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A study on compressive shock wave propagation in metallic foams

Science china(Physics,mechanics & Astronomy) 2010年第2期53卷 279-287页

作者： WANG ZhiHua1,2,ZHANG YiFen2,REN HuiLan1 & ZHAO LongMao2 1 State Key Laboratory of Explosion Science and technology,Beijing institute of technology,Beijing 100081,china 2.institute of applied mechanics and biomedical engineering,taiyuan university of technology,taiyuan 03002.,china State Key Laboratory of Explosion Science and technology Beijing Institute of Technology Beijing China institute of applied mechanics and biomedical engineering Taiyuan University of Technology Taiyuan China

Metallic foam can dissipate a large amount of energy due to its relatively long stress plateau,which makes it widely applicable in the design of structural crashworthiness. However,in some experimental studies,stress enhancement has been observed when the specimens are subjected to intense impact loads,leading to severe damage to the objects being protected. This paper studies this phenomenon on a 2D mass-spring-bar model. With the model,a constitutive relationship of metal foam and corresponding loading and unloading criteria are presented; a nonlinear kinematics equilibrium equation is derived,where an explicit integra-tion algorithm is used to calculate the characteristic of the compressive shock wave propagation within the metallic foam; the effect of heterogeneous distribution of foam microstructures on the shock wave features is also included. The results reveal that under low impact pulses,considerable energy is dissipated during the progressive collapse of foam cells,which then reduces the crush of objects. When the pulse is sufficiently high,on the other hand,stress enhancement may take place,especially in the heterogeneous foams,where high peak stresses usually occur. The characteristics of compressive shock wave propagation in the foam and the magnitude and location of the peak stress produced are strongly dependent on the mechanical properties of the foam material,amplitude and period of the pulse,as well as the homogeneity of the microstructures. This research provides valuable insight into the reliability of the metallic foams used as a protective structure.

关键词： aluminum foam heterogeneous intensive pulse loading stress enhancement

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Numerical and experimental investigation of the fracture behavior of shock loaded alumina

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Science china(Physics,mechanics & Astronomy) 2010年第2期53卷 244-252页

作者： REN HuiLan1,SHU XueFeng2 & LI Ping3 1 State Key Laboratory of Explosion Science and technology,Beijing institute of technology,Beijing 100081,china 2.institute of applied mechanics and biomedical engineering,taiyuan university of technology,taiyuan 03002.,china 3 Labroratory for Shock Wave and Detonation Physics Research,institute of Fluid Physics,CAEP,Mianyang 610059,china State Key Laboratory of Explosion Science and technology Beijing Institute of Technology Beijing China institute of applied mechanics and biomedical engineering Taiyuan University of Technology Taiyuan China Labroratory for Shock Wave and Detonation Physics Research Institute of Fluid Physics CAEP Mianyang China

Plate impact expeiments are conducted to investigate the dynamic behavior of alumina by using one stage light gas gun. A ve-locity interferometer system for reflectors (VISAR) is used to obtain Hugoniot elastic limit and the free surface velocity profile,which consists of an elastic wave followed immediately by a dispersive inelastic wave. The stress histories under different impact velocities are measured by in-material manganin gauges. Based on the experimental data a Hugoniot curve is fitted,which shows the compressive characteristics that alumina changes typically from elastic to "plastic" ,and under higher pressure it will be transferred to similar-fluid state. The turning point of the Hugoniot curve from a high pressure region to a low pressure region is about 11.4 GPa. The fracture process of alumina is simulated by way of finite element code. After the analysis of the fracture mechanism,the numerical results show an important role played by the nucleation and the growth of the cracks in the macro-scopic fracture of the alumina target. The numerical predictions of stress histories are compared with the experimental results,which indicates consistency between them.

关键词： plate impact experiment hugoniot curve fracture characteristics numerical simulation

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A NEW CONTINUUM TRAFFIC MODEL WITH THE EFFECT OF VISCOSITY

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Journal of Hydrodynamics 2011年第2期23卷 164-169页

作者： SONG Tao LI Xing-li KUANG Hua DONG Li-yun Shanghai institute of applied Mathematics and mechanics Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University Shanghai 200072 China School of applied Science Taiyuan University of Science and Technology Taiyuan 030024 China College of Physics and technology Guangxi Normal University Guilin 541004 China

Through considering the connection between microscopic car-following model and macroscopic continuum model, a new viscous vehicular flow model is proposed, in which the viscosity coefficient is determined by a more realistic constitutive relationship between averaged reaction time of drivers and the car density. Further analysis indicates that two traffic sound speeds in this viscous model may determine the existence and the stability of traveling wave solutions with an analytical method.

