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Table of Content

    15 July 2016, Volume 48 Issue 4
    Research Review
    A CRITICAL REVIEW ON CRITERIA OF FRACTURE MECHANICS
    Ji Xing
    2016, 48(4):  741-753.  DOI: 10.6052/0459-1879-16-069
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    In this paper, the K criterion for linear fracture mechanics, the G criterion for interfacial fracture mechanics, and the J criterion for elastoplastic fracture mechanics has been briefly reviewed, from the preliminary works of Inglis and Griffith to the foundation contributions of Irwin and Rice. Recently, on the basis of the G criterion for interfacial fracture mechanics, the K criterion for interfacial fracture mechanics was derived. This shows that the criteria of fracture mechanics need to be further improved. Thereupon, some debatable issues in the criteria of fracture mechanics are raised. Then, the strain discontinuity at the crack tip is assumed as the source of the stress singularity at a crack tip, and the physical meaning of the stress intensity factor is discussed. At the end, it is concluded that an improved and reliable analysis for the elastoplastic stress field near a crack tip is the key for the establishment of a criterion of elastoplastic fracture mechanics, and an improved and reliable analysis for the elastoplastic stress field near a crack tip depends on the determination of the magnitude of the stress at the crack tip, which caused the strain discontinuity at the crack tip.

    Theme Articles on Dynamics and Control of Robot
    REVIEW OF MATERIALS AND STRUCTURES IN SOFT ROBOTICS
    Li Tiefeng, Li Guorui, Liang Yiming, Cheng Tingyu, Yang Xuxu, Huang Zhilong
    2016, 48(4):  756-766.  DOI: 10.6052/0459-1879-16-159
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    Soft robot is a novel category of robotics. Possessing the characteristics of high flexibility, high environmental adaptability, high compatibility and multi-functionality, soft robots are quite promising in research and practical applications. The performances of soft robots are largely enhanced by the unique properties of smart materials, which play a crucial role in the design and application of soft robots. This paper summarizes existing soft robots by their actuating mechanisms and functions into typical categories as worm-like peristaltic moving, caterpillar-like bending actuation, fish-swimming soft robotics. Furthermore, by their actuating mechanisms, soft robots are summarized as air pressure powered, shape memory alloy (SMA), ionic polymer metal composite (IPMC), dielectric elastomer (DE), responsive hydrogel, chemical combustion powered robotics. This paper reviews and discusses the fabricating method, the current challenges and future prospects of soft robots.

    SURVEY ON UNCALIBRATED ROBOT VISUAL SERVOING CONTROL
    Tao Bo, Gong Zeyu, Ding Han
    2016, 48(4):  767-783.  DOI: 10.6052/0459-1879-16-161
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    Visual servo control is one of the most important control strategies of robot system. Uncalibrated visual servoing system reveals preferable flexibility and adaptability in comparison with the classical visual servo systems which require system calibration, therefore it becomes a significant branch and hotspot of research in the field of visual servoing. This paper reviews the research progress of uncalibrated visual servo control system in recent years from three perspectives, which are task function selection, controller design as well as motion planning. First, this paper analyzes the characteristics and applications of position-based visual servoing, image-based visual servoing as well as the hybrid visual servoing based on the form of task functions. As for the controller design, based on the fact whether robot dynamics are considered, this paper introduces the design of uncalibrated visual servo controller which takes robot kinematics or robot dynamics into consideration, and mainly emphasizes the formation and estimation of Jacobian matrixes. As for the possible problems in motion path of uncalibrated visual servo control, this paper also sets forth the existing feasible solutions from the perspective of motion path optimization and obstacle avoidance. Finally, we outline the direction in the future work of uncalibrated visual servoing research based on state of the art.

    SYMPLECTIC METHOD FOR INSTANTANEOUS OPTIMAL CONTROL OF MULTIBODY SYSTEM TRAJECTORY TRACKING
    Peng Haijun, Li Fei, Gao Qiang, Chen Biaosong, Wu Zhigang, Zhong Wanxie
    2016, 48(4):  784-791.  DOI: 10.6052/0459-1879-16-164
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    With the wide application of robot in various fields, the new requirement on dynamics and control performance for robot has been continually proposed. Especially for the intelligent robot with much more complex system and flexibility of operation, the high accuracy of trajectory tracking should be satisfied for practical mission requirement. Therefore, the aim of this paper is to satisfy the requirement of trajectory tracking mission of robot multibody system, and then the symplectic method based on differential-algebraic equations for instantaneous optimal control is proposed. First, the general dynamic equation of robot should be established by absolute coordinates of multibody system, i.e., differential-algebraic equations; then, the differential-algebraic equations are discretized in the domain of continuoustime by symplectic method, and then the present position/velocity/Lagrange multiplier are taken as unknown variables of nonlinear equations; afterward, the combination of objective tracking trajectory and weighted control input are introduced as the performance of instantaneous optimal control. The optimal control input is obtained by the theory of instantaneous optimal control; finally, the tracking mission for the objective trajectory can be continuously implemented with the updated time step. In order to test the effectiveness of the proposed method, the trajectory tacking problem of double pendulum is taken as an example, and numerical simulations show that the proposed symplectic method for instantaneous optimal control can obtain high accuracy tracking results, meanwhile, the proposed symplectic method based on differential-algebraic equations can be applied for other trajectory tracking mission of complex multibody system.

