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1.
An improved interpolating element-free Galerkin method with a nonsingular weight function for two-dimensional potential problems
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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
2.
A new complex variable element-free Galerkin method for two-dimensional potential problems
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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.
Based on the improved interpolating moving least-squares (ⅡMLS) method and the Galerkin weak form, an improved interpolating element-free Galerkin (ⅡEFG) method is presented for two-dimensional elasticity problems in this paper. Compared with the interpolating moving least-squares (IMLS) method presented by Lancaster, the ⅡMLS method uses the nonsingular weight function. The number of unknown coefficients in the trial function of the ⅡMLS method is less than that of the MLS approximation and the shape function of the ⅡMLS method satisfies the property of Kronecker δ function. Thus in the ⅡEFG method, the essential boundary conditions can be applied directly and easily, then the numerical solutions can be obtained with higher precision than those obtained by the interpolating element-free Galerkin (IEFG) method. For the purposes of demonstration, four numerical examples are solved using the ⅡEFG method. 相似文献
4.
An improved boundary element-free method (IBEFM) for two-dimensional potential problems 总被引:1,自引:0,他引:1
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The interpolating moving least-squares (IMLS) method is discussed
first in this paper. And the formulae of the IMLS method obtained by
Lancaster are revised. Then on the basis of the boundary
element-free method (BEFM), combining the boundary integral equation
(BIE) method with the IMLS method, the improved boundary
element-free method (IBEFM) for two-dimensional potential problems
is presented, and the corresponding formulae of the IBEFM are
obtained. In the BEFM, boundary conditions are applied directly, but
the shape function in the MLS does not satisfy the property of
the Kronecker δ function. This is a problem of the BEFM, and
must be solved theoretically. In the IMLS method, when the shape function
satisfies the property of the Kronecker δ function, then the
boundary conditions, in the meshless method based on the IMLS
method, can be applied directly. Then the IBEFM, based on the IMLS
method, is a direct meshless boundary integral equation method in
which the basic unknown quantity is the real solution of the nodal
variables, and the boundary conditions can be applied directly and
easily, thus it gives a greater computational precision. Some
numerical examples are presented to demonstrate the method. 相似文献
5.
The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system,
and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed
a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method
has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system.
A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation
method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless
method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are
the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method
has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method
for elastodynamics problems is presented in this paper. Finally, some numerical examples are given. 相似文献
6.
By employing the improved moving least-square (IMLS) approximation, the improved element-free Galerkin (IEFG) method is presented for the unsteady Schrödinger equation. In the IEFG method, the two-dimensional (2D) trial function is approximated by the IMLS approximation, the variation method is used to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. Because the number of coefficients in the IMLS approximation is less than in the moving least-square (MLS) approximation, fewer nodes are needed in the entire domain when the IMLS approximation is used than when the MLS approximation is adopted. Then the IEFG method has high computational efficiency and accuracy. Several numerical examples are given to verify the accuracy and efficiency of the IEFG method in this paper. 相似文献
7.
Boundary element-free method for elastodynamics 总被引:3,自引:0,他引:3
CHENG Yumin & PENG Miaojuan . Shanghai Institute of Applied Mathematics Mechanics Shanghai University Shanghai China . Department of Civil Engineering Shanghai University Shanghai China 《中国科学G辑(英文版)》2005,48(6):641-657
1 Introduction In recent years, more and more attention has been paid to researches on the meshless (or meshfree) method, which makes it a hot direction of computational mechanics[1,2]. The meshless method is the approximation based on nodes, then the large deformation and crack growth problems can be simulated with the method without the re-meshing technique. And the meshless method has some advantages over the traditional computa- tional methods, such as finite element method (FEM) and boun… 相似文献
8.
在高维情况下,首先研究了无单元Galerkin方法的形函数构造方法——移动最小二乘法在Sobolev空间Wk,p(Ω)中的误差估计.然后,在势问题的无单元Galerkin方法的基础上,研究了势问题的通过罚函数法施加本质边界条件的无单元Galerkin方法在Sobolev空间中的误差估计.当节点和形函数满足一定条件时,证明了该误差估计是最优阶的.从误差分析中可以看出,数值解的误差与权函数的影响半径密切相关.最后,通过算例验证了结论的正确性.
