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独立覆盖流形法的本质边界条件施加方法 预览 被引量:3
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作者 苏海东 颉志强 《长江科学院院报》 CSCD 北大核心 2017年第12期140-146,共7页
目前, 数值流形方法、 无网格法等新的数值计算方法存在本质边界条件不易严格施加的问题.针对笔者前期提出的独立覆盖流形法, 通过一个悬臂梁的例子, 系统地分析了本质边界条件施加问题.采用多项式覆盖函数,提出了改进边界覆盖函数和直... 目前, 数值流形方法、 无网格法等新的数值计算方法存在本质边界条件不易严格施加的问题.针对笔者前期提出的独立覆盖流形法, 通过一个悬臂梁的例子, 系统地分析了本质边界条件施加问题.采用多项式覆盖函数,提出了改进边界覆盖函数和直接设定独立覆盖函数 2种方法, 不仅严格满足边界条件, 而且能保证边界附近的近似函数逼近真实解.这 2种方法避免了常用罚函数法中的罚数取值对计算结果和方程性态的影响问题, 而且只需令部分自由度不参与计算就能实现, 操作简单.通过设置覆盖函数来施加边界条件的方式可供其他新方法借鉴. 展开更多
关键词 数值流形方法 独立覆盖 本质边界条件 多项式覆盖函数 罚函数法
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Two-dimensional fracture analysis of piezoelectric material based on the scaled boundary node method 被引量:1
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作者 陈莘莘 王娟 李庆华 《中国物理B:英文版》 SCIE EI CAS CSCD 2016年第4期22-29,共8页
A scaled boundary node method(SBNM) is developed for two-dimensional fracture analysis of piezoelectric material,which allows the stress and electric displacement intensity factors to be calculated directly and accura... A scaled boundary node method(SBNM) is developed for two-dimensional fracture analysis of piezoelectric material,which allows the stress and electric displacement intensity factors to be calculated directly and accurately. As a boundarytype meshless method, the SBNM employs the moving Kriging(MK) interpolation technique to an approximate unknown field in the circumferential direction and therefore only a set of scattered nodes are required to discretize the boundary. As the shape functions satisfy Kronecker delta property, no special techniques are required to impose the essential boundary conditions. In the radial direction, the SBNM seeks analytical solutions by making use of analytical techniques available to solve ordinary differential equations. Numerical examples are investigated and satisfactory solutions are obtained, which validates the accuracy and simplicity of the proposed approach. 展开更多
关键词 边界节点 断裂分析 压电材料 节点法 二维 电位移强度因子 KRIGING 本质边界条件
Solving unsteady Schrodinger equation using the improved element-free Galerkin method
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作者 程荣军 程玉民 《中国物理B:英文版》 SCIE EI CAS CSCD 2016年第2期35-43,共9页
By employing the improved moving least-square(EVILS) approximation,the improved element-free Galerkin(IEFG)method is presented for the unsteady Schr?dinger equation.In the E3 FG method,the two-dimensional(2D) trial fu... By employing the improved moving least-square(EVILS) approximation,the improved element-free Galerkin(IEFG)method is presented for the unsteady Schr?dinger equation.In the E3 FG 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. 展开更多
关键词 无网格伽辽金法 薛定谔方程 非定常 移动最小二乘近似 求解 本质边界条件 离散方程 近似方法
基于多边形支持域的无单元Galerkin方法研究 预览 被引量:1
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作者 张金凤 王晓东 +1 位作者 欧阳洁 冯昭 《工程数学学报》 CSCD 北大核心 2015年第3期348-358,共11页
本文针对传统无单元Galerkin方法不能直接施加本质边界条件的缺点,提出了基于多边形支持域的无单元Galerkin方法.该方法将计算点的支持域由矩形或圆形扩展为多边形,使得移动最小二乘形函数满足Kronecker函数性质,进而使无单元Galerkin... 本文针对传统无单元Galerkin方法不能直接施加本质边界条件的缺点,提出了基于多边形支持域的无单元Galerkin方法.该方法将计算点的支持域由矩形或圆形扩展为多边形,使得移动最小二乘形函数满足Kronecker函数性质,进而使无单元Galerkin方法可以直接施加本质边界条件.此外,该方法将积分背景网格与多边形支持域关联,可以避免重复的节点搜索,提高了无单元Galerkin方法的计算效率.数值结果表明,基于多边形支持域的无单元Galerkin方法不但具有较高的计算效率,且与稳定化方案耦合,可以成功克服对流占优引起的数值不稳定问题. 展开更多
关键词 多边形支持域 无单元方法 本质边界条件 GALERKIN方法
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A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation
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作者 葛红霞 程荣军 《中国物理B:英文版》 SCIE EI CAS CSCD 2014年第4期91-97,共7页
Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity,physics, engineering, and other areas of applications. In this paper, a meshfree method based on the movin... Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity,physics, engineering, and other areas of applications. In this paper, a meshfree method based on the moving Kriging interpolation is developed for a two-dimensional time-fractional diffusion equation. The shape function and its derivatives are obtained by the moving Kriging interpolation technique. For possessing the Kronecker delta property, this technique is very efficient in imposing the essential boundary conditions. The governing time-fractional diffusion equations are transformed into a standard weak formulation by the Galerkin method. It is then discretized into a meshfree system of time-dependent equations, which are solved by the standard central difference method. Numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in detail. 展开更多
