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An interpolating boundary element-free method (IBEFM) for elasticity problems

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Science china(Physics,mechanics & Astronomy) 2010年第4期53卷 758-766页

作者： REN HongPing 1 , CHENG YuMin 2 & ZHANG Wu 1 1 School of Computer Engineering and Science, shanghai university, shanghai 200072, china 2 shanghai institute of applied mathematics and mechanics, shanghai university, shanghai 200072, china 1. School of Computer Engineering and Science Shanghai University Shanghai 200072 China2. Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China

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.

关键词： moving least-squares (MLS) approximation interpolating moving least-squares (IMLS) method boundary integral equation meshless method boundary element-free method (BEFM) interpolating boundary element-free method (IBEFM) elasticity problem

Boundary element-free method for elastodynamics

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Science china(Physics,mechanics & Astronomy) 2005年第6期48卷 641-657页

作者： CHENG Yumin1 & PENG Miaojuan2 1. shanghai institute of applied mathematics and mechanics, shanghai university, shanghai 200072, china 2. Department of Civil Engineering, shanghai university, shanghai 200072, china 1. shanghai institute of applied mathematics and mechanics Shanghai University 200072 Shanghai China 2. Department of Civil Engineering Shanghai University 200072 Shanghai China

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.

关键词： moving least-square approximation, improved moving least-square approximation, elastodynamics, boundary integral equation, meshless method, boundary element-free method, Fourier eigen transform.

The complex variable reproducing kernel particle method for elasto-plasticity problems

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Science china(Physics,mechanics & Astronomy) 2010年第5期53卷 954-965页

作者： CHEN Li1 & CHENG YuMin2 1 Department of Engineering mechanics,Chang’an university,Xi’an 710064,china 2 shanghai institute of applied mathematics and mechanics,shanghai university,shanghai 200072,china 1. Department of Engineering mechanics Chang’an University Xi’an 710064 China2. Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China

On the basis of reproducing kernel particle method(RKPM),using complex variable theory,the complex variable reproducing kernel particle method(CVRKPM) is discussed in this *** advantage of the CVRKPM is that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is *** the CVRKPM is applied to solve two-dimensional elasto-plasticity *** Galerkin weak form is employed to obtain the discretized system equation,the penalty method is used to apply the essential boundary *** then,the CVRKPM for two-dimensional elasto-plasticity problems is formed,the corresponding formulae are obtained,and the Newton-Raphson method is used in the numerical *** numerical examples are given to show that this method in this paper is effective for elasto-plasticity analysis.

关键词： meshless method reproducing kernel particle method(RKPM) complex variable reproducing kernel particle method(CVRKPM) correction function elasto-plasticity

Embed-Solitons and Their Evolutional Behaviors of (3+1)-Dimensional Burgers System

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Communications in Theoretical Physics 2007年第7期48卷 57-62页

作者： ZHU Hai-Ping ZHENG Chun-Long College of mathematics and Physics,Lishui university,Zhejiang 323000,china2 shanghai institute of applied mathematics and mechanics,shanghai university,shanghai 200072,china College of mathematics and Physics Lishui University Zhejiang 323000 China

With the help of an extended mapping approach and a linear variable separation method,new families ofvariable separation solutions with arbitrary functions for the(3+1)-dimensional Burgers system are *** onthe derived exact solutions, some novel and interesting localized coherent excitations such as embed-solitons are revealedby selecting appropriate boundary conditions and/or initial *** time evolutional properties of the novellocalized excitation are also briefly investigated.

关键词： extended mapping method (3+1)-dimensional Burgers system embed-soliton evolutional behavior

Virtual multi-dimensional internal bonds model and its application in simulation of rock mass

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Science china(Technological Sciences) 2008年第2期51卷 192-201页

作者： ZHANG ZhenNan1,2 & GE XiuRun3,4 1 Department of Civil Engineering,shanghai university,shanghai 200072,china 2 shanghai institute of applied mathematics and mechanics,shanghai university,shanghai 200072, china 3 institute of Geotechnical Engineering,shanghai Jiao Tong university,shanghai 200030,china 4 institute of Rock and Soil mechanics,Chinese Academy of Sciences,Wuhan 430071,china 1. Department of Civil Engineering Shanghai University Shanghai 200072 China 2. shanghai institute of applied mathematics and mechanics Shanghai University Shanghai 200072 China 3. institute of Geotechnical Engineering Shanghai Jiao Tong University Shanghai 200030 China 4. institute of Rock and Soil mechanics Chinese Academy of Sciences Wuhan 430071 China