    SLIDING BIFURCATIONS OF RECTILINEAR MOTION OF A THREE-PHASE VIBRATION-DRIVEN SYSTEM SUBJECT TO COULOMB DRY FRICTION
    Chen Qi, Zhan Xiong, Xu Jian
    2016, 48(4):  792-803.  DOI: 10.6052/0459-1879-16-157
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    In recent years, mobile robots' locomotion becomes diversified assisted by the continuous development of technologies in designing them. Inspired from bionics, earthworms' peristalsis becomes an object that quite a few robot designers want their robots to imitate. To this end, vibration-driven system has been put forward and researched by scholars. In this paper, the stick-slip motion of a one-module vibration-driven system moving on isotropic rough surface is studied. In consideration of the discontinuity caused by dry friction, the system considered here is of Filippov type. Based on sliding bifurcation theory in Filippov system, different types of stick-slip motions are studied. According to the values of driving parameters, 4 situations with different sliding regions can be seen. By analyzing these situations one by one, 6 kinds of motions can be achieved. By combining these motions, 4 different stick-slip motion types are finally concluded and conditions for judging occurrence of them are also derived analytically from the view point of sliding bifurcation. In the bifurcation conditions, there are 3 bifurcation parameters which can be changed in drawing bifurcation graphs. Assisted by these bifurcation graphs, detailed analysis is given about how stick-slip motion types change from one to another when parameters change and physical explanations from the perspective of bifurcation theory are also given. At last, the original differential motion equation is solved in a numerical way and one can see that 4 different stick-slip motion types derived numerically correspond with the former analytical results, which verifies the correctness of the bifurcation analysis in this paper well.

    RESEARCH ON THE INERTIA COUPLING PROPERTY OF A 3-PRS PARALLEL ROBOT
    Wang Dong, Wu Jun, Wang Liping, Liu Xinjun
    2016, 48(4):  804-812.  DOI: 10.6052/0459-1879-16-160
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    Inertia is the main factor which a ects the dynamic performance of a robot, due to the multi-close-loop structure of parallel robots, and the inertia of each driving shaft in joint space exists coupling property which will result in negative phenomena such as control overshoot and vibration especially when parallel robots work with high velocity and high acceleration. Thus, it is significant to study and evaluate the inertia coupling property of parallel robots. In this paper, based on the 3-PRS parallel robot, the inertia matrix is obtained through the principle of virtual work and an inertia coupling index is proposed, the coupling index represents the size of coupling inertia of each driving shaft when the robot works at different poses in the workspace. Then the distribution law of the index in workspace is analysed. Finally, a validation experiment is carried out on a typical 3-PRS parallel robot, the experimental results show that the load of each driving shaft will be changed by the coupling inertia, then the dynamic performance of the robot will be a ected by the variation of load. Meanwhile, the variation of load increases when the inertia coupling index becomes larger. The experimental results agree well with the theoretical analysis. This research result can be used to evaluate the dynamic coupling property of parallel robots, and it can also be used to optimize the structural parameters and design control parameters to further improve the dynamic performance of parallel robots.

    HYDRODYNAMIC PARAMETER IDENTIFICATION OF HYBRID-DRIVEN UNDERWATER GLIDER
    Niu Wendong, Wang Yanhui, Yang Yanpeng, Zhu Yaqiang, Wang Shuxin
    2016, 48(4):  813-822.  DOI: 10.6052/0459-1879-16-162
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    Compared with traditional autonomous underwater gliders (AUGs), hybrid-driven underwater gliders (HUGs) can achieve different motion modes by buoyancy driven system and propeller driven system, which are characterized by low power consumption, long endurance and high manoeuvrability, thus being widely used in various oceanographic monitoring missions. An accurate dynamics model with a series of exact enough hydrodynamic parameters is the basis of control system as well as navigation. The main issue of this paper is how to get the accurate hydrodynamic parameters based on the known dynamic model of HUG. In this paper, an HUG named as Petrel which is developed by Tianjin University is selected as the research object. A new method based on large data statistical analysis which combines computational fluid dynamics (CFD) and parameter identification is proposed for hydrodynamic parameter identification. Firstly, dynamic model of Petrel with hydrodynamic model is established. Secondly, lift coefficient is solved by CFD method. Then, other hydrodynamic parameters in the buoyancy driven gliding mode are calculated by large data statistical analysis using a large amount of experimental data. Finally a set of hydrodynamic parameters including the propeller thrust coefficient is obtained. The simulation results show a good agreement with the experimental results, thus verifying validity and availability of this method. And this work paves the way for further design.

