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The refined theory of deep rectangular beams based on general solutions of elasticity

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science china(Physics,{2. & Astronomy) 2006年第3期49卷 291-303页

作者： GAO Yang1 & WANG Minzhong2.1. College of science, china Agricultural University, {2. 100083, china 2. State Key Laboratory for Turbulence and Complex Systems and department of mechanics and Engi- neering science, Peking University, beijing 100871, china College of science China Agricultural University Beijing 100083 China State Key Laboratory for Turbulence Complex Systems department of mechanics engineering science Peking University Beijing 100871 China

The problem of deducing one-dimensional theory from two-dimensional the- ory for a homogeneous isotropic beam is investigated. Based on elasticity theory, the re- fined theory of rectangular beams is derived by using Papkovich-Neuber solution and Lur’e method without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by the angle of rotation and the deflection of the neutral surface. Based on the refined beam theory, the exact equations for the beam without transverse surface loadings are derived and consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beam under transverse loadings are derived directly from the refined beam theory and are almost the same as the governing equations of Timoshenko beam theory. In two ex- amples, it is shown that the new theory provides better results than Levinson’s beam the- ory when compared with those obtained from the linear theory of elasticity.

关键词： deep rectangular beams,the refined theory,Papkovich-Neuber solution,Lur'e method,governing equation

The refined theory of transversely isotropic piezoelectric rectangular beams

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science china(Physics,{2. & Astronomy) 2006年第4期49卷 473-486页

作者： GAO Yang1 & WANG Minzhong2.1. College of science, china Agricultural University, {2. 100083, china 2. State Key Laboratory for Turbulence and Complex Systems and department of mechanics and Engi- neering science, Peking University, beijing 100871, china 1. College of science China Agricultural University Beijing 100083 China 2. State Key Laboratory for Turbulence and Complex Systems and department of mechanics and {2. science Peking University Beijing 100871 China

The problem of deducing one-dimensional theory from two-dimensional theory for a transversely isotropic piezoelectric rectangular beam is investigated. Based on the piezoelasticity theory, the refined theory of piezoelectric beams is derived by using the general solution of transversely isotropic piezoelasticity and Lur'e method without ad hoc assumptions. Based on the refined theory of piezoelectric beams, the exact equations for the beams without transverse surface loadings are derived, which consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beams under transverse loadings are derived directly from the refined beam theory. As a special case, the governing differential equations for transversely isotropic elastic beams are obtained from the corresponding equations of piezoelectric beams. To illustrate the application of the beam theory developed, a uniformly loaded and simply supported piezoelectric beam is examined.

关键词： rectangular beams, the refined theory, piezoelectric, transversely isotropic.

Steady States of Some Models for Van derWaals Fluids

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Communications in Nonlinear science and Numerical Simulation 1998年第3期3卷 163-167页

作者： Shaoqiang TANG(department of mechanics and {2. science, Peking University, beijing 100871,china) department of mechanics and {2. science Peking University Beijing 100871 China

We study the steady states of some models for van der Waals fluid. Inparticular, for a mass viscosity model, we show that there is no "cavitation’ wave. Wealso consider the closed orbits, heterocliaic orbits, and the... 详细信息

关键词： steady state phase transition mixed-type problem

Intermediate processes and critical phenomena: Theory, method and progress of fractional operators and their applications to modern mechanics

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science china(Physics,{2. & Astronomy) 2006年第3期49卷 257-272页

作者： XU Mingyu1 & TAN Wenchang2.1. Institute of Applied Mathematics, School of Math & System science, Shandong University, Jinan 2.0100, china 2. State Key Laboratory of Turbulence and Complex Systems & {2. of mechanics and engineering science, Peking University, beijing 100871, china 1. Institute of Applied Mathematics School of Math & System Science Shandong University Jinan 250100 China 2. State Key Laboratory of Turbulence and Complex Systems & department of mechanics and {2. science Peking University Beijing 100871 China

From point of view of physics, especially of mechanics, we briefly introduce fractional operators (with emphasis on fractional calculus and fractional differential equa- tions) used for describing intermediate processes and critical phenomena in physics and mechanics, their progress in theory and methods and their applications to modern me- chanics. Some authors’ researches in this area in recent years are included. Finally, prospects and evaluation for this subject are made.

关键词： fractional operators,intermediate processes,critical phenomena,modern mechanics

The refined theory of deep rectangular beams for symmetrical deformation

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science china(Physics,{2. & Astronomy) 2009年第6期52卷 919-925页

作者： GAO Yang1 & WANG MinZhong2.1 College of science, china Agricultural University, {2. 100083, china 2.State Key Laboratory for Turbulence and Complex Systems and department of mechanics and Aerospace engineering, Peking University, beijing 100871, china College of science China Agricultural University Beijing 100083 China State Key Laboratory for Turbulence and Complex Systems and department of mechanics and Aerospace {2. Peking University Beijing 100871 China

Based on elasticity theory, various one-dimensional equations for symmetrical deformation have been deduced systematically and directly from the two-dimensional theory of deep rectangular beams by using the Papkovich-Neuber solution and the Lur'e method without ad hoc assumptions, and they construct the refined theory of beams for symmetrical deformation. It is shown that the displacements and stresses of the beam can be represented by the transverse normal strain and displacement of the mid-plane. In the case of homogeneous boundary conditions, the exact solutions for the beam are derived, and the exact equations consist of two governing differential equations: the second-order equation and the transcendental equation. In the case of non-homogeneous boundary conditions, the approximate governing differential equations and solutions for the beam under normal loadings only and shear loadings only are derived directly from the refined beam theory, respectively, and the correctness of the stress assumptions in classic extension or compression problems is revised. Meanwhile, as an example, explicit expressions of analytical solutions are obtained for beams subjected to an exponentially distributed load along the length of beams.

