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An improved complex variable element-free Galerkin method for two-dimensional elasticity problems 被引量:3
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作者 Bai Fu-Nong Li Dong-Ming +1 位作者 Wang Jian-Fei Cheng Yu-Min 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第2期56-65,共10页
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
关键词 meshless method improved complex variable moving least-squares approximation improved complex variable element-free galerkin method ELASTICITY
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Analysis of elastoplasticity problems using an improved complex variable element-free Galerkin method 被引量:3
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作者 程玉民 刘超 +1 位作者 白福浓 彭妙娟 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第10期16-25,共10页
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
关键词 meshless method complex variable moving least-squares approximation improved complex vari- able element-free galerkin method elastoplasticity
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A new complex variable element-free Galerkin method for two-dimensional potential problems 被引量:4
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作者 程玉民 王健菲 白福浓 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第9期43-52,共10页
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
关键词 meshless method improved complex variable moving least-square approximation im- proved complex variable element-free galerkin method potential problem
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Complex variable element-free Galerkin method for viscoelasticity problems 被引量:2
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作者 程玉民 李荣鑫 彭妙娟 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第9期60-71,共12页
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
关键词 meshless method complex variable moving least-square approximation complex variableelement-free galerkin method VISCOELASTICITY
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An improved interpolating element-free Galerkin method with a nonsingular weight function for two-dimensional potential problems 被引量:15
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作者 王聚丰 孙凤欣 程玉民 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第9期53-59,共7页
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 5 function. The weight function used in the II... 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 5 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. 展开更多
关键词 meshless method improved interpolating moving least-square method improved inter-polating element-free galerkin method potential problem
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The improved element-free Galerkin method forthree-dimensional wave equation 被引量:16
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作者 Zan Zhang Dong-Ming Li +1 位作者 Yu-Min Cheng Kim Moew Liew 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2012年第3期808-818,共11页
The paper presents the improved element-free Galerkin (IEFG) method for three-dimensional wave propa- gation. The improved moving least-squares (IMLS) approx- imation is employed to construct the shape function, w... The paper presents the improved element-free Galerkin (IEFG) method for three-dimensional wave propa- gation. The improved moving least-squares (IMLS) approx- imation is employed to construct the shape function, which uses an orthogonal function system with a weight function as the basis function. Compared with the conventional moving least-squares (MLS) approximation, the algebraic equation system in the IMLS approximation is not ill-conditioned, and can be solved directly without deriving the inverse matrix. Because there are fewer coefficients in the IMLS than in the MLS approximation, fewer nodes are selected in the IEFG method than in the element-free Galerkin method. Thus, the IEFG method has a higher computing speed. In the IEFG method, the Galerkin weak form is employed to obtain a dis- cretized system equation, and the penalty method is applied to impose the essential boundary condition. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the wave equations and the boundary-initial conditions depend on time, the scal- ing parameter, number of nodes and the time step length are considered for the convergence study. 展开更多
关键词 Weighted orthogonal function improved mov-ing least squares (IMLS) approximation. improved element-free galerkin (IEFG) method Penalty method Temporaldiscretization Wave equation
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An improved interpolating element-free Galerkin method for elasticity 被引量:4
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作者 孙凤欣 王聚丰 程玉民 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第12期43-50,共8页
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 proble... 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. 展开更多
关键词 meshless method improved interpolating moving least-squares (ⅡMLS) method improved interpolating element-free galerkin (ⅡEFG) method elasticity
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The Improved Element-Free Galerkin Method for Anisotropic Steady-State Heat Conduction Problems
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作者 Heng Cheng Zebin Xing Miaojuan Peng 《Computer Modeling in Engineering & Sciences》 SCIE EI 2022年第9期945-964,共20页
In this paper,we considered the improved element-free Galerkin(IEFG)method for solving 2D anisotropic steadystate heat conduction problems.The improved moving least-squares(IMLS)approximation is used to establish the ... In this paper,we considered the improved element-free Galerkin(IEFG)method for solving 2D anisotropic steadystate heat conduction problems.The improved moving least-squares(IMLS)approximation is used to establish the trial function,and the penalty method is applied to enforce the boundary conditions,thus the final discretized equations of the IEFG method for anisotropic steady-state heat conduction problems can be obtained by combining with the corresponding Galerkin weak form.The influences of node distribution,weight functions,scale parameters and penalty factors on the computational accuracy of the IEFG method are analyzed respectively,and these numerical solutions show that less computational resources are spent when using the IEFG method. 展开更多