    PATH PLANNING OF FREE FLOATING SPACE ROBOT USING LEGENDRE PSEUDOSPECTRAL METHOD
    Ge Xinsheng, Chen Kaijie
    2016, 48(4):  823-831.  DOI: 10.6052/0459-1879-16-158
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    Based on the Legendre pseudospectral method, the optimal control of free floating space robots path planning problems are studied. Free floating is the working status for the space robots in task and path planning is the foundation for them to fulfil a complex space task. Because the space robots have no fixed pedestal and there are nonholonomic constraints between the manipulator and the carrier, and it makes the path planning for free floating space robots different from those on the ground. In this paper, the Legendre pseudospectral method which can realize the optimal control of free floating space robots path planning problem is presented. Firstly, a dynamic model of free floating space robots is established by using multi-body dynamics theory. The path planning problem of Bolza with certain initial and terminal stance is then obtained. Here, we select the minimum joint dissipation as performance index and consider the actual control input saturation. Then, by applying the Legendre pseudospectral method, the state and control variables are discretized at Legendre-Gauss-Lobatto (LGL) point and Lagrange interpolation polynomials are constructed to approximate the state and control variables. The problem of continuous path optimization is discretized to solve a nonlinear programming problem. Finally, results of the numerical simulation show that using the application of Legendre pseudospectral method to solve the problem of free floating space robot path planning can get the optimal trajectory of manipulator and carrier. It can fit various constraint conditions well. And this method is with fast simulation calculation, high accuracy and good real-time performance.

    MECHANICAL ANALYSIS AND CALM CONTROL OF DUAL-ARM SPACE ROBOT FOR CAPTURING A SATELLITE
    Cheng Jing, Chen Li
    2016, 48(4):  832-842.  DOI: 10.6052/0459-1879-16-156
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    As the technology of space science develops rapidly, space robot system is expected to capture the noncooperative satellite on-orbit. Space robot with dual-arm obviously has more comparative advantage in this respect compared with the one with single arm. Because of the complicated condition in outer space it makes the dynamics and control problems related to satellite-capturing operation by space robot system with dual-arm to be extremely complicated, and there are some unique characteristics, such as, nonholonomic dynamics restriction, change of system configuration, transfer of linear momentum, angular momentum and energy, topology transfer from open to closed loop system, and the constraints of closed-loop geometry and kinematics during satellite-capturing operation. In this paper, the dynamic evolution for space robot with dual-arm capturing a spin satellite and calm control for unstable closed chain composite system are discussed. At first, with the Lagrangian approach, the dynamic model of open chain space robot with dual-arm before capture operation is established, and dynamic model of satellite is derived by Newton-Euler method. On that basis, based on the law of conservation of momentum and the law of force transfer, the impact effect after collision of space robot with dual-arm to capture the target is analyzed and solved by the process of integration and simplification, and the suitable capture operation strategy is given. Closed chain constraint equations are obtained by the constraints of closed-loop geometry and kinematics of closed chain system. With the closed chain constraint equations, the composite system dynamic model is derived. For the unstable closed chain composite system after the capture, the fuzzy H control scheme for calm motion is designed. The fuzzy logic system is applied to overcome the influence of uncertainty part and the robust H control item is used to eliminate the approximate error, to guarantee the tracking precision. The global stability of the system is proved by the Lyapunov theory. The weighted minimum-norm theory is introduced to distribute torques guaranteeing that the cooperative operation between manipulators. At last, numerical examples simulated the response of collision are used to verify the efficiency of the control scheme.

    DYNAMIC MODELING AND SIMULATION OF FLEXIBLE ROBOTS BASED ON DIFFERENT DISCRETIZATION METHODS
    Fan Jihua, Zhang Dingguo
    2016, 48(4):  843-856.  DOI: 10.6052/0459-1879-16-163
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    Dynamic modeling and simulation of flexible robots based on different discretization methods are investigated in this paper. Firstly, the physical model of flexible robots consisting of n links and n revolute joints is established. Secondly, the assumed mode method, finite element method, Bezier interpolation method and B-spline interpolation method are used to describe the deformation of the flexible link. Then, kinematics of both rotary-joint motion and link deformation is described by 4×4 homogenous transformation matrices, and the Lagrangian equations are used to derive the governing equations of motion of the system. The longitudinal deformation and the transverse deformation of the flexible link are considered, and the coupling term of the deformation which is caused by the transverse deformation is included in the total longitudinal deformation. Then, a software package for the dynamic simulation of the flexible robots based on the different discretization methods is developed, after that, the dynamic analysis for flexible robots are studied by three examples. The simulation results show that the computational efficiency of finite element method is the lowest, and the Bezier interpolation method and B-spline interpolation method are better than the assumed mode method in dealing with the large deformation dynamic problem. As new discretization methods, Bezier interpolation method and B-spline interpolation method can be used to describe the deformation of the flexible link, and they can be extended to the dynamic modeling for spatial flexible robots.

