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Element-free Galerkin method for free vibration of rectangular plates with interior elastic point supports and elastically restrained edges 被引量:1
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作者 王砚 王忠民 阮苗 《Journal of Shanghai University(English Edition)》 CAS 2010年第3期187-195,共9页
The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton's principle for t... The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton's principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed. 展开更多
关键词 element free method rectangular thin plates interior elastic point supports elastically restrained edges free vibration
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An improved boundary element-free method (IBEFM) for two-dimensional potential problems 被引量:8
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作者 任红萍 程玉民 张武 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第10期4065-4073,共9页
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 (B... 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 ~ 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 5 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. 展开更多
关键词 moving least-squares approximation interpolating moving least-squares method mesh- less method improved boundary element-free method potential problem
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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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Buckling analysis of super-long rock-socketed filling piles in soft soil area by element free Galerkin method 被引量:2
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作者 邹新军 赵明华 刘光栋 《Journal of Central South University of Technology》 EI 2007年第6期858-863,共6页
In order to discuss the buckling stability of super-long rock-socketed filling piles widely used in bridge engineering in soft soil area such as Dongting Lake, the second stability type was adopted instead of traditio... In order to discuss the buckling stability of super-long rock-socketed filling piles widely used in bridge engineering in soft soil area such as Dongting Lake, the second stability type was adopted instead of traditional first type, and a newly invented numerical analysis method, i.e. the element-free Galerkin method (EFGM), was introduced to consider the non-concordant deformation and nonlinearity of the pile-soil interface. Then, based on the nonlinear elastic-ideal plastic pile-soil interface model, a nonlinear iterative algorithm was given to analyze the pile-soil interaction, and a program for buckling analysis of piles by the EFGM (PBAP-EFGM) and arc length method was worked out as well. The application results in an engineering example show that, the shape of pile top load-settlement curve obtained by the program agrees well with the measured one, of which the difference may be caused mainly by those uncertain factors such as possible initial defects of pile shaft and the eccentric loading during the test process. However, the calculated critical load is very close with the measured ultimate load of the test pile, and the corresponding relative error is only 5.6%, far better than the calculated values by linear and nonlinear incremental buckling analysis (with a greater relative error of 37.0% and 15.4% respectively), which also verifies the rationality and feasibility of the present method. 展开更多
关键词 super-long rock-socketed filling pile buckling analysis element free Galerkin method critical load
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Adaptive element free Galerkin method applied to analysis of earthquake induced liquefaction 被引量:5
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作者 荚颖 唐小微 +1 位作者 栾茂田 杨庆 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2008年第2期217-224,共8页
An automatically adaptive element free method is presented to analyze the seismic response of liquefiable soils. The method is based on the element free Galerkin method (EFGM) and the fission procedure that is part ... An automatically adaptive element free method is presented to analyze the seismic response of liquefiable soils. The method is based on the element free Galerkin method (EFGM) and the fission procedure that is part of h-refinement, indicated by error estimation. In the proposed method, a posteriori error estimate procedure that depends on the energy norm of stress and the T-Belytschko (TB) stress recovery scheme is incorporated. The effective cyclic elasto-plastic constitutive model is used to describe the nonlinear behavior of the saturated soil. The governing equations are established by u-p formulation. The proposed method can effectively avoid the volumetric locking due to large deformation that usually occurs in numerical computations using the finite element method (FEM). The efficiency of the proposed method is demonstrated by evaluating the seismic response of an embankment and comparing it to results obtained through FEM. It is shown that the proposed method provides an accurate seismic analysis of saturated soil that includes the effects of liquefaction . 展开更多
关键词 adaptive element-free Galerkin method soil liquefaction large deformation error estimation seismic response
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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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Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems 被引量:2
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作者 唐耀宗 李小林 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第3期215-225,共11页
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... 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. 展开更多
关键词 meshless method moving least squares approximation element-free Galerkin method error esti-mate
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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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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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Element-free Galerkin (EFG) method for a kind of two-dimensional linear hyperbolic equation 被引量:2
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作者 程荣军 葛红霞 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第10期4059-4064,共6页
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 tes... 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. 展开更多
关键词 element-free Galerkin (EFG) method meshless method hyperbolic problem
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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 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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Mixed finite element and differential quadrature method for free and forced vibration and buckling analysis of rectangular plates 被引量:6
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作者 S. A. EFTEKHARI A. A. JAFARI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2012年第1期81-98,共18页
This paper presents a combined application of the finite element method (FEM) and the differential quadrature method (DQM) to vibration and buckling problems of rectangular plates. The proposed scheme combines the... This paper presents a combined application of the finite element method (FEM) and the differential quadrature method (DQM) to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development. 展开更多