VMIB (virtual multi-dimensional internal bonds) is a multiscale mechanical model developed from the VIB (virtual internal bond) theory. In VIB theory,the solid mate-rial is considered to consist of random-distributed material particles in microscale. These particles are connected with normal bonds. The macro constitutive relation is derived from the cohesive law between particles. However,in VMIB,the micro particles are connected with both normal and shear bonds. The macro constitutive relation is derived in terms of bond stiffness coefficients. It has been theoretically certified that there exists a corresponding relationship between the two bond stiffness coefficients and the two macro material constants,i.e. the Young’s modulus and Poisson ratio. This corresponding relationship suggests that it should be necessary and sufficient to simultaneously account for the normal and shear interactions between particles. Due to the fact that the fracture criterion is directly incorporated into the constitutive relation,both VIB and VMIB present many advantages in simulating fractures of materials. In the damage model of rock mass,a damage tensor is usually defined to describe the distribution of cracks. The damage value in one direction determines the relative stiffness of rock mass in this direction. In VMIB solid,the relative distribution density of micro bonds in one direction determines the relative macro stiffness of the material in this direction. The effects of the damage value and the relative distribution density of bonds are consistent. To simulate the failure behavior of rock mass with VMIB,the presented paper sets up a quantitative relationship between the damage tensor and the rela-tive distribution density of bonds. Comparison of the theoretical and the experi-mental results shows that VMIB model can represent the effect of distributed cracks on rock mass with this relationship. The presented work provides a founda-tion for further simulating fracture behavior

关键词： VMIB (virtual multi-dimensional internal bonds) rock mass VIB (virtual internal bonds) multi-cracked body numerical simulation

A complex variable meshless method for fracture problems

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Science china(Physics,mechanics & Astronomy) 2006年第1期49卷 46-59页

作者： CHENG Yumin1 & LI Jiuhong2 1. shanghai institute of applied mathematics and mechanics, shanghai university, shanghai 200072, china 2. Department of Building Engineering, Xi’an university of Technology, Xi’an 710048, china shanghai institute of applied mathematics mechanics Shanghai University Shanghai 200072 China Department of Building Engineering Xi’an University of Technology Xi’an 710048 China

Based on the moving least-square (MLS) approximation, the complex variable moving least-square approximation (CVMLS) is discussed in this paper. The complex variable moving least-square approximation cannot form ill-conditioned equations, and has greater precision and computational efficiency. Using the analytical solution near the tip of a crack, the trial functions in the complex variable moving least-square approxi- mation are extended, and the corresponding approximation function is obtained. And from the minimum potential energy principle, a complex variable meshless method for fracture problems is presented, and the formulae of the complex variable meshless method are obtained. The complex variable meshless method in this paper has greater precision and computational efficiency than the conventional meshless method. Some examples are given.

关键词： moving least-square approximation, complex variable moving least-square approximation, meshless method, complex variable meshless method, fracture.

Exact Solution to(1+1)-Dimensional Higher-Order SchrSdinger Equation via an Extended Mapping Approach

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Communications in Theoretical Physics 2006年第1期45卷 127-130页

作者： ZHU Hai-Ping~1 ZHENG Chun-Long~(1,2,+) FANG Jian-Ping~11 Department of Physics,Zhejiang Lishui university,Lishui 323000,china2 shanghai institute of applied mathematics and mechanics,shanghai university,shanghai 200072,china

Starting from a special variable transformation and with the help of an extended mapping approach,the high-order Schr■dinger equation(n=3,4)is solved.A new family of variable separation solutions with arbitraryfuncti... 详细信息

关键词： extended mapping approach Schr■dinger equation exact solution

长短波相互作用方程的Jacobi椭圆函数求解

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物理学报 2003年第11期52卷 2660-2663页

作者：郭冠平张解放浙江师范大学教育科学与技术学院金华321004 上海大学应用数学和力学研究所

推广了Jacobi椭圆函数展开方法 ,研究了复非线性演化方程组的求解问题 ,得到了长短波相互作用方程的准确包络周期解 .该结果在一定条件下包含了相应的孤波解 .

关键词：长短波相互作用方程孤波解 Jacobi椭圆函数法非线性科学行波解数学物理方法

相对论性Birkhoff系统的对称性摄动及其逆问题

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物理学报 2003年第11期52卷 2664-2670页

作者：傅景礼陈立群谢凤萍商丘师范学院数学力学和数学物理研究所商丘476000 上海大学上海市应用数学和力学研究所上海200072

研究在小干扰力作用下相对论性Birkhoff系统的对称性摄动问题 .建立了相对论性Birkhoff系统的基本原理、运动方程和小扰动方程 .讨论该系统的Lie对称性变换和守恒量 .研究在无限小变换下该系统的对称性摄动 ,构造了s阶绝热不变量 .给出... 详细信息

研究在小干扰力作用下相对论性Birkhoff系统的对称性摄动问题 .建立了相对论性Birkhoff系统的基本原理、运动方程和小扰动方程 .讨论该系统的Lie对称性变换和守恒量 .研究在无限小变换下该系统的对称性摄动 ,构造了s阶绝热不变量 .给出了绝热不变量存在的条件和形式 .研究该系统的对称性摄动逆问题 ,当系统存在s阶绝热不变量时 ,得到了该系统的无限小变换的对称性摄动 .研究相对论性Birkhoff系统和经典Birkhoff系统对称性摄动之间的关系 .

关键词：相对论 Lie对称性对称性摄动绝热不变量 Birkhoff方程哈密顿系统数学物理方法