共查询到16条相似文献,搜索用时 250 毫秒
1.
A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems 下载免费PDF全文
On the basis of the complex variable moving least-square (CVMLS) approximation, a complex variable meshless local Petrov-Galerkin (CVMLPG) method is presented for transient heat conduction problems. The method is developed based on the CVMLS approximation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for a domain integral in symmetric weak form. In the construction of the well-performed shape function, the trial function of a two-dimensional (2D) problem is formed with a one-dimensional (1D) basis function, thus improving computational efficiency. The numerical results are compared with the exact solutions of the problems and the finite element method (FEM). This comparison illustrates the accuracy as well as the capability of the CVMLPG method. 相似文献
2.
A new complex variable element-free Galerkin method for two-dimensional potential problems 下载免费PDF全文
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. 相似文献
3.
In this paper, based on the improved complex variable moving least-square (ICVMLS) approximation, an improved complex variable meshless method (ICVMM) for two-dimensional advection-diffusion problems is developed. The equivalent functional of two-dimensional advection-diffusion problems is formed, the variation method is used to obtain the equation system, and the penalty method is employed to impose the essential boundary conditions. The difference method for two-point boundary value problems is used to obtain the discrete equations. Then the corresponding formulas of the ICVMM for advection-diffusion problems are presented. Two numerical examples with different node distributions are used to validate and investigate the accuracy and efficiency of the new method in this paper. It is shown that the ICVMM is very effective for advection-diffusion problems, and has good convergent character, accuracy, and computational efficiency. 相似文献
4.
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. 相似文献
5.
<正>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. 相似文献
6.
The complex variable reproducing kernel particle method for two-dimensional elastodynamics 下载免费PDF全文
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. 相似文献
7.
REN HongPing CHENG YuMin & ZHANG Wu School of Computer Engineering Science Shanghai University Shanghai China 《中国科学:物理学 力学 天文学(英文版)》2010,(4)
The paper begins by discussing the interpolating moving least-squares (IMLS) method. Then the formulae of the IMLS method obtained by Lancaster are revised. On the basis of the boundary element-free method (BEFM), combining the boundary integral equation method with the IMLS method improved in this paper, the interpolating boundary element-free method (IBEFM) for two-dimensional elasticity problems is presented, and the corresponding formulae of the IBEFM for two-dimensional elasticity problems are obtained. In the IMLS method in this paper, the shape function satisfies the property of Kronecker δ function, and then in the IBEFM the boundary conditions can be applied directly and easily. The IBEFM is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution to the nodal variables. Thus it gives a greater computational precision. Numerical examples are presented to demonstrate the method. 相似文献
8.
An improved interpolating element-free Galerkin method with a nonsingular weight function for two-dimensional potential problems 下载免费PDF全文
In this paper, an improved interpolating moving least-square (IIMLS) method is presented. The shape function of the IIMLS method satisfies the property of the Kronecker δ function. The weight function used in the IIMLS method is nonsingular. Then the IIMLS method can overcome the difficulties caused by the singularity of the weight function in the IMLS method. The number of unknown coefficients in the trial function of the IIMLS method is less than that of the moving least-square (MLS) approximation. Then by combining the IIMLS method with the Galerkin weak form of the potential problem, the improved interpolating element-free Galerkin (IIEFG) method for two-dimensional potential problems is presented. Compared with the conventional element-free Galerkin (EFG) method, the IIEFG method can directly use the essential boundary conditions. Then the IIEFG method has higher accuracy. For demonstration, three numerical examples are solved using the IIEFG method. 相似文献
9.
Element-free Galerkin (EFG) method for a kind of two-dimensional linear hyperbolic equation 下载免费PDF全文
The present paper deals with the numerical solution of
a two-dimensional linear hyperbolic equation by using the element-free
Galerkin (EFG) method which is based on the moving least-square
approximation for the test and trial functions. A variational method
is used to obtain the discrete equations, and the essential boundary
conditions are enforced by the penalty method. Compared with
numerical methods based on mesh, the EFG method for hyperbolic
problems needs only the scattered nodes instead of meshing the
domain of the problem. It neither requires any element connectivity
nor suffers much degradation in accuracy when nodal arrangements are
very irregular. The effectiveness of the EFG method for two-dimensional
hyperbolic problems is investigated by two numerical examples in
this paper. 相似文献
10.
Analysis of variable coefficient advection-diffusion problems via complex variable reproducing kernel particle method 下载免费PDF全文
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. 相似文献
11.
A complex variable meshless method for fracture problems 总被引:4,自引:0,他引:4
CHENG Yumin & LI Jiuhong . Shanghai Institute of Applied Mathematics Mechanics Shanghai University Shanghai China . Department of Building Engineering Xi’an University of Technology Xi’an China 《中国科学G辑(英文版)》2006,49(1):46-59
1 Introduction The meshless (or meshfree) method has been a hot topic and the development trend of numerical methods for many science and engineering problems in recent years. Comparing with the conventional numerical methods, such as the finite element method and the boundary element method, the meshless method is an approximation based on nodes, and does not form a mesh to determine the shape function in the domain, in which a problem is to be solved. The meshless method has some advantages … 相似文献
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13.
An improved complex variable element-free Galerkin method for two-dimensional elasticity problems 下载免费PDF全文
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 EFG 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. 相似文献
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15.
In this paper,an improved complex variable meshless method(ICVMM) for two-dimensional advection-diffusion problems is developed based on improved complex variable moving least-square(ICVMLS) approximation.The equivalent functional of two-dimensional advection-diffusion problems is formed,the variation method is used to obtain the equation system,and the penalty method is employed to impose the essential boundary conditions.The difference method for twopoint boundary value problems is used to obtain the discrete equations.Then the corresponding formulas of the ICVMM for advection-diffusion problems are presented.Two numerical examples with different node distributions are used to validate and investigate the accuracy and efficiency of the new method in this paper.It is shown that ICVMM is very effective for advection-diffusion problems,and has a good convergent character,accuracy,and computational efficiency. 相似文献
16.
将滑动Kriging插值法与无网格局部Petrov-Galerkin法相结合,采用Heaviside分段函数作为局部弱形式的权函数,提出改进的无网格局部Petrov-Galerkin法,进一步将这种无网格法应用于位势问题,并推导相应的离散方程.因为滑动Kriging插值法构造的形函数满足Kronecker函数性质,所以本文建立的改进的无网格局部Petrov-Galerkin法可以像有限元法一样直接施加边界条件;由于采用Heaviside分段函数作为局部弱形式的权函数,因此在计算刚度矩阵时只涉及边界积分,而没有区域积分.此外,还对本方法中一些重要参数的选取进行了研究.数值算例表明,本文建立的改进的无网格局部Petrov-Galerkin法具有数值实现简单、计算量小以及方便施加边界条件等优点. 相似文献