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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 {2., shanghai 2.0072. china 2. Department of Civil Engineering, shanghai {2., shanghai 2.0072. 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.

Transverse patterns and spatiotemporal instability of a photorefractive oscillator

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Chinese Science Bulletin 1997年第9期42卷 724-729页

作者： ZHUANG Jun and TAN Weihan1. shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, shanghai 2.1800,{2. 2. shanghai university, shanghai 2.1800,{2. shanghai Institute of Optics and Fine Mechanics Chinese Academy of Sciences Shanghai China shanghai university Shanghai China

IN time realm,instability and chaos phenomena of a nonlinear optical system have been dis-cussed *** recent years,as much interest was attracted to the transverse ef-fects in nonlinear optics,the study was developed t... 详细信息

关键词： photorefractive oscillator spatiotemporal instability transverse patterns.

Research on nonlinear constitutive relationship of permanent deformation in asphalt pavements

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Science china(Physics,Mechanics & Astronomy) 2006年第6期49卷 671-682页

作者： PENG Miaojuan1 & XU Zhihong2.1. Department of Civil Engineering,shanghai university,shanghai 2.0072.china 2. School of Transportation Engineering,Tongji university,shanghai 2.0092.china Department of Civil Engineering Shanghai University Shanghai China School of Transportation Engineering Tongji University Shanghai China

To predict correctly the rut depths in asphalt pavements,a new nonlinear viscoelastic-elastoplastic constitutive model of permanent deformation in asphalt pave-ments is presented. The model combines a generalized Maxwell model with an elasto-plastic one. Then from the creep theory,the linear and nonlinear constitutive equations of the generalized Maxwell model are obtained. From the nonlinear finite element method for the rutting of the asphalt pavement,the rut depths of 4 asphalt-aggregate mixtures are obtained. And the results are compared with the ones from the finite element method by SHRP and the experiments by SWK/UN. The results in this paper are better than the ones by SHRP,and agree with the ones of the experiment by SWK/UN. This shows that the nonlinear viscoelastic-elastoplastic constitutive model,which is presented in this paper for the rutting of the asphalt pavement,is effective. The properties,such as nonlinear elastic-ity,plasticity,viscoelasticity and nonlinear viscoelasticity,which affect the rutting of an asphalt pavement,can be shown in the model. And the characteristics of the permanent deformation of the asphalt pavement can be presented entirely in the model.

关键词： asphalt pavement,permanent deformation,nonlinear viscoelastic-elastoplastic constitutive relationship,generalized Maxwell model,creep compliance.

A New Combination of Mutated loxPs in a Vector for Construction of Phage Antibody Libraries

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Acta Biochimica et Biophysica Sinica 2005年第7期37卷 495-500页

作者： Yu GAN~(1,2. Xin-Tai ZHAO~2. 1 shanghai Medical College,Fudan university,shanghai 2.0032.china 2.Laboratory for Cellular and Molecular Immunology,Cancer Institute,shanghai Jiaotong university,shanghai 2.0032.china shanghai Medical College Fudan UniversityShanghai 200032 China Laboratory for Cellular and Molecular Immunology Cancer Institute Shanghai Jiaotong UniversityShanghai 200032 China

In the construction of large antibody libraries by in vivo recombination,two non-homogeneousloxP sites are required for the exchange of V genes between phagemids to create many new *** mutated loxP511 was designed not to recombine with the wild-type loxP （loxPwt） in early studies anda combination of the two has been used to construct antibody *** recent reports have shown thatrecombination occurs between loxPwt and *** suggests that the combinational use of loxP511and loxPwt might lead to the loss of the V gene diversity of antibody ***,it is necessary tofind a new combination of loxPs to avoid the excision recombination in the antibody *** this study,we found that the excision recombination between loxP511 and loxP2.72.another mutated loxP sequence,was undetectable within one phagemid,while the excision recombination between loxP511 and loxPwtoccurred at a frequency of 40%.higher than that reported ***,the in vivo recombinationof different phagemids with loxP511 and loxP2.72.showed that the V gene exchange was efficiently mediatedto produce new *** was concluded that the loxP511 and loxP2.72.combination wasmore favorable for reducing the excision recombination and constructing large phage antibody libraries withhigh diversity.

关键词： mutated loxP excision recombination phage antibody library

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 {2., shanghai 2.0072. china 2. Department of Building Engineering, Xi’an {2. of Technology, Xi’an 710048, china shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai China Department of Building Engineering Xi’an University of Technology Xi’an 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.

Population-size-dependent branching processes in Markovian random environments

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Chinese Science Bulletin 1998年第8期43卷 635-638页

作者： WANG Hanxing 1 and DAI Yonglong 2.1. Department of Mathematics, shanghai university,{2., china 2. Department of Mathematics, Zhongshan university, Guangzhou 5102.5, china Department of Mathematics Shanghai University Shanghai China Department of Mathematics Zhongshan University Gunngzhou China

A branching model {Z n} n≥0is considered where the offspring distribution of the population’s evolution is not only dependent on the population size, but also controlled by a Markovian environmental process {ξ n} n≥0. For this model, asymptotic behaviour is studied such as limn→∞Z n and limn→∞Z n/m n in the case that the mean m k, θof the offspring distribution converges to m>1 as the population size k grows to ∞. In the case that {ξ n} n≥0is an irreducible positive recurrent Markov chain, certain extinction (i.e. P(Z n=0 for some n)=1) and noncertain extinction (i.e. P(Z n=0 for some n)<1) are studied.

关键词： Markov chains in random environments stochastic population models branching processes.

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 Mechanics, shanghai {2., shanghai 2.0072. china 2.Department of Mechanics, shanghai {2., shanghai 2.0444, china shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai China Department of Mechanics Shanghai University Shanghai 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 2.0072. china 2.shanghai Institute of Applied Mathematics and Mechanics, shanghai university, shanghai 2.0072. 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

Steady-state responses of axially accelerating viscoelastic beams: Approximate analysis and numerical confirmation

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Science china(Physics,Mechanics & Astronomy) 2008年第11期51卷 1707-1721页

作者： CHEN LiQun1,2.& DING Hu2.1 Department of Mechanics, shanghai university, shanghai 2.0444, china 2.shanghai Institute of Applied Mathematics and Mechanics, shanghai 2.0070, china Department of Mechanics Shanghai University Shanghai China shanghai Institute of Applied Mathematics and Mechanics Shanghai China

Nonlinear parametric vibration of axially accelerating viscoelastic beams is inves-tigated via an approximate analytical method with numerical confirmations. Based on nonlinear models of a finite-small-stretching slender beam moving at a speed with a periodic fluctuation, a solvability condition is established via the method of multiple scales for subharmonic resonance. Therefore, the amplitudes of steady-state periodic responses and their existence conditions are derived. The amplitudes of stable steady-state responses increase with the amplitude of the axial speed fluctuation, and decrease with the viscosity coefficient and the nonlinear coefficient. The minimum of the detuning parameter which causes the existence of a stable steady-state periodic response decreases with the amplitude of the axial speed fluctuation, and increases with the viscosity coefficient. Nu-merical solutions are sought via the finite difference scheme for a nonlinear par-tial-differential equation and a nonlinear integro-partial-differential equation. The calculation results qualitatively confirm the effects of the related parameters pre-dicted by the approximate analysis on the amplitude and the existence condition of the stable steady-state periodic responses. Quantitative comparisons demonstrate that the approximate analysis results have rather high precision.

关键词： nonlinearity parametric vibration axially accelerating beam method of multiple scales numerical confir-mation