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
An interpolating reproducing kernel particle method for two-dimensional （2D） scatter points is introduced. It elim- inates the dependency of gridding in numerical calculations. The interpolating shape function in th...An interpolating reproducing kernel particle method for two-dimensional （2D） scatter points is introduced. It elim- inates the dependency of gridding in numerical calculations. The interpolating shape function in the interpolating repro- ducing kernel particle method satisfies the property of the Kronecker delta function. This method offers a mathematics basis for recognition technology and simulation analysis, which can be expressed as simultaneous differential equations in science or project problems. Mathematical examples are given to show the validity of the interpolating reproducing kernel particle method.展开更多
In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE metho...In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.展开更多
The Reproducing Kernel Particle Method (RKPM) is one of several new meshless numerical methods de- veloped internationally in recent years. The ideal elasto-plastic constitutive model of material under a Taylor impact...The Reproducing Kernel Particle Method (RKPM) is one of several new meshless numerical methods de- veloped internationally in recent years. The ideal elasto-plastic constitutive model of material under a Taylor impact is characterized by the Jaumann stress- and strain-rates. An updated Lagrangian format is used for the calculation in a nu- merical analysis. With the RKPM, this paper deals with the calculation model for the Taylor impact and deduces the control equation for the impact process. A program was developed to simulate numerically the Taylor impact of projec- tiles composed of several kinds of material. The simulation result is in good accordance with both the test results and the Taylor analysis outcome. Since the meshless method is not limited by meshes, it is believed to be widely applicable to such complicated processes as the Taylor impact, including large deformation and strain and to the study of the dy- namic qualities of materials.展开更多
In this paper, the normal derivative of the radial basis function （RBF） is introduced into the reproducing kernel particle method （RKPM）, and the improved reproducing kernel particle method （IRKPM） is proposed. ...In this paper, the normal derivative of the radial basis function （RBF） is introduced into the reproducing kernel particle method （RKPM）, and the improved reproducing kernel particle method （IRKPM） is proposed. The method can decrease the errors on the boundary and improve the accuracy and stability of the algorithm. The proposed method is applied to the numerical simulation of piezoelectric materials and the corresponding governing equations are derived. The numerical results show that the IRKPM is more stable and accurate than the RKPM.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
To study the non-linear fracture, a non-linear constitutive model for piezoelectric ceramics was proposed, in which the polarization switching and saturation were taken into account. Based on the model, the non-linear...To study the non-linear fracture, a non-linear constitutive model for piezoelectric ceramics was proposed, in which the polarization switching and saturation were taken into account. Based on the model, the non-linear fracture analysis was implemented using reproducing kernel particle method （RKPM）. Using local J-integral as a fracture criterion, a relation curve of fracture loads against electric fields was obtained. Qualitatively, the curve is in agreement with the experimental observations reported in literature. The reproducing equation, the shape function of RKPM, and the transformation method to impose essential boundary conditions for meshless methods were also introduced. The computation was implemented using object-oriented programming method.展开更多
Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attr...Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson＇s equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method （RKPM）. A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples.展开更多
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.
基金supported by the National Natural Science Foundation of China(Grant No.11171208)the Natural Science Foundation of Shanxi Province,China(Grant No.2013011022-6)
文摘An interpolating reproducing kernel particle method for two-dimensional （2D） scatter points is introduced. It elim- inates the dependency of gridding in numerical calculations. The interpolating shape function in the interpolating repro- ducing kernel particle method satisfies the property of the Kronecker delta function. This method offers a mathematics basis for recognition technology and simulation analysis, which can be expressed as simultaneous differential equations in science or project problems. Mathematical examples are given to show the validity of the interpolating reproducing kernel particle method.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11171208)the Special Fund for Basic Scientific Research of Central Colleges of Chang’an University, China (Grant No. CHD2011JC080)
文摘In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.
基金Project /s50674002 supported by the National Natural Science Foundation of China
文摘The Reproducing Kernel Particle Method (RKPM) is one of several new meshless numerical methods de- veloped internationally in recent years. The ideal elasto-plastic constitutive model of material under a Taylor impact is characterized by the Jaumann stress- and strain-rates. An updated Lagrangian format is used for the calculation in a nu- merical analysis. With the RKPM, this paper deals with the calculation model for the Taylor impact and deduces the control equation for the impact process. A program was developed to simulate numerically the Taylor impact of projec- tiles composed of several kinds of material. The simulation result is in good accordance with both the test results and the Taylor analysis outcome. Since the meshless method is not limited by meshes, it is believed to be widely applicable to such complicated processes as the Taylor impact, including large deformation and strain and to the study of the dy- namic qualities of materials.
基金Project supported by the National Natural Science Foundation of China(Grant No.11271234)the Shandong Provincial Science Foundation,China(Grant No.ZR2017MA028)
文摘In this paper, the normal derivative of the radial basis function （RBF） is introduced into the reproducing kernel particle method （RKPM）, and the improved reproducing kernel particle method （IRKPM） is proposed. The method can decrease the errors on the boundary and improve the accuracy and stability of the algorithm. The proposed method is applied to the numerical simulation of piezoelectric materials and the corresponding governing equations are derived. The numerical results show that the IRKPM is more stable and accurate than the RKPM.
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.
基金Foundation of Southwest Jiaotong Univer-sity (No.2005B25)
文摘To study the non-linear fracture, a non-linear constitutive model for piezoelectric ceramics was proposed, in which the polarization switching and saturation were taken into account. Based on the model, the non-linear fracture analysis was implemented using reproducing kernel particle method （RKPM）. Using local J-integral as a fracture criterion, a relation curve of fracture loads against electric fields was obtained. Qualitatively, the curve is in agreement with the experimental observations reported in literature. The reproducing equation, the shape function of RKPM, and the transformation method to impose essential boundary conditions for meshless methods were also introduced. The computation was implemented using object-oriented programming method.
基金supported by the Natural Science Foundation of Ningbo,China (Grant Nos.2009A610014 and 2009A610154)the Natural Science Foundation of Zhejiang Province,China (Grant No.Y6090131)
文摘Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson＇s equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method （RKPM）. A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples.