    Fluid Mechanics
    STUDY ON THE GROWTH AND COLLAPSE OF CAVITATION BUBBLE WITHIN A DROPLET
    Lü Ming, Ning Zhi, Sun Chunhua
    2016, 48(4):  857-866.  DOI: 10.6052/0459-1879-15-434
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    Cavitation bubbles always exist in the diesel jet leaving the nozzle and in the diesel droplets breaking up from the jet as a result of supercavitation of the diesel within the injection nozzle, and it can increase the instability of jet and droplets in part due to the two-phase mixture, while the mechanism of this effect is still unclear. Growth and collapse of spherically symmetric bubble within the diesel droplet has been then simulated numerically based on the volume of fluid (VOF) method. The numerical results show that the process of bubble growth is divided into three stages, including surface tension controlled domain, comprehensive competition controlled domain with the surface tension, the inertial force and the viscous force, and inertial force controlled domain. In addition, the bubble collapse within a droplet consists of multiple collapse and rebound stages, similar to the vibration process of a damping spring oscillator. According to the variation of bubble radius with time at the end of each cycle, the process of bubble collapse can be divided into fast, slow and stable stages.

    INFLUENCE OF GEOMETRY CONFIGURATIONS ON THE MICRODROPLETS IN FLOWFOCUSING MICROFLUIDICS
    Liu Zhaomiao, Yang Yang
    2016, 48(4):  867-876.  DOI: 10.6052/0459-1879-16-063
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    Micro flow-focusing devices were widely used in the synthesis of particulate material, drug packaging, cell culture and other areas owing to the convenience and effectiveness to produce highly monodisperse and precisely sizecontrollable droplets. To optimize the channel structure and geometry parameters deeply is of benefit to achieve the precise regulation of droplets' diameter, uniformity and the size ranges. For the adaptive design, channel depth, orifice length and the angle in continuous and discrete phase are taken into account to investigate the influence of geometry configurations on the microdroplet diameter and its generated cycle stages in flow focusing microchannel by making use of numerical simulation. It is shown that the droplet diameter approximately increases linearly with the channel depth, meanwhile, when the channel depth is less than 30 μm, the droplet's cycle increases suddenly under the application of strong capillary force. The microdroplet diameter and its cycle are both the shortest while the angle of the continuous phase and discrete phase θ is nearly 90°, and too large or too small angles are both not conductive to generate droplets with uniform diameter and well controlled particle size. Orifice length is used to adjust the alteration of the microdroplet diameter and its cycle, which lead to the average rangeability within 3%~5%. In addition, the width of orifice region is an important factor a ecting the microdroplet diameter and its cycle in cross microchannel. When the channel depth is fixed, the wider the orifice region is, the greater the microdroplet diameter and its cycle are.

    LEADING EDGE OPTIMIZATION AND PARAMETER ANALYSIS OF HIGH PRESSURE CAPTURING WINGS
    Li Guangli, Cui Kai, Xiao Yao, Xu Yingzhou
    2016, 48(4):  877-885.  DOI: 10.6052/0459-1879-16-036
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    In this paper, an aerodynamic optimization is carried out to analyze the effect of leading edge shape on the aerodynamic performance for high pressure capturing wing (HCW) configurations. First, a parameterized method for the wing leading edge of an HCW is developed by combining a power function and a cosine function. The lift-to-drag ratio of the configuration is chosen as the goal of maximization. Next, a numerical optimization flow is constructed by combining with the uniform experimental design method, the computational fluid dynamics, the radial basis function surrogate model method and the genetic algorithm on the basis of the comparison of the accuracy between the polynomial surrogate model and the radial basis functional surrogate model. At last, the sensitivity analysis of optimization results for each parameter is implemented. As the comparison of the optimal to the baseline, the results show that the lift coefficient increased by 8.1%, the drag coefficient is decreased by 12.2%, the lift-to-drag ratio increased by 23.4%. In addition, the sensitivity analysis results show that the lift-to-drag ratio presents non-linear relationship with the five design parameters and the angle of wingspan had the greatest influence, followed by the exponential curve parameter, the effect of other three parameters on the lift-to-drag ratio is relatively weak.

