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The mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate-temporal mode

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Science china(Physics,mechanics & Astronomy) 2005年第5期48卷 614-625页

作者： HUANG Zhangfeng 1, CAO Wei 1,2.& ZHOU Heng 1,2.1. department of mechanics, Tianjin {2., Tianjin 300072. china 2. Liu-Hui Center of Applied Mathematics, Nankai {2. and Tianjin {2., Tianjin 300072. china 1. department of mechanics Tianjin University 300072 Tianjin China 2. Liu-Hui Center of Applied Mathematics Nankai University and Tianjin University 300072 Tianjin China

Temporal mode direction numerical simulation has been done for the transition of a supersonic boundary layer on a flat plate with Mach number 4.5. Analysis of the result showed that during the breakdown process in laminar-turbulent transition, the mechanism causing the mean flow profile to evolve swiftly from laminar to turbulent was that the modification of mean flow profile by the disturbances,when they became larger,led to a remarkable change of its stability characteristics. Though the most unstable T-S wave was of second mode for laminar flow, the first mode waves played the key role in the breakdown process in laminar-turbulent transition.

关键词： supersonic boundary layer, transition, breakdown.

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 2.0072.{2. 2. department of Building Engineering, Xi’an university of Technology, Xi’an 710048,{2. Shanghai Institute of Applied Mathematics mechanics Shanghai University Shanghai 200072 China department of Building Engineering Xi’an University of Technology Xi’an 710048 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.

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 2.0072.{2. 2. department of Civil Engineering, Shanghai university, Shanghai 2.0072.{2. 1. Shanghai Institute of Applied Mathematics and mechanics Shanghai University 200072 Shanghai China 2. department of Civil Engineering Shanghai University 200072 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.

Direct numerical simulation of a supersonic turbulent boundary layer on a flat plate and its analysis

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Science china(Physics,mechanics & Astronomy) 2005年第5期48卷 626-640页

作者： HUANG Zhangfeng1, ZHOU Heng1,2.& LUO Jisheng1,2.1. department of mechanics, Tianjin {2., Tianjin 300072. china 2. Liu-Hui Center of Applied Mathematics, Nankai {2. and Tianjin {2., Tianjin 300072. china 1. department of mechanics Tianjin University 300072 Tianjin China 2. Liu-Hui Center of Applied Mathematics Nankai University and Tianjin University 300072 Tianjin China

Temporal mode direct numerical simulation (DNS) has been done for a supersonic turbulent boundary layer on a flat plate with Mach number 4.5. It was found that the mean flow profile, the normal-wise distribution of turbulent Mach number and the root mean square (RMS) of the fluctuations of various variables, as well as the Reynolds stresses, bore similarity in nature, when the turbulence reached a fully developed state. But the compressibility effect was strong and must be considered. The strong Reynolds analogy (SRA) and the Morkovin hypothesis were no longer valid. From the end of transition to the fully developed state of turbulence, it was in the transient period, for which the similarity did not hold.

关键词： turbulence, similarity, compressibility effect, supersonic boundary layer, direct numerical simulation.

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. department of Modern {2., 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.

Influence of moisture content and time on the mechanical behavior of polymer material

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Science china(Technological Sciences) 2004年第5期47卷 595-607页

作者： ZHENG Gaofei1, 2. KANG Yilan1, SHENG Jing3, QIN Qinghua1, WANG Huaiwen1 & FU Donghui1 1. department of mechanics, Tianjin {2., Tianjin 300072. china 2. department of mechanics, Tianjin polytechnic {2., Tianjin 300160, china 3. department of Material Engineering, Tianjin {2., Tianjin 300072. china Correspondence should be addressed to Kang Yilan 1. department of mechanics Tianjin University 300072 Tianjin China 2. department of mechanics Tianjin Polytechnic University 300160 Tianjin China 3. department of Material Engineering Tianjin University 300072 Tianjin China

The effects of moisture content and time on mechanical behavior of polymer materials are investigated both theoretically and experimentally in this paper. An equivalence relationship between time intervals and the moisture content for polymer nylon-6 has been established by way of experimental observation and measured results. The relationship shows that there exists equivalence between moisture and service time in affecting mechanical properties. In other words, an increase in moisture can be replaced by prolonging acting time in producing the same effect on material properties. Consequently, a moisture-time superposition principle is presented based on the experimental results and the analogy of temperature-time superposition principle. Numerical results such as stress-strain curves with different moisture contents are presented to verify the applicability and correctness. The proposed method appears very promising in study on the effect of moisture content on mechanical behavior of polymer materials.