关键词 分数阶扩散方程 无网格方法 克里金插值 时间 移动 二维 GALERKIN方法 本质边界条件
Combining the complex variable reproducing kernel particle method and the finite element method for solving transient heat conduction problems
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作者 陈丽 马和平 程玉民 《中国物理B:英文版》 SCIE EI CAS CSCD 2013年第5期67-74,共8页
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 no... 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
关键词 有限元方法 热传导问题 瞬态 粒子 本质边界条件 边界值问题 计算效率 时间离散
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 《中国物理B:英文版》 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 equivale... 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 对流扩散问题 无网格方法 复变量 移动最小二乘 本质边界条件 离散方程 罚函数法 区别方法
Analysis of variable coefficient advection-diffusion problems via complex variable reproducing kernel particle method
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作者 翁云杰 程玉民 《中国物理B:英文版》 SCIE EI CAS CSCD 2013年第9期197-202,共6页
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 f... 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
关键词 对流扩散问题 变系数 粒子法 复变量 重构 本质边界条件 计算效率 形状函数
The improved element-free Galerkin method for three-dimensional transient heat conduction problems 被引量:4
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作者 ZHANG Zan WANG JianFei +1 位作者 CHENG YuMin LIEW Kim Meow 《中国科学:物理学、力学、天文学英文版》 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 无网格伽辽金法 热传导问题 三维瞬态 本质边界条件 瞬态热传导方程 偏微分方程 移动最小二乘 边界值问题
NEW TREATMENT OF ESSENTIAL BOUNDARY CONDITIONS IN EFG METHOD BY COUPLING WITH RPIM 被引量:1
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作者 Yang Cao Linquan Yao Yu Yin 《固体力学学报:英文版》 SCIE EI CSCD 2013年第3期302-316,共15页
在用移动的 meshfree 方法的实现的主要困难之一最不摆平(MLS ) 当近似不通过节的参数价值,近似例如没有元素的 Galerkin 方法(EFG ) ,是必要边界条件的负担。完全自从它的近似函数在影响域通过每个节点,因此,它的形状工作,基于光... 在用移动的 meshfree 方法的实现的主要困难之一最不摆平(MLS ) 当近似不通过节的参数价值,近似例如没有元素的 Galerkin 方法(EFG ) ,是必要边界条件的负担。完全自从它的近似函数在影响域通过每个节点,因此,它的形状工作,基于光线的基础点,插值能满足必要边界的 meshfree 方法的另一个类调节拥有三角洲功能的性质。在这份报纸, a coupled 没有元素的 Galerkin (EFG ) 光线的点插值方法(RPIM ) 被建议提高他们的优点并且避免他们的劣势。平衡的 Discretized 方程分别地在 RPIM 区域和 EFG 区域被获得。然后,一条搭配途径被介绍联合 RPIM 和 EFG 方法。这个方法确切满足线性一致性并且能维持僵硬矩阵对称。数字测试证明这个方法给与理论一致的相当精确的结果。 展开更多
关键词 本质边界条件 EFG 耦合 无网格伽辽金法 无网格方法 治疗 移动最小二乘 逼近函数
An improved interpolating element-free Galerkin method for elasticity 被引量:1
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作者 孙凤欣 王聚丰 程玉民 《中国物理B:英文版》 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 problems in ... 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 无网格伽辽金法 弹性问题 插值 移动最小二乘 EFG法 本质边界条件 S方法 MLS
A MESH-FREE ALGORITHM FOR DYNAMIC IMPACT ANALYSIS OF HYPERELASTICITY
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作者 De’an Hu Zhanhua Sun +1 位作者 Chao Liang Xu Han 《固体力学学报:英文版》 SCIE EI CSCD 2013年第4期362-372,共11页
基于本地 Petrov-Galerkin,明确的表达被介绍解决 hyperelastic 材料的动态影响问题的一个没有网孔的方法。在现在的方法,简单海维赛德测试功能为简化领域积分被选择。试用功能被使用结合的光线的基础功能(RBF ) 构造多项式基础功能... 基于本地 Petrov-Galerkin,明确的表达被介绍解决 hyperelastic 材料的动态影响问题的一个没有网孔的方法。在现在的方法,简单海维赛德测试功能为简化领域积分被选择。试用功能被使用结合的光线的基础功能(RBF ) 构造多项式基础功能,形状功能在拥有 kronecker 三角洲功能性质。那么,另外的处理没为强加必要边界条件被要求。除了数字集成能在现在的方法在本地领域上被实现之外,管理影响问题的方程被建立并且由在一个本地领域使用一个明确的时间集成算法由节点解决了节点,它很类似于搭配方法的。几个例子的数字结果证明现在的方法表现很好在处理 hyperelastic 材料的动态影响问题。 展开更多
关键词 超弹性材料 积分算法 网状 免费 本质边界条件 径向基函数 DELTA 测试功能
A new complex variable element-free Galerkin method for two-dimensional potential problems 被引量:1
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作者 程玉民 王健菲 白福浓 《中国物理B:英文版》 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-free ... 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 无网格伽辽金方法 复变量 无单元伽辽金法 移动最小二乘 二维 本质边界条件 拉格朗日乘子 无网格方法
A new complex variable meshless method for transient heat conduction problems 被引量:3
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作者 王健菲 程玉民 《中国物理B:英文版》 SCIE EI CAS CSCD 2012年第12期42-50,共9页
<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 prese... <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. 展开更多
关键词 热传导问题 无网格方法 复变量 瞬态 移动最小二乘 本质边界条件 时间离散 边界值问题
Complex variable element-free Galerkin method for viscoelasticity problems 被引量:1