    STUDIES ON VORTEX INTERACTION MECHANISM AND AERODYNAMIC CHARACTERISTIC OF SCISSORS TAIL ROTOR
    Zhu Zheng, Zhao Qijun, Wang Bo
    2016, 48(4):  886-896.  DOI: 10.6052/0459-1879-15-338
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    The design of the unconventional scissors tail rotor has a powerful influence on the overall aerodynamic performance of helicopter, and the aerodynamic interaction mechanism of the unconventional tail rotor has been investigated due to its complexity. To get the interaction mechanism and aerodynamic characteristic of scissors tail rotor, a numerical method based on computational fluid dynamics (CFD) technique is established to simulate the vortex flowfield of scissors tail rotor in hover. Based on the embedded grid system, a CFD simulation method is developed by solving the compressible Reynolds-averaged Navier-Stokes (RANS) equations. Based on the validation of the CFD method, the evolution laws of position and strength of blade-tip vortex for two different scissors tail rotors are obtained by quantitative analysis in hover. Thus, close vortex-surface interactions, impingement and burst motions in the process of blade-vortex interaction are analyzed in detail, also the interaction and mergence process among the different scales vortex has been captured accurately. Furthermore, the influences of the two configuration parameters (scissors angle and vertical space) on their aerodynamic characteristics have been analyzed in hover. The simulated results demonstrate that the flowfield of the scissors tail rotor is very complicated due to various blade-vortex and vortex-vortex interaction. In addition, the configuration parameters of scissors tail rotor have important effects on its aerodynamic characteristics, and configuration L shows more advantages of improving the aerodynamic performance than configuration U has.

    INVESTIGATION OF THE SOURCE AND IMPROVEMENT OF NON-PHYSICAL SOLUTIONS IN HIGH-ORDER HARMONIC BALANCE
    Liu Nan, Bai Junqiang, Hua Jun, Liu Yan
    2016, 48(4):  897-906.  DOI: 10.6052/0459-1879-15-157
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    The time derivatives in unsteady equations are eliminated by high-order harmonic balance HOHB method by expanding solutions into Fourier series containing several harmonics, which can reduce computational consumes of periodic unsteady problems significantly. In this paper, the source of non-physical solutions in HOHB method is investigated by Duffing oscillator. It is illustrated that the left and right terms of equations are not strictly equal because of the processing of nonlinear terms in the derivation process, which induces non-physical solutions. According to the characteristics of nonlinear term, sub-time solutions are extended. Besides, higher order harmonics of nonlinear term are also truncated. Thus, the left and right sides of HOHB equations are enforced strictly to be equal. It is manifested that not only non-physical solutions are eliminated, but also the numbers of required harmonics are reduced through the numerical simulation of Duffing oscillator equation. Comparing with results in references, the accuracy and simulation ability of improved method and classical harmonic balance method with same number of harmonics are almost equivalent, which proves the feasibility of the improved method. Lastly the improved method is applied in nonlinear aeroelastic system with cubic nonlinearity, which validates its engineering applicability. However, when there are excessive number of nonlinear terms in dynamic system, the computational consume of improved method will increase.

    Solid Mechanics
    SCALE EFFECT ANALYSIS FOR THE VIBRO-ACOUSTIC PERFORMANCE OF A MICRO-PLATE
    Tang Yufan, Ren Shuwei, Xin Fengxian, Lu Tianjian
    2016, 48(4):  907-916.  DOI: 10.6052/0459-1879-15-354
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    Micro electromechanical system (MEMS) is an electromechanical device of microscale, in which micro-plate is the most typical structure. Its acoustical and mechanical properties influence the design of MEMS significantly. The vibroacoustic performance of simply supported micro-plate subjected to simultaneous stimulation of sound pressure and gas film (squeeze film) damping force is analyzed theoretically, the latter induced by the vibration of a micro-plate having similar size. By applying the Cosserat theory and the Hamilton principle, micro scale effects due to characteristic length and Knudsen number are taken into account. The governing equations are subsequently solved using the method of multiple Fourier transform to quantify sound transmission loss (STL) across the micro-plate. In the frequency domain, the effects of squeeze film under different circumstances (e.g., different characteristic lengths and Knudsen numbers, different vibration frequencies and amplitudes) on STL are investigated systematically. This work demonstrates the great influence of micro-scale effects, as well as vibration, on STL. Decreasing the vibration amplitude and increasing the distance between micro-plates lead to better performance of sound transmission. Results presented in this study provide useful theoretical guidance to the practical design of micro-plates in MEMS.

    NUMERICAL STUDY ON NANOINDENTATION OF DEFECTIVE BILAYER GRAPHENE
    Hua Jun, Wu Xiaxia, Duan Zhirong
    2016, 48(4):  917-925.  DOI: 10.6052/0459-1879-15-427
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    Comparing with pristine graphene, graphene with various defects produced by the current technology still has a certain application value. Therefore it is necessary to investigate the influence of defects on graphene properties. In this paper, interaction between carbon atoms that forms the covalent bonds of graphene is modeled with Tersoffff potential, the long range interactions of carbon atoms are characterized by Lennard-Jones potential. The nanoindentation of spherical diamond indenter into defective bilayer graphene is studied by molecular dynamics simulations. The Lernnard-Jones potential function optimal value of cut-o radius is discussed and typical load-depth curves are obtained. The effects including Stone-Thrower-Wales (STW) defect, vacancy (single and double vacancy defects) and hole defect in different positions and numbers on the mechanical properties of graphene are studied. The results show that when defect is in the film's center, it makes intensity decrease significantly; when vacancy defect is in the region covered by indenter, the critical load increases linearly with the increase of distance which is from the defect to the film's center; The more vacancy defect, the lower Young's modulus and intensity. The number of hole defects reaching a certain concentration outside the region covered by indenter radius which makes the mechanical properties of graphene decrease apparently. It is concluded that graphene with the stable structure is not sensitive to small defects and defective graphene still has good performance and practical value.

