We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the auth...We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the authors. Under this topology X becomes a Frechet space Apart from finding the characterization of continuous linear functionals, linear transformation on X, we have obtained the necessary and sufficient conditions for a double sequence in X to be a proper bases.展开更多
A problem of topology identification for complex dynamical networks is investigated in this paper. An adaptive observer is proposed to identify the topology of a complex dynamical networks based on the Lyapunov stabil...A problem of topology identification for complex dynamical networks is investigated in this paper. An adaptive observer is proposed to identify the topology of a complex dynamical networks based on the Lyapunov stability theory. Here the output of the network and the states of the observer are used to construct the updating law of the topology such that the communication resources from the network to its observer are saved. Some convergent criteria of the adaptive observer are derived in the form of linear inequality matrices. Several numerical examples are shown to demonstrate the effectiveness of the proposed observer.展开更多
In this paper, based on the conjugate of the complex basis function, a new complex variable moving least-squares approximation is discussed. Then using the new approximation to obtain the shape function, an improved c...In this paper, based on the conjugate of the complex basis function, a new complex variable moving least-squares approximation is discussed. Then using the new approximation to obtain the shape function, an improved complex variable element-free Galerkin（ICVEFG） method is presented for two-dimensional（2D） elastoplasticity problems. Compared with the previous complex variable moving least-squares approximation, the new approximation has greater computational precision and efficiency. Using the penalty method to apply the essential boundary conditions, and using the constrained Galerkin weak form of 2D elastoplasticity to obtain the system equations, we obtain the corresponding formulae of the ICVEFG method for 2D elastoplasticity. Three selected numerical examples are presented using the ICVEFG method to show that the ICVEFG method has the advantages such as greater precision and computational efficiency over the conventional meshless methods.展开更多
Based on the complex variable moving least-square（CVMLS） approximation and a local symmetric weak form,the complex variable meshless local Petrov-Galerkin（CVMLPG） method of solving two-dimensional potential proble...Based on the complex variable moving least-square（CVMLS） approximation and a local symmetric weak form,the complex variable meshless local Petrov-Galerkin（CVMLPG） method of solving two-dimensional potential problems is presented in this paper.In the present formulation,the trial function of a two-dimensional problem is formed with a one-dimensional basis function.The number of unknown coefficients in the trial function of the CVMLS approximation is less than that in the trial function of the moving least-square（MLS） approximation.The essential boundary conditions are imposed by the penalty method.The main advantage of this approach over the conventional meshless local Petrov-Galerkin（MLPG） method is its computational efficiency.Several numerical examples are presented to illustrate the implementation and performance of the present CVMLPG method.展开更多
This paper, at the first time, considers the problem of decentralized variable structure control of complex giant singular uncertainty systems by using the property of diagonally dominant matrix and Frobenius-Person t...This paper, at the first time, considers the problem of decentralized variable structure control of complex giant singular uncertainty systems by using the property of diagonally dominant matrix and Frobenius-Person theorem. The splendid selection of switching manifold for each subsystem makes the design relatively straightforward and can be easily realized. An illustrate example is given.展开更多
In this paper, structure identification of an uncertain network coupled with complex-variable chaotic systems is in- vestigated. Both the topological structure and the system parameters can be unknown and need to be i...In this paper, structure identification of an uncertain network coupled with complex-variable chaotic systems is in- vestigated. Both the topological structure and the system parameters can be unknown and need to be identified. Based on impulsive stability theory and the Lyapunov function method, an impulsive control scheme combined with an adaptive strategy is adopted to design effective and universal network estimators. The restriction on the impulsive interval is relaxed by adopting an adaptive strategy. Further, the proposed method can monitor the online switching topology effectively. Several numerical simulations are provided to illustrate the effectiveness of the theoretical results.展开更多
The complex variable reproducing kernel particle method （CVRKPM） of solving two-dimensional variable coefficient advection-diffusion problems is presented in this paper. The advantage of the CVRKPM is that the shape...The complex variable reproducing kernel particle method （CVRKPM） of solving two-dimensional variable coefficient advection-diffusion problems is presented in this paper. The advantage of the CVRKPM is that the shape function of a two-dimensional problem is formed with a one-dimensional basis function. The Galerkin weak form is employed to obtain the discretized system equation, and the penalty method is used to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional variable coefficient advection-diffusion problems are obtained. Two numerical examples are given to show that the method in this paper has greater accuracy and computational efficiency than the conventional meshless method such as reproducing the kernel particle method （RKPM） and the element- free Galerkin （EFG） method.展开更多