关键词 improved element-free galerkin method penalty method weak form anisotropic steady-state heat conduction improved moving least-squares approximation
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The complex variable meshless local Petrov-Galerkin method of solving two-dimensional potential problems 被引量:1
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作者 杨秀丽 戴保东 张伟伟 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第10期49-55,共7页
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
关键词 meshless method complex variable moving least-square method complex variable meshless local Petrov-galerkin method potential problems
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A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems
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作者 王启防 戴保东 栗振锋 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第8期238-244,共7页
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 ... 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. 展开更多
关键词 meshless method complex variable moving least-square method complex variable meshless localPetrov-galerkin method transient heat conduction problems
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A new complex variable meshless method for transient heat conduction problems 被引量:5
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作者 王健菲 程玉民 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第12期42-50,共9页
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
关键词 meshless method improved complex variable moving least-square approximation com-plex variable meshless method transient heat conduction problem
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The dimension split element-free Galerkin method for three-dimensional potential problems 被引量:4
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作者 Z.J.Meng H.Cheng +1 位作者 L.D.Ma Y.M.Cheng 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2018年第3期462-474,共13页
This paper presents the dimension split element-free Galerkin (DSEFG) method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-d... This paper presents the dimension split element-free Galerkin (DSEFG) method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares (IMLS) approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method. 展开更多
关键词 Dimension split method improved moving least-squares (IMLS) approximation improved element-free galerkin (IEFG) method Finite difference method (FDM) Dimension split element-free galerkin (DSEFG) method Potential problem
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New complex variable meshless method for advection-diffusion problems 被引量:1
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作者 王健菲 程玉民 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第3期92-98,共7页
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 equi... 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. 展开更多
关键词 meshless method improved complex variable moving least-square approximation improved complex variable meshless method advection-diffusion problem
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A Fast Element-Free Galerkin Method for 3D Elasticity Problems
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作者 Zhijuan Meng Yanan Fang Yumin Cheng 《Computer Modeling in Engineering & Sciences》 SCIE EI 2022年第7期55-79,共25页
In this paper,a fast element-free Galerkin(FEFG)method for three-dimensional(3D)elasticity problems is established.The FEFG method is a combination of the improved element-free Galerkin(IEFG)method and the dimension s... In this paper,a fast element-free Galerkin(FEFG)method for three-dimensional(3D)elasticity problems is established.The FEFG method is a combination of the improved element-free Galerkin(IEFG)method and the dimension splitting method(DSM).By using the DSM,a 3D problem is converted to a series of 2D ones,and the IEFG method with a weighted orthogonal function as the basis function and the cubic spline function as the weight function is applied to simulate these 2D problems.The essential boundary conditions are treated by the penalty method.The splitting direction uses the finite difference method(FDM),which can combine these 2D problems into a discrete system.Finally,the system equation of the 3D elasticity problem is obtained.Some specific numerical problems are provided to illustrate the effectiveness and advantages of the FEFG method for 3D elasticity by comparing the results of the FEFG method with those of the IEFG method.The convergence and relative error norm of the FEFG method for elasticity are also studied. 展开更多
关键词 improved element-free galerkin method dimension splitting method finite difference method fast element-free galerkin method ELASTICITY
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The improved element-free Galerkin method for three-dimensional transient heat conduction problems 被引量:20
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作者 ZHANG Zan WANG JianFei +1 位作者 CHENG YuMin LIEW Kim Meow 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2013年第8期1568-1580,共13页