    NUMERICAL SIMULATION ON TWO-HOLE BLASTING OF ROCK UNDER DIFFERENT JOINT ANGLES AND IN-SITU STRESS CONDITIONS
    Wei Chenhui, Zhu Wancheng, Bai Yu, Li Shuai
    2016, 48(4):  926-935.  DOI: 10.6052/0459-1879-15-259
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    Drilling and blasting is still the most widely used method for rock breaking in mining engineering, underground tra c engineering, hydro-power engineering, etc. The in-situ stress field and structural plane such as joint and fault all have great impacts on blasting load propagation and rock fragmentation. In the present model, a mechanical model for rock blasting is established with consideration of in-situ stress field, in which rock blasting duration is considered as two consecutive stages, i.e. firstly the dynamic stage caused by the stress wave and then the static stage caused by explosion gas pressure. The seepage equation is used to describe the explosion gas propagation in cracks and the mechanical effect of quasi-static pressure of explosion gas near the crack tip is reflected based on seepage-mechanical coupling theory. Blasting stress wave mainly initiates crush zone and radial microcrack zone, while explosion gas pressure can then squeeze into the cracks and lead to crack extension. The proposed model can reproduce the whole process of initiation and extension of crush zone and radial cracks. Numerical simulations on two-hole blasting of rock under different joint angles and in-situ stress conditions are carried out and it indicates that in-situ stress conditions would go against the initiation and propagation of blasting induced crack, while the existing joint would play a positive role on crack extension as well as a guide role on crack propagation along joint orientation.

    EXPERIMENTAL STUDY ON MECHANICS CHARACTERISTICS OF SANDSTONE UNDER AXIAL UNLOADING AND RADIAL UNLOADING PATH
    Han Tielin, Shi Junping, Chen Yunsheng, Li Weihong
    2016, 48(4):  936-943.  DOI: 10.6052/0459-1879-15-367
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    This article take the actual rock mass project as a background, triaxial compression for sandstone specimen under axial unloading and radial unloading—this path is realized on WDT-1500 reactive material testing machine. The test results show that the failure of sandstone specimen don't appear peak stress under axial unloading and radial unloading— this path, to define the inflection point of stress drop of (The maximum principal stress -minimum principal stress) the minimum principal stress curves of sandstone for failure strength. The stress drop and the axial strain of resilience of sandstone specimens were happened under axial unloading and radial unloading, which had no obvious elasticity and yield step before rock specimens' failure. The lateral deformation is larger than the axial deformation in the process of test,and volumetric strain of the sandstone specimen is always in a state of expansion. The strength of sandstone is reduced relative to triaxial compression. the deformation property and strength property of sandstone under this path are mainly influenced by initial axial pressure and initial radial pressure,but the influence of the unloading speed of radial pressure is not clear. The failure characteristics of samples often present mixed zhang-shear failure under axial unloading and radial unloading.

    A NEW PROPOSAL FOR MULTIAXIAL LOW-CYCLE FATIGUE LIFE PREDICTION UNDER NON-PROPORTIONAL LOADING
    Zhao Ernian, Qu Weilian
    2016, 48(4):  944-952.  DOI: 10.6052/0459-1879-15-377
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    Engineering components are always in multiaxial and non-proportional stress states under complex service loading, and multiaxial fatigue is the primary failure mode during the long term vibration. In the present paper, the accuracy of multiaxial fatigue life estimation by the widely discussed Kandil-Brown-Miller (KBM) and FS model is investigated while the shortcoming of Fatemi-Socie (FS) parameter on fatigue life prediction of materials without additional cycle hardening is pointed out. Considering the dual influence of the additional cycle hardening and the rotation of principal stress/strain axes caused by non-proportional loading on multiaxial fatigue, which results in more fatigue damage, a new non-proportional influence factor is proposed, which is adopted for a modification to FS critical plane approach. Experimental results of five materials from tubular specimens under axial-torsional straining using sinusoidal wave forms in the literature are selected for the model verification. Comparing with FS parameter, the proposed critical plane damage parameter can significantly improve the accuracy of multiaxial fatigue lifetime prediction, especially for the materials without additional cycle hardening due to the non-proportionality of cycle loading.