关键词： deep rectangular beams the refined theory symmetrical deformation the Papkovich-Neuber solution the Lur’e method

Two-dimensional simulation of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect

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Progress in Natural science:Materials International 2007年第12期17卷 1389-1396页

作者： Hu Jun1 and Yin Xieyuan2.1. Institute of Applied Physics and Computational Mathematics, beijing 100088, china 2. {2. of Modern mechanics, University of science and Technology of china, Hefei 2.002., china) Institute of Applied Physics and Computational Mathematics Beijing 100088 China department of Modern mechanics University of Science and Technology of China Hefei 230027 China

Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect are directly simulated by a mixed finite element method. A temperature perturbation is used as an initial disturbed source for the basic parallel flows. The whole spatio-temporal evolution of the binary fluid flows is exhibited: initially only the disturbed mode with the wavenumber k=π is amplified while others are damped, and continuously the amplified mode grows further and the nonlinear effect becomes important; after a nonlinear evolution transition the flow system evolves finally into a periodic right traveling wave.

关键词： Poiseuille-Rayleigh-Bénard flow Soret effect through-flow.

THE APPLICATION OF DISCRETE ELEMENT METHOD IN SOLVING THREE-DIMENTIONAL IMPACT DYNAMICS PROBLEMS

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Acta Mechanica Solida Sinica 2003年第3期16卷 256-261页

作者： Liu Kaixin Gao Lingtian (department of mechanics and {2. science,Peking University,beijing 100871,china) department of mechanics and {2. science Peking University Beijing 100871 China

A three-dimensional discrete element model of the connective type is presented. Moreover,a three-dimensional numerical analysis code,which can carry out the transitional pro- cess from connective model(for continuum)to contact model(for non-continuum),is developed for simulating the mechanical process from continuum to *** wave propagation process in a concrete block(as continuum)made of cement grout under impact loading is numer- ically simulated with this *** comparing its numerical results with those by LS-DYNA,the calculation accuracy of the model and algorithm is ***,the failure process of the concrete block under quasi-static loading is demonstrated,showing the basic dynamic tran- sitional process from continuum to *** results of calculation can be displayed by *** damage modes are similar to the experimental *** two numerical examples above prove that our model and its code are powerful and efficient in simulating the dynamic failure problems accompanying the transition from continuum to *** also shows that the discrete element method(DEM)will have broad prospects for development and application.

关键词： discrete element method three-dimensional model impact stress wave dynamic failure

Parameter estimation for whole-body kinetic model of FDG metabolism

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Progress in Natural science:Materials International 2006年第11期16卷 1164-1170页

作者： CUI Yunfeng~1, BAI Jing~1**, CHEN Yingmao~2.and TIAN Jiahe~2.1. department of Biomedical engineering, Tsinghua University, {2. 100084, china 2. department of Nuclear Medicine, General Hospital of PLA, {2. 100853, china) [a]department of Biomedical engineering Tsinghua University Beijing China [b]department of Nuclear Medicine General Hospital of PLA Beijing China

Based on the radioactive tracer [ ~ 18 F]2.fluoro-2.deoxy-D-glucose （FDG）, positron emission tomography （PET）, and compartment model, the tracer kinetic study has become an important method to investigate the glucose metabolic kinetics in human body. In this work, the kinetic parameters of three-compartment and four-parameter model for the FDG metabolism in the tissues of myocardium, lung, liver, stomach, spleen, pancreas, and marrow were estimated through some dynamic FDG-PET experiments. Together with published brain and skeletal muscle parameters, a relatively complete whole-body model was presented. In the liver model, the dual blood supply from the hepatic artery and the portal vein to the liver was considered for parameter estimation, and the more accurate results were obtained using the dual-input rather than the single arterial-input. The established whole-body model provides the functional information of FDG metabolism in human body. It can be used to further investigate the glucose metabolism, and also be used for the simulation and visualization of FDG metabolic process in human body.

关键词： compartment model FDG PET parameter estimation.

On Catastrophe and Cavitation for SphericalCavity

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Communications in Nonlinear science and Numerical Simulation 1999年第4期4卷 249-254页

作者： Ming JIN Kefu HUANG Jike WU(department of mechanics and {2. science, Peking University, beijing 100871,china) department of mechanics and {2. science Peking University Beijing 100871 China

IntroductionInrecelltyears,theresearchesoncavitationandcatastropheofacavitysu***therwithbifllrcationtheory... 详细信息

IntroductionInrecelltyears,theresearchesoncavitationandcatastropheofacavitysu***therwithbifllrcationtheory...

关键词： nonlinearity bifurcation Hooke material