planet with self-gravity were discussed.In addition,we also developed the incremental equation theory to investigate the stability of the double-layered planet under its own gravity.It is concluded that instability is more likely to occur on the planet with smaller liquid cores when the outer radius and density of the planets are constant.Although we only study special double-layered planets,these methods can be conveniently extended to complex multi-layered planets.