关键词： viscosity continuum traffic model reaction time traffic sound speed traveling wave

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The complex variable reproducing kernel particle method for elasto-plasticity problems

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Science china(Physics,mechanics & Astronomy) 2010年第5期53卷 954-965页

作者： CHEN Li1 & CHENG YuMin2 1 Department of engineering mechanics,Chang’an university,Xi’an 710064,china 2 Shanghai institute of applied Mathematics and mechanics,Shanghai university,Shanghai 200072,china Department of engineering mechanics Chang’an University Xi’an China Shanghai institute of applied Mathematics and mechanics Shanghai University Shanghai China

On the basis of reproducing kernel particle method(RKPM),using complex variable theory,the complex variable reproducing kernel particle method(CVRKPM) is discussed in this *** advantage of the CVRKPM is that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is *** the CVRKPM is applied to solve two-dimensional elasto-plasticity *** Galerkin weak form is employed to obtain the discretized system equation,the penalty method is used to apply the essential boundary *** then,the CVRKPM for two-dimensional elasto-plasticity problems is formed,the corresponding formulae are obtained,and the Newton-Raphson method is used in the numerical *** numerical examples are given to show that this method in this paper is effective for elasto-plasticity analysis.

关键词： meshless method reproducing kernel particle method(RKPM) complex variable reproducing kernel particle method(CVRKPM) correction function elasto-plasticity

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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 university, Shanghai 200072, china 2. Department of Building engineering, Xi’an university 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.

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SIMULATION OF THE OIL SLICK MOVEMENT IN TIDAL WATER-WAYS

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Journal of Hydrodynamics 2010年第1期22卷 96-102页

作者： WUZhao-chun WANG Dao-zeng Shanghai institute of applied Mathematics and mechanics Shanghai University Shanghai 200072 China School of Construction and Safety engineering Shanghai Institute of Technology Shanghai 200235 China

Based on particle approach and tidal flow model this article studies the behavior of the oil slick on the water surface in the Huangpu River, a tidal waterway in Shanghai. In order to track the oil slick motion, a two-dimensional oil trajectory model is used. The dynamical properties of spilled oil characterized by advection, oil spreading and turbulent diffusion are considered in the model. The simulation results consistent with the flume experimental data show that the model is applicable. Both simulation and experiment illustrate that the tidal flow has a great influence on the oil slick motion. The calculated results can be used as a reference for the response to oil spill accidents in rivers.

关键词： particle approach track of oil slick numerical simulation

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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 Shanghai institute of applied Mathematics and mechanics, Shanghai university, Shanghai 200072, 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

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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 university, Shanghai 200072, china 2. Department of Civil engineering, Shanghai university, Shanghai 200072, 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.

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Method of Green’s function of nonlinear vibration of corrugated shallow shells

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Science china(Physics,mechanics & Astronomy) 2008年第6期51卷 678-686页

作者： YUAN Hong Key Laboratory of Disaster Forecast and Control in engineering, Ministry of Education of china, institute of applied mechanics, Jinan university, Guangzhou 510632, china Key Laboratory of Disaster Forecast and Control in engineering Ministry of Education of China Institute of Applied Mechanics Jinan University Guangzhou China

Based on the dynamic equations of nonlinear large deflection of axisymmetric shallow shells of revolution, the nonlinear free vibration and forced vibration of a corrugated shallow shell under concentrated load acting at the center have been investigated. The nonlinear partial differential equations of shallow shell were re-duced to the nonlinear integral-differential equations by using the method of Green’s function. To solve the integral-differential equations, the expansion method was used to obtain Green’s function. Then the integral-differential equations were reduced to the form with a degenerate core by expanding Green’s function as a series of characteristic function. Therefore, the integral-differential equations be-came nonlinear ordinary differential equations with regard to time. The ampli-tude-frequency relation, with respect to the natural frequency of the lowest order and the amplitude-frequency response under harmonic force, were obtained by considering single mode vibration. As a numerical example, nonlinear free and forced vibration phenomena of shallow spherical shells with sinusoidal corrugation were studied. The obtained solutions are available for reference to the design of corrugated shells.

关键词： corrugated shells spherical shells Green’s function integral equation nonlinear vibration

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Shear Failure of a Clamped Dented Tubular Beam Under Lateral Impact

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china Ocean engineering 1996年第2期11卷 161-168页

作者： Wang Deyu and Zhang Shanyuan Associate Prof., Depart, of Naval Archi. and Ocean engineering, Shanghai Jiaotong university, Shanghai 200030 Prof., Research institute of applied mechanics, taiyuan university of technology, taiyuan 03002. Depart. Naval Archi. and Ocean Eng. Shanghai Jiaotong University Shanghai 200030 Res. institute of applied mechanics Taiyuan University of Technology Taiyuan 030024

The shear failure of a rigid-plastic dented clamped tubular beam under the lateral impact of a mass is investigated. Both the denting and the impact point are in the middle span of the beam. It is assumed that denting does not spread during the shear sliding. Numerical results show that the axial force and lateral deflection of the beam are very small at the moment of the occurence of shear failure, which means that the finite deformation effect can be neglected in the shear failure analysis. Also, some aspects of the initial impact energy are investigated.

关键词： shear sliding failure tubular member local denting collosion finite deformation

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