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The numerical method for three-dimensional impact with friction of multi-rigid-body system

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science china(Physics,{2. & Astronomy) 2006年第1期49卷 102-118页

作者： ZHAO Zhen1,2. LIU Caishan2.& CHEN Bin2.1. beijing Institute of Graphic Communication, beijing 102.00, {2. 2. department of mechanics & engineering science, peking university, beijing 1.0871. china beijing Institute of Graphic Communication Beijing 102600 China department of mechanics & {2. science Peking University Beijing 100871 China

The differential equations for planar impacts reduce to an algebraic form, and can be easily solved. For three dimensional impacts with friction, there is no closed-form solution, and numerical integration is required due to the swerve behavior of tangential impulse during collisions. The dynamic governing equations in the impact process are built up in impulse space based on the Lagrangian equation in this paper. The coefficient of restitution defined by Poisson is used as the condition of impact termination. A valid nu- merical method for solving three-dimensional frictional impact of multi-rigid body system is established. The singular cases of tangential movement in sticking point are especially noticed and analyzed. Several examples are present to reveal the different kinds of tan- gential movement modes varied with the normal impulse during collision.

关键词： multi-rigid body, impact, friction.

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 1.0871.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

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 1.0871.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

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 {2., beijing 100083, china 2. State Key Laboratory for Turbulence and Complex Systems and department of mechanics and Engi- neering science, peking university, beijing 1.0871. 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 {2., beijing 100083, china 2. State Key Laboratory for Turbulence and Complex Systems and department of mechanics and Engi- neering science, peking university, beijing 1.0871. 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.

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 {2. science, State Key Laboratory for TurbulenceResearch, peking university, beijing 1.0871. china) department of mechanics and {2. 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

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 {2., beijing 100083, china 2.State Key Laboratory for Turbulence and Complex Systems and department of mechanics and Aerospace engineering, peking university, beijing 1.0871. 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

New discrete element models for elastoplastic problems

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Acta Mechanica Sinica 2009年第5期25卷 629-637页

作者： Ming Cheng Weifu Liu Kaixin Liu LTCS and department of mechanics and Aerospace {2.,College of {2., peking university, 1.0871.beijing, china LTCS and department of mechanics and Aerospace {2. College of Engineering Peking University 100871 Beijing China

The discrete element method （DEM） has attractive features for problems with severe damages, but lack of theoretical basis for continua behavior especially for nonlinear behavior has seriously restricted its application. The present study proposes a new approach to developing the DEM as a general and robust technique for modeling the elastoplastic behavior of solid materials. New types of connective links between elements are proposed, the interelement parameters are theoretically determined based on the principle of energy equivalence and a yield criterion and a flow rule for DEM are given for describing nonlinear behavior of materials. Moreover, a numerical scheme, which can be applied to modeling the behavior of a continuum as well as the transformation from a continuum to a discontinuum, is obtained by introducing a fracture criterion and a contact model into the DEM. The elastoplastic stress wave propagations and the tensile failure process of a steel plate are simulated, and the numerical results agree well with those obtained from the finite element method （FEM） and corresponding experiment, and thus the accuracy and efficiency of the DEM scheme are demonstrated.

关键词： DEM Continuum Plasticity Fracture

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, {2. 2. State Key Laboratory of Turbulence and Complex Systems & department of mechanics and engineering science, peking university, beijing 1.0871. 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