In this work, a conceptual numerical solution of the two-dimensional wave partial differential equation (PDE) is developed by coupling the Complex Variable Boundary Element Method (CVBEM) and a generalized Fourier ser...In this work, a conceptual numerical solution of the two-dimensional wave partial differential equation (PDE) is developed by coupling the Complex Variable Boundary Element Method (CVBEM) and a generalized Fourier series. The technique described in this work is suitable for modeling initial-boundary value problems governed by the wave equation on a rectangular domain with Dirichlet boundary conditions and an initial condition that is equal on the boundary to the boundary conditions. The new numerical scheme is based on the standard approach of decomposing the global initial-boundary value problem into a steady-state component and a time-dependent component. The steady-state component is governed by the Laplace PDE and is modeled with the CVBEM. The time-dependent component is governed by the wave PDE and is modeled using a generalized Fourier series. The approximate global solution is the sum of the CVBEM and generalized Fourier series approximations. The boundary conditions of the steady-state component are specified as the boundary conditions from the global BVP. The boundary conditions of the time-dependent component are specified to be identically zero. The initial condition of the time-dependent component is calculated as the difference between the global initial condition and the CVBEM approximation of the steady-state solution. Additionally, the generalized Fourier series approximation of the time-dependent component is fitted so as to approximately satisfy the derivative of the initial condition. It is shown that the strong formulation of the wave PDE is satisfied by the superposed approximate solutions of the time-dependent and steady-state components.展开更多
This note illustrates the multidimensional dispersion relations that connect the real and imaginary parts of the matrixwhere z(p)) is the boundary value of the impedance
In this paper, the equation of axisymmetrical deformation problems for a general shell of revolution is derived in one complex variable under the usual Love-Kirchhoff assumption. In the case of circular ring shells, t...In this paper, the equation of axisymmetrical deformation problems for a general shell of revolution is derived in one complex variable under the usual Love-Kirchhoff assumption. In the case of circular ring shells, this equation may be simplified into the equation given by F.Tdlke(1938)[3]. R.A. Clark(1950 )[4] and V. V.Novozhilov(1951)[5]. When the horizontal radius of the shell of revolution is much larger than the average radius of curvature of meridian curve, this equation in complex variable may be simplified into the equation for slander ring shells. If the ring shell is circular in shape, then this equation can be reduced into the equation in complex variable for slander circular ring shells given by this author (1979)[6]. If the form of elliptic cross-section is near a circle, then the equation of slander ring shell with near-circle ellipitic cross-section may be reduced to the complex variable equation similar in form for circular slander ring shells.展开更多
The 2020 TKK Young Scientist Award in Mathematics&Physics went to Prof.GUAN Qi'an,a young talented mathematician from Peking University,for his solutions (joint with ZHOU Xiangyu)of a series of problems in sev...The 2020 TKK Young Scientist Award in Mathematics&Physics went to Prof.GUAN Qi'an,a young talented mathematician from Peking University,for his solutions (joint with ZHOU Xiangyu)of a series of problems in several complex variables,particularly for his proof(joint with ZHOU Xiangyu)of the Demailly's strong openness conjecture.CUAN has mainly engaged himself in the study of several complex variables,which explores the properties and structures of holomorphic functions of several variables,and is also called c complex analysis of several variables.展开更多
In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems a...In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders.By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate k-holomorphic kernels,the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion,and the integral expressions of the solutions are obtained.展开更多
In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fracti...In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.展开更多
In this paper, based on the improved complex variable moving least-square （ICVMLS） approximation, a new complex variable meshless method （CVMM） for two-dimensional （2D） transient heat conduction problems is pres...In this paper, based on the improved complex variable moving least-square （ICVMLS） approximation, a new complex variable meshless method （CVMM） for two-dimensional （2D） transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. As the transient heat conduction problems are related to time, the Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization. Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained. In order to demonstrate the applicability of the proposed method, numerical examples are given to show the high convergence rate, good accuracy, and high efficiency of the CVMM presented in this paper.展开更多