    Dynamics, Vibration and Control
    COMPLICATED BEHAVIORS AS WELL AS THE MECHANISM IN BVP OSCILLATOR WITH SWITCHES RELATED TO TWO STATES
    Chen Zhangyao, Wang Yaming, Zhang Chun, Bi Qinsheng
    2016, 48(4):  953-962.  DOI: 10.6052/0459-1879-16-044
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    The dynamics of nonlinear switched systems which possess wide engineering background and cannot be explored directly by traditional nonlinear theory, become one of hot and frontier tasks at home and abroad for the time being. The complicated behaviors as well as the mechanism of the vector field alternated between two subsystems by two different critical states are investigated in this paper. Upon employing the typical generalized BVP oscillator as an example, by introducing bilateral switch, the nonlinear dynamical model alternated between two subsystems related two states is established, the different movement forms as well as the dynamical evolution of which caused by switches are explored in details. Based on the Poincaré theory of nonlinear system, the computational equation of Lyapunov exponents of switched system is derived. Combined with the bifurcation analysis of subsystems, different oscillations of the system are discussed, upon which the nonlinear behaviors such as sudden changes of period in periodic oscillations and the route to chaos with period-doubling bifurcations as well as the related essence are presented. Different from the systems with fixed time or single state switch, much more nonlinear phenomena may be observed in the dynamic systems with two state switches in which there may exist more switch points with changeable positions. Furthermore, different from the cascading of period-doubling bifurcations in smooth systems, the period-doubling bifurcations in switched systems correspond to the doubling of the number of switch points, which usually does not correspond to the doubling of the real periodic length of the movements.

    DYNAMIC ANALYSIS OF A ROTATING FLEXIBLE BEAM WITH ELASTIC BOUNDARY CONDITIONS
    Huang Yixin, Tian Hao, Zhao Yang
    2016, 48(4):  963-971.  DOI: 10.6052/0459-1879-16-083
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    The dynamic characteristics of a flexible beam rotating in a plane with elastic boundary condition are investigated by the Chebyshev spectral method. The discrete equations of motion are obtained based on Gauss-Lobatto sampling and Chebyshev polynomials. Employing projection matrices, fixed and elastic boundary conditions are incorporated in the same form. Numerical solutions of natural frequencies and mode shapes are gained by Chebyshev spectral method and compared with the results of finite element and weighted residual methods to verify its correctness. The effects of various parameters, such as connection sti ness, angular velocity, hub radius ratio and slenderness ratio of the beam, on the vibration of the beam are analyzed. The results show that there is a veering phenomenon of natural frequencies loci accompanied by exchanges of the corresponding mode shape,due to the difference in sensitivity to system parameters between bending mode and strength mode. With the increasing of connection sti ness, angular velocity and hub radius ratio, a lower bending mode frequency will surpass its adjacent higher strength mode frequency. Similarly, strength mode frequencies will also surpass their adjacent higher bending mode frequencies with the increasing of slenderness ratio of the beam.

    FREE MOTION OF HOLONOMIC SYSTEM WITH REDUNDANT COORDINATES
    Chen Ju, Wu Huibin, Mei Fengxiang
    2016, 48(4):  972-975.  DOI: 10.6052/0459-1879-15-392
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    If the parameters are not completely independent for holonomic systems, it is called holonomic systems with redundant coordinates. In order to study the forces of constraints for holonomic systems, we use the Lagrange equations with multiplicators of redundant coordinates or the first kind of Lagrange equations. Because there are no forces of constraints in the second kind of Lagrange equations. In some mechanical problems, the forces of constraints should not be equal to zero. In other conditions, the forces of constraints are very tiny. However, if the forces of constraints are all equal to zero, we called the free motion of constraints mechanical systems. This paper presents the free motion of holonomic system with redundant coordinates. At first, the differential equations of motion of the system are established according to d'Alembert-Lagrange principle. Secondly, the form of forces of constraints is determined by using the equations of constraints and the equations of motion. Finally, the condition under which the system has a free motion is obtained. The number of this conditions is equal to the constraints equation's, its depend on the kinetic energy, generalized forces and constraints equations. If the two arbitrary conditions are given, the third one should be obtained when the system becomes free motion. At the end, some examples are given to illustrate the application of the methods and results.

    Biomechanics, Engineering and Interdiscipliary Mechanics
    STABILITY ANALYSIS OF PILLAR BASED ON ENERGY LAW
    Zhao Kang, Yan Huabiao, Feng Xiao, Wang Xiaojun, Zhang Junping, Zhao Kui
    2016, 48(4):  976-983.  DOI: 10.6052/0459-1879-15-449
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    The energy law is favored due that it does not need to study the complicated stress process during the stope structure failure. Artificial pillar is an important mining field structure in underground mines. Due to the complicated stress and strain in the failure process, we evaluated the stability of the overlying strata by means of the energy conservation. The simplified mechanical model is established through analyzing the mechanical properties and failure mode of the artificial pillar. The equation describing total energy of artificial pillar is derived fromthe energy conservation law. Note that the total energy is has taken account of external load work, gravity potential energy and the strain energy. We also deduced the expression of potential energy function of artificial pillar. Using the catastrophe theory, energy limit-state equation of stability design of artificial pillar is built considering elastic modulus and the ratio of height to width. We discussed and analyzed the external load effect on the stability of artificial pillar. The impact on artificial pillar from external loads was quantitatively evaluated. The practical application of relevant results in the Jiaochong Gold Mine proved the validity of research methods for years. The results of the study show that the established energy limit-state equation of artificial pillar, can provide theoretical guides for the artificial pillar's scientific design and mechanics basis in metal mines.

