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The refined theory of deep rectangular beams for symmetrical deformation

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Science china(Physics,mechanics & Astronomy) 2009年第6期52卷 919-925页

作者： GAO Yang1 & WANG MinZhong2 1 College of Science, china Agricultural university, beijing 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 engineering 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 KINDS OF HARMONIC PROBLEMS IN CONTROL systems

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Journal of systems Science & complexity 2009年第4期22卷 587-596页

作者： Zhisheng DUAN Lin HUANG state key Lab for turbulence and complex systems and department of mechanics and aerospace engineering,College of engineering,peking university,beijing 100871,china. state key Lab for turbulence and complex systems and department of mechanics and aerospace engineering College of Engineering Peking University Beijing 100871 China

This paper discusses the harmonic problems in control systems from two aspects:Oneis the harmonic control among different subsystems,and the other is the harmonic control amongmultiple *** intrinsic problems in such systems are *** is pointed out that somesubsystems must be unstable to stabilize the whole interconnected system by an *** discrete-time multi-input systems,a necessary and sufficient condition is presented for the strictdecrease of the quadratic optimal performance index with the control input *** showsan essential difference between single-input and multi-input control ***,some futureresearch directions are discussed in harmonic control of interconnected systems,allocation of multi-control inputs,fault-tolerant control,and fault-diagnosis.

关键词： Interconnected system quadratic optimal control redundant inputs Riccati equation simplectic matrix.

A computational investigation on random packings of sphere-spherocylinder mixtures

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Science china(Physics,mechanics & Astronomy) 2010年第12期53卷 2284-2292页

作者： LU Peng, LI ShuiXiang , ZHAO Jian & MENG LingYi state key laboratory for turbulence and complex systems, department of mechanics & aerospace engineering, College of engineering, peking university, beijing 100871, china 1. state key laboratory for turbulence and complex systems Department of Mechanics & Aerospace Engineering College of Engineering Peking University Beijing 100871 China

Random packings of binary mixtures of spheres and spherocylinders with the same volume and the same diameter were simulated by a sphere assembly model and relaxation algorithm. Simulation results show that, independently of the component volume fraction, the mixture packing density increases and then decreases with the growth of the aspect ratio of spherocylinders, and the packing density reaches its maximum at the aspect ratio of 0.35. With the same volume particles, results show that the dependence of the mixture packing density on the volume fraction of spherocylinders is approximately linear. With the same diameter particles, the relationship between the mixture packing density and component volume fraction is also roughly linear for short spherocylinders, but when the aspect ratio of spherocylinders is greater than 1.6, the curves turn convex which means the packing of the mixture can be denser than either the sphere or spherocylinder packing alone. To validate the sphere assembly model and relaxation algorithm, binary mixtures of spheres and random packings of spherocylinders were also simulated. Simulation results show the packing densities of sphere mixtures agree with previous prediction models and the results of spherocylinders correspond with the simulation results in literature.

关键词： packing binary mixture sphere spherocylinder packing density aspect ratio

On the dynamics in a transitional boundary layer

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Communications in Nonlinear Science and Numerical Simulation 2001年第3期6卷 111-171页

作者： C. B. LEE and R. LEE department of mechanics and engineering Science/state key laboratory for Studies of turbulence and complex systems, peking university, beijing 100871, china department of engineering mechanics, Tsinghua university, beijing 100084, Chi department of mechanics and engineering Science / state key laboratory for Studies of turbulence and complex systems Peking University Beijing 100871 China department of engineering mechanics Tsinghua University Beijing 100084 China

A model is presented to describe the dynamic physical processes that occur in a transitional boundary layer flow. The CS-solitons, the closed vortex, the secondary closed vortex and the chain of ring-like vortices are postulated to be the basic flow structures of the transitional boundary layer as well as the turbulent boundary layer. It is argued that the central features of transitional and developed turbulent boundary layer flows can be explained in terms of how the series vortices interact with each other, and with the CS-solitons. The physical process that leads to the regeneration of the new closed vortex along the border of the CS-soliton, as well as the processes of evolution of the vortices to high frequency vortices, is described. The model is supported by the important developments in a number of "kernel" experiments, which illustrate both transitional and developed turbulent boundary layer. An important aspect of the model is that it has been formulated to be consistent with accepted rational mechanics concepts that are known to provide a proper physical description of other flows.

关键词： boundary layer transition dynamic processes onset of turbulence

The theoretical research of basic function method in incompressible viscous flow and its simulations in three-dimensional aneurysms

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Science china(Physics,mechanics & Astronomy) 2009年第6期52卷 909-918页

作者： SHEN Fang1 & WU WangYi2 1 state key laboratory for Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, beijing 100190, china 2.state key laboratory of turbulence and complex systems & department of mechanics and engineering Science, peking university, beijing 100871, china 1. state key laboratory for Space Weather Center for Space Science and Applied Research Chinese Academy of Sciences Beijing 100190 China 2. state key laboratory of turbulence and complex systems & department of mechanics and engineering Science Peking University Beijing 100871 China

Basic function method is developed to treat the incompressible viscous flow. Artificial compressibility coefficient, the technique of flux splitting method and the combination of central and upwind schemes are applied to construct the basic function scheme of trigonometric function type for solving three-dimensional incompressible Navier-Stokes equations numerically. To prove the method, flows in finite-length-pipe are calculated, the velocity and pressure distribution of which solved by our method quite coincide with the exact solutions of Poiseuille flow except in the areas of entrance and exit. After the method is proved elementary, the hemodynamics in two-and three-dimensional aneurysms is researched numerically by using the basic function method of trigonometric function type and unstructured grids generation technique. The distributions of velocity, pressure and shear force in steady flow of aneurysms are calculated, and the influence of the shape of the aneurysms on the hemodynamics is studied.

关键词： basic function unstructured grid aneurysm viscous incompressible flow artificial compressibility flux splitting

The refined theory of transversely isotropic piezoelectric rectangular beams

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Science china(Physics,mechanics & Astronomy) 2006年第4期49卷 473-486页

作者： GAO Yang1 & WANG Minzhong2 1. College of Science, china Agricultural university, beijing 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 engineering 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.

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

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Science china(Physics,mechanics & Astronomy) 2006年第3期49卷 291-303页

作者： GAO Yang1 & WANG Minzhong2 1. College of Science, china Agricultural university, beijing 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

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,mechanics & 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 250100, china 2. state key laboratory of turbulence and complex systems & department 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 engineering 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

Constructions of Some Exact VortexSuperposition Solutions

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Communications in Nonlinear Science and Numerical Simulation 1999年第4期4卷 3-5页

作者： Xin HU Yonghan HUANG(department of mechanics and engineering Science, state key laboratory for turbulenceResearch, peking university, beijing 100871, china) department of mechanics and engineering Science State Key Laboratory for Turbulence Research Peking University Beijing 100871 China

IntroductionOneofthemostusefulmethodstosolvetheN-Sequationistodecomposethevelocity（l）(z)where.（'）--acNow,***3=w3（t）,wewillthengetco3=coear(jb（t）dt).Ifwetakeg=--M（axl+fixs）+ac,T=--M（Axf+Bx;）+cohere,goandcos... 详细信息

关键词： exact solution Stokes-Helmholtz decomposition vorticity equation