In this paper, based on the element-free Galerkin （EFG） method and the improved complex variable moving least- square （ICVMLS） approximation, a new meshless method, which is the improved complex variable element-f...In this paper, based on the element-free Galerkin （EFG） method and the improved complex variable moving least- square （ICVMLS） approximation, a new meshless method, which is the improved complex variable element-free Galerkin （ICVEFG） method for two-dimensional potential problems, is presented. In the method, the integral weak form of control equations is employed, and the Lagrange multiplier is used to apply the essential boundary conditions. Then the corresponding formulas of the ICVEFG method for two-dimensional potential problems are obtained. Compared with the complex variable moving least-square （CVMLS） approximation proposed by Cheng, the functional in the ICVMLS approximation has an explicit physical meaning. Furthermore, the ICVEFG method has greater computational precision and efficiency. Three numerical examples are given to show the validity of the proposed method.展开更多
In this paper, the improved complex variable moving least-squares （ICVMLS） approximation is presented. The ICVMLS approximation has an explicit physics meaning. Compared with the complex variable moving least-squar...In this paper, the improved complex variable moving least-squares （ICVMLS） approximation is presented. The ICVMLS approximation has an explicit physics meaning. Compared with the complex variable moving least-squares （CVMLS） approximations presented by Cheng and Ren, the ICVMLS approximation has a great computational precision and efficiency. Based on the element-free Galerkin （EFG） method and the ICVMLS approximation, the improved complex variable element-free Galerkin （ICVEFG） method is presented for two-dimensional elasticity problems, and the corresponding formulae are obtained. Compared with the conventional EFC method, the ICVEFG method has a great computational accuracy and efficiency. For the purpose of demonstration, three selected numerical examples are solved using the ICVEFG method.展开更多
A new type of displacement pile, the X-section cast-in-place concrete （XCC） pile, has recently been developed in China. Extensive field tests and laboratory experi- ments are undertaken to evaluate its performance a...A new type of displacement pile, the X-section cast-in-place concrete （XCC） pile, has recently been developed in China. Extensive field tests and laboratory experi- ments are undertaken to evaluate its performance and quantify the non-uniform deforma- tion effect （NUDE） of the X-shaped cross section during installation. This paper develops a simplified theoretical model that attempts to capture the NUDE. Based on the theory of complex variable plane elasticity, closed-form solutions of the stress and displacement for the X-shaped cavity boundary value problem are given. Subsequently, the analytical solution is used to evaluate the NUDE, the concrete filling index （CFI）, and the perimeter reduction coefficient of the XCC pile cross section. The computed results are compared with field test results, showing reasonable agreement. The present simplified theoretical model reveals the deformation mechanism of the X-shaped cavity and facilitates applica- tion of the newly developed XCC pile technique in geotechnical engineering.展开更多
Based on the complex variable moving least-square （CVMLS） approximation, the complex variable element-free Galerkin （CVEFG） method for two-dimensional viscoelasticity problems under the creep condition is presente...Based on the complex variable moving least-square （CVMLS） approximation, the complex variable element-free Galerkin （CVEFG） method for two-dimensional viscoelasticity problems under the creep condition is presented in this paper. The Galerkin weak form is employed to obtain the equation system, and the penalty method is used to apply the essential boundary conditions, then the corresponding formulae of the CVEFG method for two-dimensional viscoelasticity problems under the creep condition are obtained. Compared with the element-free Galerkin （EFG） method, with the same node distribution, the CVEFG method has higher precision, and to obtain the similar precision, the CVEFG method has greater computational efficiency. Some numerical examples are given to demonstrate the validity and the efficiency of the method.展开更多
On the basis of the reproducing kernel particle method （RKPM）, a new meshless method, which is called the complex variable reproducing kernel particle method （CVRKPM）, for two-dimensional elastodynamics is present...On the basis of the reproducing kernel particle method （RKPM）, a new meshless method, which is called the complex variable reproducing kernel particle method （CVRKPM）, for two-dimensional elastodynamics is presented in this paper. The advantages of the CVRKPM are that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is obtained. The Galerkin weak form is employed to obtain the discretised system equations, and implicit time integration method, which is the Newmark method, is used for time history analysis. And the penalty method is employed to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional elastodynamics are obtained. Three numerical examples of two-dimensional elastodynamics are presented, and the CVRKPM results are compared with the ones of the RKPM and analytical solutions. It is evident that the numerical results of the CVRKPM are in excellent agreement with the analytical solution, and that the CVRKPM has greater precision than the RKPM.展开更多
文摘We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the authors. Under this topology X becomes a Frechet space Apart from finding the characterization of continuous linear functionals, linear transformation on X, we have obtained the necessary and sufficient conditions for a double sequence in X to be a proper bases.