关键词 finite element method (FEM) differential quadrature method (DQM) rectangular plate free and forced vibration buckling analysis
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NEW ALGORITHM OF COUPLING ELEMENT-FREE GALERKIN WITH FINITE ELEMENT METHOD
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作者 ZHAO Guang-ming(赵光明) SONG Shun-cheng(宋顺成) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第8期982-988,共7页
Through the construction of a new ramp function, the element-flee Galerkin method and finite element coupling method were applied to the whole field, and was made fit for the structure of element nodes within the inte... Through the construction of a new ramp function, the element-flee Galerkin method and finite element coupling method were applied to the whole field, and was made fit for the structure of element nodes within the interface regions, both satisfying the essential boundary conditions and deploying meshless nodes and finite elements in a convenient and flexible way, which can meet the requirements of computation for complicated field. The comparison between the results of the present study and the corresponding analytical solutions shows this method is feasible and effective. 展开更多
关键词 element-free Galerkin method COUPLING ramp function finite element
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Application in metal rheological forming of element-free Galerkin method
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作者 罗迎社 殷水平 余敏 《Journal of Central South University》 SCIE EI CAS 2008年第S1期187-191,共5页
The element-free method is a new numerical technique presented in recent years.It uses the moving least square(MLS) approximation as its shape function,and it is determined by the basic function and weight function.Th... The element-free method is a new numerical technique presented in recent years.It uses the moving least square(MLS) approximation as its shape function,and it is determined by the basic function and weight function.The weight function is the mainly determining factor,so it greatly affects the accuracy of the computational results.The element-free Galerkin method(EFGM) was applied for the solution to plastic large deformation.The simulation of metal rheological forming was successfully done by programming and its results were visualized by using the plotting and data analyses software Tecplot.Then plastic strain under different stages during rheological forming and the three principal stresses at the last deformation were obtained.The example shows the feasibility of EFGM used for metal rheological forming and provides a new method for numerical simulation of rheological forming of complex parts. 展开更多
关键词 element-free GALERKIN method WEIGHT FUNCTION RHEOLOGICAL FORMING NUMERICAL simulation
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Element-free Galerkin method for a kind of KdV equation
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作者 王聚丰 孙凤欣 程荣军 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第6期7-12,共6页
The present paper deals with the numerical solution of the third-order nonlinear KdV equation using the element-free Calerkin (EFG) method which is based on the moving least-squares approximation. A variational meth... The present paper deals with the numerical solution of the third-order nonlinear KdV equation using the element-free Calerkin (EFG) method which is based on the moving least-squares approximation. A variational method is used to obtain discrete equations, and the essential boundary conditions are enforced by the penalty method. Compared with numerical methods based on mesh, the EFG method for KdV equations needs only scattered nodes instead of meshing the domain of the problem. It does not require any element connectivity and does not suffer much degradation in accuracy when nodal arrangements are very irregular. The effectiveness of the EFG method for the KdV equation is investigated by two numerical examples in this paper. 展开更多
关键词 element-free Galerkin method meshless method KdV equation
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The element-free Galerkin method of numerically solving a regularized long-wave equation
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作者 程荣军 葛红霞 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第4期32-37,共6页
The element-free Galerkin (EFG) method is used in this paper to find the numerical solution to a regularized long-wave (RLW) equation. The Galerkin weak form is adopted to obtain the discrete equations, and the es... The element-free Galerkin (EFG) method is used in this paper to find the numerical solution to a regularized long-wave (RLW) equation. The Galerkin weak form is adopted to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. The effectiveness of the EFG method of solving the RLW equation is investigated by two numerical examples in this paper. 展开更多
关键词 element-free Galerkin method meshless method regularized long wave equation solitary wave
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An improved element-free Galerkin method for solving the generalized fifth-order Korteweg-de Vries equation
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作者 冯昭 王晓东 欧阳洁 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第7期320-327,共8页
In this paper, an improved element-free Galerkin (IEFG) method is proposed to solve the generalized fifth-order Korteweg-de Vries (gfKdV) equation. When the traditional element-free Galerkin (EFG) method is used... In this paper, an improved element-free Galerkin (IEFG) method is proposed to solve the generalized fifth-order Korteweg-de Vries (gfKdV) equation. When the traditional element-free Galerkin (EFG) method is used to solve such an equation, unstable or even wrong numerical solutions may be obtained due to the violation of the consistency conditions of the moving least-squares (MLS) shape functions. To solve this problem, the EFG method is improved by employing the improved moving least-squares (IMLS) approximation based on the shifted polynomial basis functions. The effectiveness of the IEFG method for the gfKdV equation is investigated by using some numerical examples. Meanwhile, the motion of single solitary wave and the interaction of two solitons are simulated using the IEFG method. 展开更多
关键词 element-free Galerkin method shifted polynomial basis generalized fifth-order Korteweg–de Vries equation solitary wave
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An element-free Galerkin(EFG) method for numerical solution of the coupled Schrdinger-KdV equations
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作者 刘永庆 程荣军 葛红霞 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第10期79-87,共9页
The present paper deals with the numerical solution of the coupled Schrodinger-KdV equations using the elementfree Galerkin (EFG) method which is based on the moving least-square approximation. Instead of traditiona... The present paper deals with the numerical solution of the coupled Schrodinger-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. 展开更多
关键词 element-free Galerkin (EFG) method meshless method the coupled Schr6dinger-KdV equations
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