关键词： equivalence relationship of moisture-time, moisture content, mechanical properties, shift function.

A low frequency piezoelectric power harvester using a spiral-shaped bimorph

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Science china(Physics,mechanics & Astronomy) 2006年第6期49卷 649-659页

作者： HU Yuantai1,2.HU Hongping2.& YANG Jiashi3 1. Institute of mechanics and Sensing Technology,Central South university,Changsha 410083,{2. 2. department of mechanics,Huazhong university of Science and Technology,Wuhan 430074,{2. 3. department of Engineering mechanics,university of Nebraska,Lincoln,NE 68588-052.,USA 1. Institute of mechanics and Sensing Technology Central South University Changsha 410083 China 2. department of mechanics Huazhong University of Science and Technology Wuhan 430074 China 3. department of Engineering mechanics University of Nebraska Lincoln NE 68588-0526 USA

We propose a spiral-shaped piezoelectric bimorph power harvester operating with coupled flexural and extensional vibration modes for applications to low frequency energy sources. A theoretical analysis is performed and the computational results show that the spiral structure has relatively low operating frequency compared to beam power harvesters of the same size. It is found that to optimize the performance of a piezoelectric spiral-shaped harvester careful design is needed.

关键词： spiral-shaped bimorph,piezoelectric harvester,power density.

Two-dimensional thermoelasticity solution for functionally graded thick beams

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Science china(Physics,mechanics & Astronomy) 2006年第4期49卷 451-460页

作者： Lü Chaofeng1, CHEN Weiqiu1 & ZHONG Zheng2.1. department of Civil Engineering, Zhejiang university, Hangzhou 31002.,{2. 2. Key Laboratory of Solid mechanics of Ministry of Education, School of Aerospace Engineering and Ap- plied mechanics, Tongji university, Shanghai 2.0092.{2. department of Civil Engineering Zhejiang University Hangzhou 310027 China Key Laboratory of Solid mechanics of Ministry of Education School of Aerospace Engineering Applied mechanics Tongji University Shanghai 200092 China

Two-dimensional thermoelasticity analysis of functionally graded thick beams is presented using the state space method coupled with the technique of differential quadrature. Material properties vary continuously and smoothly through the beam thickness, leading to variable coefficients in the state equation derived from the elasticity equations. Approximate laminate model is employed to translate the state equation into the one with constant coefficients in each layer. To avoid numerical instability, joint coupling matrices are introduced according to the continuity conditions at interfaces in the approximate model. The differential quadrature procedure is applied to discretizing the beam in the axial direction to make easy the treatment of arbitrary end conditions. A simply-supported beam with exponentially varying material properties is considered to validate the present method. Numerical examples are performed to investigate the influences of relative parameters.

关键词： state equation differential quadrature approximate laminate model joint coupling matrices thermal stresses.

Analysis on cohesive crack opening displacement considering the strain softening effect

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Science china(Physics,mechanics & Astronomy) 2006年第1期49卷 88-101页

作者： WANG Limin1, XU Shilang2.& ZHAO Xiqiang3 1. mechanics department, Shandong {2. of Technology, Zibo 2.5049, china 2. Civil Engineering department, Dalian {2. of Technology, Dalian 11602., china 3. Mathematics department, Ocean {2. of china, Qingdao 2.6071, china mechanics department Shandong University of Technology Zibo 255049 China Civil Engineering department Dalian University of Technology Dalian 116024 China Mathematics department Ocean University of China Qingdao 266071 China

In order to investigate the crack propagation in quasi-brittle materials like rock, ceramic and concrete, Hillerborg and his co-researchers abstracted the fracture process zone in front of a stress free crack in terms of a “fictitious crack zone”. On the fictitious crack zone, cohesive stresses distribute following a given softening relationship of stress vs. crack opening. Based on the polynomial or power series expression of cohesive crack opening displacement, the relationship of the cohesive stress vs. the crack opening displacement is established using elastic theory and integral equation, and some unknown physics variables are obtained using variation approach. The calculation results gained in this paper are close to the experimentally test ones.

关键词： cohesive crack, softening, dissipation work, variation approach.