基金supported in part by the National Natural Science Foundation of China (Grant Nos.60874091 and 61104103)the Natural Science Fund for Colleges and Universities in Jiangsu Province,China (Grant No.10KJB120001)the Climbing Program of Nanjing University of Posts & Telecommunications,China (Grant Nos.NY210013 and NY210014)
文摘A problem of topology identification for complex dynamical networks is investigated in this paper. An adaptive observer is proposed to identify the topology of a complex dynamical networks based on the Lyapunov stability theory. Here the output of the network and the states of the observer are used to construct the updating law of the topology such that the communication resources from the network to its observer are saved. Some convergent criteria of the adaptive observer are derived in the form of linear inequality matrices. Several numerical examples are shown to demonstrate the effectiveness of the proposed observer.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11171208 and U1433104)
文摘In this paper, based on the conjugate of the complex basis function, a new complex variable moving least-squares approximation is discussed. Then using the new approximation to obtain the shape function, an improved complex variable element-free Galerkin（ICVEFG） method is presented for two-dimensional（2D） elastoplasticity problems. Compared with the previous complex variable moving least-squares approximation, the new approximation has greater computational precision and efficiency. Using the penalty method to apply the essential boundary conditions, and using the constrained Galerkin weak form of 2D elastoplasticity to obtain the system equations, we obtain the corresponding formulae of the ICVEFG method for 2D elastoplasticity. Three selected numerical examples are presented using the ICVEFG method to show that the ICVEFG method has the advantages such as greater precision and computational efficiency over the conventional meshless methods.
基金Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11102125)
文摘Based on the complex variable moving least-square（CVMLS） approximation and a local symmetric weak form,the complex variable meshless local Petrov-Galerkin（CVMLPG） method of solving two-dimensional potential problems is presented in this paper.In the present formulation,the trial function of a two-dimensional problem is formed with a one-dimensional basis function.The number of unknown coefficients in the trial function of the CVMLS approximation is less than that in the trial function of the moving least-square（MLS） approximation.The essential boundary conditions are imposed by the penalty method.The main advantage of this approach over the conventional meshless local Petrov-Galerkin（MLPG） method is its computational efficiency.Several numerical examples are presented to illustrate the implementation and performance of the present CVMLPG method.
文摘This paper, at the first time, considers the problem of decentralized variable structure control of complex giant singular uncertainty systems by using the property of diagonally dominant matrix and Frobenius-Person theorem. The splendid selection of switching manifold for each subsystem makes the design relatively straightforward and can be easily realized. An illustrate example is given.
基金Project supported by the Tianyuan Special Funds of the National Natural Science Foundation of China(Grant No.11226242)the Natural Science Foundation of Jiangxi Province of China(Grant No.20122BAB211006)
文摘In this paper, structure identification of an uncertain network coupled with complex-variable chaotic systems is in- vestigated. Both the topological structure and the system parameters can be unknown and need to be identified. Based on impulsive stability theory and the Lyapunov function method, an impulsive control scheme combined with an adaptive strategy is adopted to design effective and universal network estimators. The restriction on the impulsive interval is relaxed by adopting an adaptive strategy. Further, the proposed method can monitor the online switching topology effectively. Several numerical simulations are provided to illustrate the effectiveness of the theoretical results.
基金supported by the National Natural Science Foundation of China (Grant No. 11171208)the Leading Academic Discipline Project of Shanghai City,China (Grant No. S30106)
文摘The complex variable reproducing kernel particle method （CVRKPM） of solving two-dimensional variable coefficient advection-diffusion problems is presented in this paper. The advantage of the CVRKPM is that the shape function of a two-dimensional problem is formed with a one-dimensional basis function. The Galerkin weak form is employed to obtain the discretized system equation, and the penalty method is used to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional variable coefficient advection-diffusion problems are obtained. Two numerical examples are given to show that the method in this paper has greater accuracy and computational efficiency than the conventional meshless method such as reproducing the kernel particle method （RKPM） and the element- free Galerkin （EFG） method.