关键词:
无网格方法
无单元Galerkin方法
势问题
误差估计 相似文献
9.
10.
The improved element-free Galerkin(IEFG) method of elasticity is used to solve the topology optimization problems.In this method, the improved moving least-squares approximation is used to form the shape function. In a topology optimization process, the entire structure volume is considered as the constraint. From the solid isotropic microstructures with penalization, we select relative node density as a design variable. Then we choose the minimization of compliance to be an objective function, and compute its sensitivity with the adjoint method. The IEFG method in this paper can overcome the disadvantages of the singular matrices that sometimes appear in conventional element-free Galerkin(EFG) method. The central processing unit(CPU) time of each example is given to show that the IEFG method is more efficient than the EFG method under the same precision, and the advantage that the IEFG method does not form singular matrices is also shown. 相似文献
11.
An improved complex variable element-free Galerkin method for two-dimensional elasticity problems
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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
12.
Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method
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In this paper, we analyze the generalized Camassa and Holm (CH) equation by the improved element-free Galerkin (IEFG) method. By employing the improved moving least-square (IMLS) approximation, we derive the formulas for the generalized CH equation with the IEFG method. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Because there are fewer coefficients in the IMLS approximation than in the MLS approximation, and in the IEFG method, fewer nodes are selected in the entire domain than in the conventional EFG method, the IEFG method should result in a higher computing speed. The effectiveness of the IEFG method for the generalized CH equation is investigated by numerical examples in this paper. 相似文献
13.
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
14.
基于移动最小二乘法在Sobolev空间Wk,p(Ω)中的误差估计以及弹性力学问题的变分弱形式中出现的双线性形式的连续性和强制性,研究了弹性力学问题的无单元Galerkin方法的误差分析以及数值解的误差和影响域半径之间的关系,给出了弹性力学问题的无单元Galerkin方法在Sobolev空间中的误差估计定理,并证明了当节点和形函数满足一定条件时该误差估计是最优阶的.从误差分析中可以看出,数值解的误差与权函数的影响域半径密切相关.最后,通过算例验证了结论的正确性.
关键词:
无网格方法
无单元Galerkin方法
弹性力学
误差估计 相似文献
15.
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
16.
An element-free Galerkin(EFG) method for numerical solution of the coupled Schrdinger-KdV equations
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The present paper deals with the numerical solution of the coupled Schrdinger-KdV equations using the elementfree Galerkin(EFG) method which is based on the moving least-square approximation.Instead of traditional mesh oriented methods such as the finite difference method(FDM) and the finite element method(FEM),this method needs only scattered nodes in the domain.For this scheme,a variational method is used to obtain discrete equations and the essential boundary conditions are enforced by the penalty method.In numerical experiments,the results are presented and compared with the findings of the finite element method,the radial basis functions method,and an analytical solution to confirm the good accuracy of the presented scheme. 相似文献
17.
Element-free Galerkin (EFG) method for analysis of the time-fractional partial differential equations
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The present paper deals with the numerical solution of time-fractional partial differential equations using the element-free Galerkin (EFG) method, which is based on the moving least-square approximation. Compared with numerical methods based on meshes, the EFG method for time-fractional partial differential equations needs only scattered nodes instead of meshing the domain of the problem. It neither requires element connectivity nor suffers much degradation in accuracy when nodal arrangements are very irregular. In this method, the first-order time derivative is replaced by the Caputo fractional derivative of order α (0<α ≤1). The Galerkin weak form is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Several numerical examples are presented and the results we obtained are in good agreement with the exact solutions. 相似文献
18.
Analysis of elastoplasticity problems using an improved complex variable element-free Galerkin method
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《中国物理 B》2015,(10)
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. 相似文献
19.
Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems
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We first give a stabilized improved moving least squares(IMLS) approximation, which has better computational stability and precision than the IMLS approximation. Then, analysis of the improved element-free Galerkin method is provided theoretically for both linear and nonlinear elliptic boundary value problems. Finally, numerical examples are given to verify the theoretical analysis. 相似文献