With the improved moving least-squares (IMLS) approximation, an orthogonal function system with a weight function is used as the basis function. The combination of the element-free Galerkin (EFG) method and the IMLS a... With the improved moving least-squares (IMLS) approximation, an orthogonal function system with a weight function is used as the basis function. The combination of the element-free Galerkin (EFG) method and the IMLS approximation leads to the development of the improved element-free Galerkin (IEFG) method. In this paper, the IEFG method is applied to study the partial differential equations that control the heat flow in three-dimensional space. With the IEFG technique, the Galerkin weak form is employed to develop the discretized system equations, and the penalty method is applied to impose the essential boundary conditions. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the transient heat conduction equations and the boundary and initial conditions are time dependent, the scaling parameter, number of nodes and time step length are considered in a convergence study. 展开更多
关键词 weighted orthogonal function improved moving least-squares (IMLS) approximation improved element-free galerkin (IEFG) method penalty method transient heat conduction
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势问题的复变量无单元Galerkin方法 被引量:2
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作者 刘沛 彭妙娟 程玉民 《计算机辅助工程》 2009年第4期10-14,共5页
为提高无单元Galerkin(Element-Free Galerkin,EFG)方法的计算效率,将复变量移动最小二乘法与EFG方法结合,利用控制方程的积分弱形式并采用Lagrange乘子法引入边界条件,提出势问题的复变量无单元Galerkin(Complex Variable EFG,CVEFG)方... 为提高无单元Galerkin(Element-Free Galerkin,EFG)方法的计算效率,将复变量移动最小二乘法与EFG方法结合,利用控制方程的积分弱形式并采用Lagrange乘子法引入边界条件,提出势问题的复变量无单元Galerkin(Complex Variable EFG,CVEFG)方法,并推导相关公式.与传统的EFG方法相比,该方法采用复变量移动最小二乘法可以减少试函数中的待定系数,从而减少计算量、提高计算效率.最后,给出数值算例验证该方法的有效性. 展开更多
关键词 无网格方法 复变量移动最小二乘法 复变量无单元galerkin方法 势问题
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The dimension splitting element-free Galerkin method for 3D transient heat conduction problems 被引量:8
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作者 ZhiJuan Meng Heng Cheng +1 位作者 LiDong Ma YuMin Cheng 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS CSCD 2019年第4期45-56,共12页
By transforming a 3D problem into some related 2D problems, the dimension splitting element-free Galerkin(DSEFG) method is proposed to solve 3D transient heat conduction problems. The improved element-free Galerkin(IE... By transforming a 3D problem into some related 2D problems, the dimension splitting element-free Galerkin(DSEFG) method is proposed to solve 3D transient heat conduction problems. The improved element-free Galerkin(IEFG) method is used for 2D transient heat conduction problems, and the finite difference method is applied in the splitting direction. The discretized system equation is obtained based on the Galerkin weak form of 2D problem; the essential boundary conditions are imposed with the penalty method; and the finite difference method is employed in the time domain. Four exemplary problems are chosen to verify the efficiency of the DSEFG method. The numerical solutions show that the efficiency and precision of the DSEFG method are greater than ones of the IEFG method for 3D problems. 展开更多
关键词 improved element-free galerkin (IEFG) method DIMENSION SPLITTING method finite DIFFERENCE method DIMENSION SPLITTING element-free galerkin (DSEFG) method TRANSIENT heat conduction problem
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The interpolating element-free Galerkin method for elastic large deformation problems 被引量:5
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作者 WU Qiang PENG PiaoPiao CHENG YuMin 《Science China(Technological Sciences)》 SCIE EI CAS CSCD 2021年第2期364-374,共11页
This paper presents an interpolating element-free Galerkin(IEFG) method for solving the two-dimensional(2D) elastic large deformation problems. By using the improved interpolating moving least-squares method to form s... This paper presents an interpolating element-free Galerkin(IEFG) method for solving the two-dimensional(2D) elastic large deformation problems. By using the improved interpolating moving least-squares method to form shape function, and using the Galerkin weak form of 2D elastic large deformation problems to obtain the discrete equations, we obtain the formulae of the IEFG method for 2D elastic large deformation problems. As the displacement boundary conditions can be applied directly, the IEFG method can acquire higher computational efficiency and accuracy than the traditional element-free Galerkin(EFG)method, which is based on the moving least-squares approximation and can not apply the displacement boundary conditions directly. To analyze the influences of node distribution, scale parameter of influence domain and the loading step on the numerical solutions of the IEFG method, three numerical examples are proposed. The IEFG method has almost the same high accuracy as the EFG method, and for some 2D elastic large deformation problems the IEFG method even has higher computational accuracy. 展开更多
关键词 meshless method improved interpolating moving least-squares method interpolating element-free galerkin method elastic large deformation
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移动最小二乘法研究进展与述评 被引量:41
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作者 程玉民 《计算机辅助工程》 2009年第2期5-11,20,共8页
为使移动最小二乘法能更好地应用到无网格方法中,详细阐述移动最小二乘逼近法、移动最小二乘插值法、MUKHERJEE改进的移动最小二乘法以及程玉民等提出的改进的移动最小二乘法和复变量移动最小二乘法等的研究进展,述评各种移动最小二乘... 为使移动最小二乘法能更好地应用到无网格方法中,详细阐述移动最小二乘逼近法、移动最小二乘插值法、MUKHERJEE改进的移动最小二乘法以及程玉民等提出的改进的移动最小二乘法和复变量移动最小二乘法等的研究进展,述评各种移动最小二乘法的优缺点,并概述各种移动最小二乘法形成的无网格方法的研究进展. 展开更多
关键词 移动最小二乘逼近法 移动最小二乘插值法 改进的移动最小二乘法 复变量移动最小 二乘法 无网格方法
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基于复变量微分法的改进反分析方法及其验证
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作者 彭争光 刘成学 尤建新 《地下空间与工程学报》 CSCD 北大核心 2012年第4期752-755,776,共5页
对Levenberg-Marquit优化方法中利用差分法计算偏导数带来的计算精度与效率偏低等缺点,通过采用复变量微分法取代常用的差分法进行偏导数计算,从而实现了对Leven-berg-Marquit优化方法的改进,对地下巷道弹性位移优化反分析构造了一种改... 对Levenberg-Marquit优化方法中利用差分法计算偏导数带来的计算精度与效率偏低等缺点,通过采用复变量微分法取代常用的差分法进行偏导数计算,从而实现了对Leven-berg-Marquit优化方法的改进,对地下巷道弹性位移优化反分析构造了一种改进算法。该方法以复函数泰勒级数展开为理论基础构造复变量微分法,通过函数计算直接求得偏导数,由此形成了改进的Levenberg-Marquit优化反分析方法,并编制相关计算程序。最后,通过地下巷道弹性位移优化反分析实际算例表明,建立的改进反分析方法在计算的精度与速度方面都明显优于以往的方法,可用于工程实际。 展开更多
关键词 地下巷道 反分析 改进venberg-Marquit方法 复变量微分法 验证
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