文摘In this work, a conceptual numerical solution of the two-dimensional wave partial differential equation (PDE) is developed by coupling the Complex Variable Boundary Element Method (CVBEM) and a generalized Fourier series. The technique described in this work is suitable for modeling initial-boundary value problems governed by the wave equation on a rectangular domain with Dirichlet boundary conditions and an initial condition that is equal on the boundary to the boundary conditions. The new numerical scheme is based on the standard approach of decomposing the global initial-boundary value problem into a steady-state component and a time-dependent component. The steady-state component is governed by the Laplace PDE and is modeled with the CVBEM. The time-dependent component is governed by the wave PDE and is modeled using a generalized Fourier series. The approximate global solution is the sum of the CVBEM and generalized Fourier series approximations. The boundary conditions of the steady-state component are specified as the boundary conditions from the global BVP. The boundary conditions of the time-dependent component are specified to be identically zero. The initial condition of the time-dependent component is calculated as the difference between the global initial condition and the CVBEM approximation of the steady-state solution. Additionally, the generalized Fourier series approximation of the time-dependent component is fitted so as to approximately satisfy the derivative of the initial condition. It is shown that the strong formulation of the wave PDE is satisfied by the superposed approximate solutions of the time-dependent and steady-state components.
文摘This note illustrates the multidimensional dispersion relations that connect the real and imaginary parts of the matrixwhere z(p)) is the boundary value of the impedance
文摘In this paper, the equation of axisymmetrical deformation problems for a general shell of revolution is derived in one complex variable under the usual Love-Kirchhoff assumption. In the case of circular ring shells, this equation may be simplified into the equation given by F.Tdlke(1938)[3]. R.A. Clark(1950 )[4] and V. V.Novozhilov(1951)[5]. When the horizontal radius of the shell of revolution is much larger than the average radius of curvature of meridian curve, this equation in complex variable may be simplified into the equation for slander ring shells. If the ring shell is circular in shape, then this equation can be reduced into the equation in complex variable for slander circular ring shells given by this author (1979)[6]. If the form of elliptic cross-section is near a circle, then the equation of slander ring shell with near-circle ellipitic cross-section may be reduced to the complex variable equation similar in form for circular slander ring shells.
文摘The 2020 TKK Young Scientist Award in Mathematics&Physics went to Prof.GUAN Qi'an,a young talented mathematician from Peking University,for his solutions (joint with ZHOU Xiangyu)of a series of problems in several complex variables,particularly for his proof(joint with ZHOU Xiangyu)of the Demailly's strong openness conjecture.CUAN has mainly engaged himself in the study of several complex variables,which explores the properties and structures of holomorphic functions of several variables,and is also called c complex analysis of several variables.
基金supported by the NSF of Henan Province(222300420397,242300421394)Xie’s research was supported by the NSFC(11571089,11871191).
文摘In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders.By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate k-holomorphic kernels,the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion,and the integral expressions of the solutions are obtained.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62071496,61901530,and 62061008)the Natural Science Foundation of Hunan Province of China(Grant No.2020JJ5767).
文摘In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.
基金Project supported by the National Natural Science Foundation of China(Grant No.11171208)the Shanghai Leading Academic Discipline Project,China(Grant No.S30106)the Innovation Fund for Graduate Student of Shanghai University of China (Grant No.SHUCX120125)
文摘In this paper, based on the improved complex variable moving least-square （ICVMLS） approximation, a new complex variable meshless method （CVMM） for two-dimensional （2D） transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. As the transient heat conduction problems are related to time, the Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization. Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained. In order to demonstrate the applicability of the proposed method, numerical examples are given to show the high convergence rate, good accuracy, and high efficiency of the CVMM presented in this paper.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11171208)the Shanghai Leading Academic Discipline Project, China (Grant No. S30106)the Innovation Fund Project for Graduate Student of Shanghai University,China (Grant No. SHUCX112359)
文摘In this paper, based on the element-free Galerkin （EFG） method and the improved complex variable moving least- square （ICVMLS） approximation, a new meshless method, which is the improved complex variable element-free Galerkin （ICVEFG） method for two-dimensional potential problems, is presented. In the method, the integral weak form of control equations is employed, and the Lagrange multiplier is used to apply the essential boundary conditions. Then the corresponding formulas of the ICVEFG method for two-dimensional potential problems are obtained. Compared with the complex variable moving least-square （CVMLS） approximation proposed by Cheng, the functional in the ICVMLS approximation has an explicit physical meaning. Furthermore, the ICVEFG method has greater computational precision and efficiency. Three numerical examples are given to show the validity of the proposed method.
