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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 Department of Engineering mechanics Chang’an University Xi’an China shanghai institute of applied mathematics and mechanics Shanghai University Shanghai 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

NUMERICAL SOLUTION FOR TIDAL FLOW IN OPENING CHANNEL USING COMBINED MACCORMACK-FINITE ANALYSIS METHOD

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Journal of Hydrodynamics 2009年第4期21卷 505-511页

作者： WU Zhao-chun WANG Dao-zeng shanghai institute of applied mathematics and mechanics Shanghai University Shanghai 200072 China School of Construction and Safety Engineering Shanghai Institute of Technology Shanghai 200235 China

A new numerical scheme for solving the tidal flow in an opening channel using the advective-diffusion shallow-water equations as the governing equations is proposed based on the combination of the MacCormack and the finite analysis methods. In the present scheme, the finite analysis method is used to discretize the momentum equation and the MacCormack technique is used to discretize the continuity equation in a single grid system. The matrix of the discretized momentum equation is characterized by predominantly main diagonal elements, which ensures favorable convergence and stability for the numerical simulation by the combined method. To verify the present method, hydraulics simulation is carried out for a section down mainstream of the Huangpu River. The computational results agree with the measured data. By use of orthogonal curvilinear coordinate system, the methods can be easily extended to the numerical simulation of the tidal flow in a tortuous channel.

关键词： MacCormack technique finite analysis method tidal flow shallow water equation numerical simulation

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 School of Computer Engineering and Science Shanghai University Shanghai China shanghai institute of applied mathematics and mechanics Shanghai University Shanghai 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

A LATTICE BOLTZMANN METHOD FOR SIMULATION OF A THREE-DIMENSIONAL DROP IMPACT ON A LIQUID FILM

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Journal of Hydrodynamics 2008年第3期20卷 267-272页

作者： SHI Zi-yuan YAN Yong-hua YAN-G Fan QIAN Yue-hong HU Guo-hui shanghai institute of applied mathematics and mechanics Shanghai University Shanghai 200072 China shanghai Key Laboratory of mechanics in Energy and Environment Engineering Shanghai 200072 China shanghai East Pump （Group） Co. Ltd Shanghai 201907 China

A single-phase free surface tracking model based on the Lattice Boltzmann Method （LBM）, which has capability of simulating liquid-gas system with the assumption that the gas phase has only negligible influence on the liquid phase, is utilized to simulate the flow of a drop impacting on a liquid film. Three typical outcomes in the flows, i.e., deposition, crown and splash, which have been observed in the previous experiments, are obtained in the present three dimensional numerical simulations. The numerical results are consistent with the experimental and analytical results available.

关键词： Lattice Boltzmann Method (LBM) drop impact two-phase flows thin film

Approximate Analytical Solution of Blasius'Equation

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Communications in Nonlinear Science and Numerical Simulation 1998年第4期3卷 260-263页

作者： Jihuan HE(shanghai University, shanghai institute of applied mathematics and mechanics,shanghai 200072, china)Email: glliu@*** shanghai University Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China

The Blasius’ equation f"’ + ff"/2=0, with boundary conditions f(0) =f,(0)0, f’ (+∞)=1 is studied in this paper. An approximate analytical solution is obtained via the variational iteration method. The comparison w... 详细信息

关键词： nonlinear technique variational iteration method Blasius’ flow variational technique

Newton-Like Iteration Method for Solving Algebraic Equations

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Communications in Nonlinear Science and Numerical Simulation 1998年第2期3卷 54-57页

作者： Jihuan HE (shanghai University, shanghai institute of applied mathematics and mechanics, shanghai ,200072, china, Email glliu@***) shanghai University Shanghai Institute of Applied mathematics and Mechanics Shanghai 200072. China

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ＩｎｔｒｏｄｕｃｔｉｏｎＩｔｃａｎｏｆｔｅｎｂｅｍｅｔｉｎｓｃｉｅｎｔｉｆｉｃａｎｄｅｎｇｉｎｅｅｒｉｎｇｐｒａｃｔｉｃｅｓｔｏｆｉｎｄａｌｒｏｏｔｓｏｆａｐｏｌｙｎｏｍｉａｌｏｒａｎａｌｇｅｂｒａｉｃｅｑｕａｔｉｏｎ．Ｔｈｅｗｅｌｋｎｏｗｎｍｅ...

关键词： nonlinearity Newton like iteration method perturbation method

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 shanghai institute of applied mathematics and mechanics Shanghai University Shanghai China Department of Civil Engineering Shanghai University 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.

Variational Theory for ChandrasekharaiahThermopiezoelectricity

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Communications in Nonlinear Science and Numerical Simulation 1999年第4期4卷 289-292页

IntroductionRecelltillterestinpiezoelectricmaterialsst***1988,Chandrasekharaiah[1]propos***,Ashida&Tauchert[2... 详细信息

IntroductionRecelltillterestinpiezoelectricmaterialsst***1988,Chandrasekharaiah[1]propos***,Ashida&Tauchert[2...

关键词： thermopiezoelectricity variational theory semi-inverse method finite element method Lagrange multiplier

A Variational Model for an AsymptoticMagnetohydrodynamic System

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Communications in Nonlinear Science and Numerical Simulation 1998年第3期3卷 176-179页

In the present paper an asymptotic gas magnetohydrodynamic system isformulated in veriational principles for the first time via the semi-inverse method proposedby He. Thus, a new theoretical basis for the trite elemen... 详细信息

关键词： variational technique semi-inverse method unsteady flow magnetohydrodynamic