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作者 程玉民 李荣鑫 彭妙娟 《中国物理B:英文版》 SCIE EI CAS CSCD 2012年第9期60-71,共12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-free ... 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 无网格伽辽金方法 弹性问题 GALERKIN 移动最小二乘 本质边界条件 计算效率 节点分布 复变量
The complex variable meshless local Petrov-Galerkin method of solving two-dimensional potential problems
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作者 杨秀丽 戴保东 张伟伟 《中国物理B:英文版》 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 problems i... 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 无网格局部PETROV-GALERKIN方法 无网格局部Petrov-Galerkin法 二维 求解 移动最小二乘 试探函数 本质边界条件 局部对称
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 《中国物理B:英文版》 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 essent... 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 正则长波方程 无网格伽辽金方法 数值求解 Galerkin 无网格伽辽金法 本质边界条件 RLW方程 离散方程
A scaled boundary node method applied to two-dimensional crack problems 被引量:1
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作者 陈莘莘 李庆华 刘应华 《中国物理B:英文版》 SCIE EI CAS CSCD 2012年第11期55-62,共8页
A boundary-type meshless method called the scaled boundary node method(SBNM) is developed to directly evaluate mixed mode stress intensity factors(SIFs) without extra post-processing.The SBNM combines the scaled bound... A boundary-type meshless method called the scaled boundary node method(SBNM) is developed to directly evaluate mixed mode stress intensity factors(SIFs) without extra post-processing.The SBNM combines the scaled boundary equations with the moving Kriging(MK) interpolation to retain the dimensionality advantage of the former and the meshless attribute of the latter.As a result,the SBNM requires only a set of scattered nodes on the boundary,and the displacement field is approximated by using the MK interpolation technique,which possesses the δ function property.This makes the developed method efficient and straightforward in imposing the essential boundary conditions,and no special treatment techniques are required.Besides,the SBNM works by weakening the governing differential equations in the circumferential direction and then solving the weakened equations analytically in the radial direction.Therefore,the SBNM permits an accurate representation of the singularities in the radial direction when the scaling center is located at the crack tip.Numerical examples using the SBNM for computing the SIFs are presented.Good agreements with available results in the literature are obtained. 展开更多
关键词 边界节点 裂纹问题 比例 应力强度因子 二维 应用 插值技术 本质边界条件
C^1 natural element method for strain gradient linear elasticity and its application to microstructures 预览 被引量:1
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作者 Zhi-Feng Nie Shen-Jie Zhou +2 位作者 Ru-Jun Han Lin-Jing Xiao Kai Wang 《力学学报:英文版》 SCIE EI CAS CSCD 2012年第1期 91-103,共13页
C 1 natural element method (C 1 NEM) is applied to strain gradient linear elasticity, and size effects on microstructures are analyzed. The shape functions in C 1 NEM are built upon the natural neighbor interpolation ... C 1 natural element method (C 1 NEM) is applied to strain gradient linear elasticity, and size effects on microstructures are analyzed. The shape functions in C 1 NEM are built upon the natural neighbor interpolation (NNI), with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions (EBCs) can be imposed directly in a Galerkin scheme for partial differential equations (PDEs). In the present paper, C 1 NEM for strain gradient linear elasticity is constructed, and several typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor (SCF) are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch. 展开更多
关键词 应变梯度 微观结构 自然元素 弹性 线性 应用 偏微分方程 本质边界条件
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无网格方法施加本质边界条件的主从自由度法 预览
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作者 郑子君 陈永强 陈璞 《计算物理》 EI CSCD 北大核心 2012年第2期 159-165,共7页
以SPH(smoothed particle hydrodynamics)方法为例,把无网格法中的本质边界条件和复合材料界面连续条件视为多点约束(multi-point constraint,MPC),用主从自由度法(master-slave method)来处理.典型的基体-夹杂复合材料的线弹性... 以SPH(smoothed particle hydrodynamics)方法为例,把无网格法中的本质边界条件和复合材料界面连续条件视为多点约束(multi-point constraint,MPC),用主从自由度法(master-slave method)来处理.典型的基体-夹杂复合材料的线弹性问题算例结果表明,与罚函数法相比,采用主从自由度法的精度更高,适用范围更广. 展开更多
关键词 无网格法 光滑粒子动力学 本质边界条件 多点约束 主从自由度法
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