    MULTIPLE DESIGNS APPROACH FOR CONTINUUM TOPOLOGY OPTIMIZATION
    Wang Bo, Zhou Yan, Zhou Yiming
    2016, 48(4):  984-993.  DOI: 10.6052/0459-1879-15-441
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    Topology optimization can provide creative conceptual designs for structure of industry product in the preliminary design stage. However, the traditional topology optimization approaches focus on searching for one optimal solution which may be invalid due to the refinements of models or the additional design requirements. This paper presents the multiple designs approach (MDA) to get two or more diverse topology designs simultaneously in conceptual design, which can reduce the risk of lacking full knowledge of the designs by providing multiple designs. This paper gives general optimization model formulations for MDA in which weighting function is used as the objective function to evaluate the performances of multiple solutions and diversity measure is used as constraint to make difference between configurations. A kind of diversity measure is presented in the paper and its physical significance and features are also discussed at the same time. This paper solves two compliance minimization problems based on variable density method as examples and gives detailed optimization model formulations and sensitivity analysis. The parameters of objective function and constraints in MDA and latent performances of different solutions are also discussed in the examples. The results show that MDA could propose multiple diverse designs for detailed design stage.

    INTEGRATED UNIT BEM AND ITS APPLICATION IN ANALYSIS OF ACTIVELY COOLING TPS
    Gao Xiaowei, Liu Jian, Peng Haifeng
    2016, 48(4):  994-1003.  DOI: 10.6052/0459-1879-15-437
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    With the fast development of hypersonic aircrafts, the traditional passive thermal protection system (TPS) can't a ord the increasing demand of the thermal protection for aircrafts and engines. As a result, the actively cooling TPS has received more and more attentions. The commonly used technologies do require a substantially much more time due to the complexity of the structures. In this paper, the integrated unit method is proposed for solving spatially periodical structural problems using the boundary element method (BEM) and it is used to solve the thermal and mechanical problems appearing in the TPS with actively cooling channels. In this method, the BEM cell equation only needs to be established for one computational cell and the integrated unit can be formed by a specified number of cell equations. The equations of final system can be formed by the integrated unit equations. The proposed integrated unit method inherits the variableelimination idea of the sub-structure technique and assimilates the easy assembling characteristic of the conventional finite and boundary elements, and therefore is suitable for fast analysis of large-scale spatially periodical structural problems. As the coefficient matrices of the integrated unit only needs to be established once and the equations of final system only includes boundary nodal variables, the computational efficiency can be improved considerably. Three numerical examples for actively cooling combustors of scramjet engine are given to demonstrate the computational accuracy and efficiency of the proposed method.

    AN EFFICIENT METHOD FOR FAILURE PROBABILITY-BASED MOMENT-INDEPENDENT SENSITIVITY ANALYSIS
    Yun Wanying, Lü Zhenzhou, Jiang Xian
    2016, 48(4):  1004-1012.  DOI: 10.6052/0459-1879-15-411
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    The failure probability-based moment-independent sensitivity index well analyzes how uncertainty in the failure probability of a model can be apportioned to different sources of uncertainty in the model inputs. At present, the existing sampling-based methods to estimate this index can not make full use of samples. Therefore, in this paper, we mainly concern how to improve the utilization of samples to accurately estimate this index. Based on the law of total variance in the successive intervals without overlapping proved in this paper, we propose an efficient method to estimate the failure probability-based moment-independent sensitivity index by combining the idea of space-partition and importance sampling, which only requires one set of input-output samples and the computational cost is independent of the dimensionality of inputs. The proposed method firstly uses importance sampling density function which can promise that a large number of samples will drop into the failure domain to generate a set of samples and then simultaneously obtain the sensitivity indices for all the input variables by repeatedly using this single set of samples. It is because of this that proposed method greatly improves the utilization of samples. Examples in this paper illustrate that our proposed method has higher efficiency, accuracy, convergence and robustness than the existing ones, and demonstrate its good prospect in engineering applications.

    Science Foundation
    REVIEW OF THE FIRST NATIONAL SYMPOSIUM ON EXPLOSION AND SHOCK DYNAMICS FOR YOUNG SCHOLARS
    Liu Yan, Wang Cheng, Zhan Shige, Zhang Panfeng
    2016, 48(4):  1013-1018.  DOI: 10.6052/0459-1879-16-133
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    In this paper, the First National Symposium on Explosion and Shock Dynamics for Young Scholars was brief introduced, and all of the scientific reports presented at this symposium were reviewed.