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Weakly nonlinear stability of ultra-thin slipping films

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Progress in Natural Science:Materials International 2005年第9期15卷 827-831页

作者： HU Guohui(shanghai Institute of applied mathematics and {3., shanghai university, shanghai 200072, china) shanghai Institute of applied mathematics and {3. Shanghai University Shanghai 200072 China

A weakly nonlinear theory is presented to study the effects of slippage on the stability of the ultra-thin polymer films. The nonlinear mathematical model is constructed for perturbations of small finite amplitude based on hydrodynamic equations with the long wave approximation. Results reveal that the nonlinearity always accelerates the rupture of the films. The influences of the slip length, film thickness, and initial amplitude of perturbations on the rupture of the films are investigated.

关键词： ultra-thin film weakly nonlinear theory hydrodynamic stability rupture of thin film.

A New Cellular Automaton Model for TrafficFlow

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Communications in Nonlinear Science and Numerical Simulation 1999年第4期4卷 264-267页

作者： Yongtao HU(shanghai institute of applied mathematics and {3., shanghai university,shanghai 200072, china) shanghai Institute of applied mathematics and {3. Shanghai University Shanghai 200072 China

IntroductionCellularautomaton(CA)***,thesemodelSareremaxkable***]introdu... 详细信息

IntroductionCellularautomaton(CA)***,thesemodelSareremaxkable***]introdu...

关键词： traffic model transportation simulation cellular automata

A uniformly valid series solution to the unsteady stagnation-point flow towards an impulsively stretching surface

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Science china(Physics,mechanics & Astronomy) 2010年第3期53卷 521-526页

作者： CHENG Jun & DAI ShiQiang shanghai Institute of applied mathematics and {3., shanghai university, shanghai 200072, china 1. shanghai Institute of applied mathematics and {3. Shanghai University Shanghai 200072 China

The paper studies the problem of the unsteady two-dimensional stagnation-point flow of an incompressible viscous fluid over a flat deformable sheet. The flow is started impulsively from rest and the sheet is suddenly stretched in its own plane with a velocity proportional to the distance from the stagnation point. An analytical series solution is obtained by means of the homotopy analysis method (HAM). Also, the homotopy-Pade′ technique is employed. An explicit formula for the local friction coefficient is provided. The present formula, different from the perturbation solution, is accurate and uniformly valid for all dimensionless time in the whole spatial region and for all possible values of physical parameter λ, defined as the ratio of the potential flow velocity to the sheet sudden stretching velocity. Numerical tests are done to verify the present formula for its validity and accuracy.

关键词： unsteady boundary-layer flows stagnation point stretching sheet homotopy analysis method

Effect of Material Property of Interply Film on the Delamination in Laminated Composites

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Communications in Nonlinear Science and Numerical Simulation 1999年第1期4卷 39-42页

作者： Wei FENG and Qian HUANG (shanghai institute of applied mathematics and {3., shanghai university, shanghai 200072, china) shanghai Institute of applied mathematics and {3. Shanghai University Shanghai 200072 China

The delamination is one of the main failure modes in laminated composites. In order to suppress and/or delay it, considerable research has been devoted to the reduction of the interlaminar stresses at the interfaces between two different plies. This paper studies the effect of isotropic layers placed at ply interface on the interlaminar behaviour of the angle-ply laminated composites. The results of the experiment and numerical analysis show that the material properties of interply film have strong influence on the interlaminar behaviour of laminated composites. In order to suppress delamination, the material of interply film has to been selected carefully due to the fact that different matrials have different results. Some materials may increase the stress values at the interfaces. Some materials may reduce the stress concertration.

关键词： laminated composite interply film stress concentration

On two transverse nonlinear models of axially moving beams

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Science china(Technological Sciences) 2009年第3期52卷 743-751页

作者： DING Hu1 & CHEN LiQun1,2 1 shanghai Institute of applied mathematics and {3., shanghai university, shanghai 200072, china 2 Department of {3., shanghai university, shanghai 200444, china 1. shanghai Institute of applied mathematics and {3. Shanghai University Shanghai 200072 China 2. Department of mechanics Shanghai University Shanghai 200444 China

Nonlinear models of transverse vibration of axially moving beams are computationally investigated. A partial-differential equation is derived from the governing equation of coupled planar motion by omit- ting its longitudinal terms. The model can be reduced to an integro-partial-differential equation by av- eraging the beam disturbed tension. Numerical schemes are respectively presented for the governing equations of coupled planar and the two governing equations of transverse motion via the finite dif- ference method and differential quadrature method under the fixed boundary and the simple support boundary. A steel beam and a copper beam are treated as examples to demonstrate the deviations of the solutions to the two transverse equations from the solution to the coupled equation. The numerical results indicate that the differences increase with the amplitude of vibration and the axial speed. Both models yield almost the same precision results for small amplitude vibration and the inte- gro-partial-differential equation gives better results for large amplitude vibration.

关键词： axially moving beam nonlinearity transverse vibration finite difference method differential quadrature method

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 {3. 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

Numerical Solution of Heat Tranfer Problemwith Flow and Solidification in Round BilletContinuous Casting of Steel

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Communications in Nonlinear Science and Numerical Simulation 1999年第3期4卷 236-239页

作者： Jiahong GUO(shanghai Institute of applied mathematics and {3., shanghai university,shanghai 200072, china)Xin HONG(College of Material Science, shanghai university, shanghai 200072, china) shanghai Institute of applied mathematics and {3. Shanghai University Shanghai 200072 China College of Material Science Shanghai University Shanghai 200072 China

IntroductionThetechnologyofc***g,***,itisimportallttostudythep... 详细信息

IntroductionThetechnologyofc***g,***,itisimportallttostudythep...

关键词： heat transfer flow and solidification round billet continuous casting

Some New Approaches to Duffing Equation with Strongly and High Order Nonlinearity (II) Parametrized Perturbation Technique

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Communications in Nonlinear Science and Numerical Simulation 1999年第1期4卷 78-83页

作者： Jihuan HE (shanghai institute of applied mathematics and {3., shanghai university, shanghai 200072, china) Email: glliu@*** shanghai Institute of applied mathematics and {3. Shanghai University Shanghai 200072 China

For the strongly nonlinear equations without small parameter, a transformation u = v can be introduced for the nonlinear equation L(u) + N(u) = 0, where L and N are general linear and nonlinear differential operators respectively, P is sufficiently small. Therefore, a strongly non-linear system is transformed into a small parameter system with respect to the new introduced parameter P, thus various traditional perturbation techniques can be applied. By Lindstedt-Poincare method, a perturbation solution for Duffing equation with sib order nonlinearity is obtained, which is valid not only for the small parameter E in the equation, but also for very large values of E.

关键词： perturbation technique nonlinear equation

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 {3., shanghai university, shanghai 200072, china 2. Department of Civil Engineering, shanghai university, shanghai 200072, china 1. shanghai Institute of applied mathematics and {3. 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.