基金supported by the National Natural Science Foundation of China (Grant No.11026223)the Shanghai Leading Academic Discipline Project,China (Grant No.S30106)the Innovation Fund Project for Graduate Student of Shanghai University,China (Grant No.SHUCX112359)
文摘In this paper, the improved complex variable moving least-squares （ICVMLS） approximation is presented. The ICVMLS approximation has an explicit physics meaning. Compared with the complex variable moving least-squares （CVMLS） approximations presented by Cheng and Ren, the ICVMLS approximation has a great computational precision and efficiency. Based on the element-free Galerkin （EFG） method and the ICVMLS approximation, the improved complex variable element-free Galerkin （ICVEFG） method is presented for two-dimensional elasticity problems, and the corresponding formulae are obtained. Compared with the conventional EFC method, the ICVEFG method has a great computational accuracy and efficiency. For the purpose of demonstration, three selected numerical examples are solved using the ICVEFG method.
基金supported by the National Natural Science Foundation of China(No.51420105013)the State Key Laboratory for Geomechanics and Deep Underground Engineering,China University of Mining and Technology(No.SKLGDUEK1713)the Fundamental Research Funds for the Central Universities(Nos.106112017CDJXY200003 and 106112017CDJPT200001)
文摘A new type of displacement pile, the X-section cast-in-place concrete （XCC） pile, has recently been developed in China. Extensive field tests and laboratory experi- ments are undertaken to evaluate its performance and quantify the non-uniform deforma- tion effect （NUDE） of the X-shaped cross section during installation. This paper develops a simplified theoretical model that attempts to capture the NUDE. Based on the theory of complex variable plane elasticity, closed-form solutions of the stress and displacement for the X-shaped cavity boundary value problem are given. Subsequently, the analytical solution is used to evaluate the NUDE, the concrete filling index （CFI）, and the perimeter reduction coefficient of the XCC pile cross section. The computed results are compared with field test results, showing reasonable agreement. The present simplified theoretical model reveals the deformation mechanism of the X-shaped cavity and facilitates applica- tion of the newly developed XCC pile technique in geotechnical engineering.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11171208)the Shanghai Leading Academic Discipline Project, China (Grant No. S30106)
文摘Based on the complex variable moving least-square （CVMLS） approximation, the complex variable element-free Galerkin （CVEFG） method for two-dimensional viscoelasticity problems under the creep condition is presented in this paper. The Galerkin weak form is employed to obtain the equation system, and the penalty method is used to apply the essential boundary conditions, then the corresponding formulae of the CVEFG method for two-dimensional viscoelasticity problems under the creep condition are obtained. Compared with the element-free Galerkin （EFG） method, with the same node distribution, the CVEFG method has higher precision, and to obtain the similar precision, the CVEFG method has greater computational efficiency. Some numerical examples are given to demonstrate the validity and the efficiency of the method.
基金supported by the National Natural Science Foundation of China (Grant No.10871124)the Innovation Program of Shanghai Municipal Education Commission,China (Grant No.09ZZ99)
文摘On the basis of the reproducing kernel particle method （RKPM）, a new meshless method, which is called the complex variable reproducing kernel particle method （CVRKPM）, for two-dimensional elastodynamics is presented in this paper. The advantages of the CVRKPM are that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is obtained. The Galerkin weak form is employed to obtain the discretised system equations, and implicit time integration method, which is the Newmark method, is used for time history analysis. And the penalty method is employed to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional elastodynamics are obtained. Three numerical examples of two-dimensional elastodynamics are presented, and the CVRKPM results are compared with the ones of the RKPM and analytical solutions. It is evident that the numerical results of the CVRKPM are in excellent agreement with the analytical solution, and that the CVRKPM has greater precision than the RKPM.
