Table of Content

    18 March 2019, Volume 51 Issue 2
    Research Review
    Yiwen Li, Yutian Wang, Lei Pang, Lianghua Xiao, Zhiwen Ding, Pengzhen Duan
    2019, 51(2):  311-321.  DOI: 10.6052/0459-1879-18-290
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    In order to realize wide-speed-range flight of high-speed vehicle, it is of great importance to maintain the performance of inlet at off-design. Compared with traditional passive control methods, plasma and magnetohydrodynaimic(MHD) flow control are novel active flow control methods, and they have attracted extensive attention worldwide, as a result of some advantages, such as simple structure, fast response and feedback control based on actual flight condition, etc. In this paper, the main applications of plasma and MHD in hyper/supersonic inlet and dynamics models are introduced. When the inlets are in supercritical state, the shockwaves can be push back to cowl as a result of the virtual surface produced by plasma and MHD, which is based on the effect of thermal chocking. This technology is expected to applied on the hypersonic missile if only short-time flow control is required. The plasma and MHD actuators can be mounted flush on the wall, so that its requirement for thermal protection is less than that of roughness at hypersonic flight condition. The applications of high-frequency plasma and MHD actuation to produce disturbances in boundary layer have been validated through supersonic wind tunnel experiment, and the physical mechanism can be interpreted from the point of stability theory. The innovative developments of plasma source technology and the way of actuation, as well as coupled model of plasma and fluid dynamics and efficient algorithms are required in future, which can provide guidance for engineering application.

    Theme Articles on
    Muqing Niu, Bintang Yang, Yikun Yang, Guang Meng, Liqun Chen
    2019, 51(2):  324-332.  DOI: 10.6052/0459-1879-18-254
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    The actuation system, which is composed of magnetostrictive actuator and compliant displacement amplifier, has the advantages of high precision and large actuation force. It is connected in parallel with passive vibration isolator. The resulting active and passive vibration isolator can make up for the deficiencies of passive isolator on low-frequency and micro-amplitude conditions. In this paper, a nonlinear magnetostrictive actuation model is proposed based on Jiles-Atherton model. Magneto-mechanical effect is comprehensively characterized by being decomposed into stress related effects on effective field, magnetization, magnetostriction and Young's modulus. A dynamic model of the isolator is established considering the coupling effects between active isolator and passive isolator. With the coupling effect, the performance of actuation system is related to passive isolator parameters. With higher passive isolator stiffness, the actuation displacement decreases and the required actuation force increases. The coupling effect also leads to the change of equivalent stiffness of the isolator due to the ?E effect of magnetostrictive material. The influence of coupling effects can be weakened by parameter design of compliant amplifier. The performances of the active and passive vibration isolator are validated by numerical simulation. Three kinds of vibration frequencies are used, which are below, around and beyond natural frequency of the isolator, respectively. Compared to passive vibration isolator, better vibration isolation performances are acquired by adding active vibration isolator on all three conditions. And the calculation results show that the proposed model considering magneto-mechanical effect can reach a higher accuracy.

    Chuyuan Liu, Zesen Liu, Hanwen Song
    2019, 51(2):  333-340.  DOI: 10.6052/0459-1879-18-265
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    The aerodynamic flutter of aerospace vehicle Rudder-airfoil structure is a catastrophic dynamic behavior. In the aeroelastic dynamic model that is on the basis of doublet lattice theory, aerodynamic load can be expressed as a closed-loop control force that is a kind of state feedback based on structural dynamic response. In fact, the aerodynamic forces received by each node are derived from the complex coefficient proportional feedback of the displacement response and velocity response of all nodes. The control law of feedback is dependent on the geometric parameters, material parameters, dynamic characteristics of the structure, flight altitude, air density and inflow velocity etc. It usually needs to be identified and validated by actual flight or wind tunnel testing. Under laboratory conditions, with the premise of equivalent modal characteristic in system dynamic responds, a strategy is put forward that is based on active control in order to track the eigenvalues of self-excited flutter in Rudder-airfoil structure under aerodynamic load. The process of solving the non-self-adjoint dynamic differential equation and its characteristic equation of the equivalent system is established and discussed. The comparison between the computed results and those results from the common software shows good consistency. Through optimization search, the optimal feedback point for displacement and velocity, the optimal actuation point, and the optimal feedback-gain factor can be obtained respectively. The fitting of the wind velocity-displacement gain curve and wind velocity-velocity gain curve can help to realize the real contribution control of the aerodynamic force of the equivalent system. Simulation example shows that the first two modal are the main modal of flutter and higher order modals do not participate in flutter, so the active control strategy focuses on the main modal of flutter. The result also shows that the predicted experimental process does not need identification or reconstruction of the unsteady aerodynamic force in time domain. Ground simulation experiment can be achieved without any other meddles. The active control reaches satisfied effects, ensure the variation characteristics of eigenvalue, achieves preliminary eigenvalue tracking of self-excited flutter, and provides a basement to further promote the active control simulation experiment and flutter parameter identification.

    Jin Wei, Dengqing Cao, Tao Yu
    2019, 51(2):  341-353.  DOI: 10.6052/0459-1879-18-356
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    With the scale enlarging and flexibility of the actual engineering structures utilized in aerospace and other fields, the issues on the study of nonlinear vibration and active vibration control of the structure become more and more important. The key process of dealing with the vibration and control for such a kind of structure is to establish the nonlinear dynamic model and formulate the state space model of the system. For composite flexible structures composed of flexible components, rigid bodies and flexible joints, because of the vibration coupling between each part of the structure, the modes of an individual flexible component with the cantilever, simply supported and free stationary boundary are different from the real mode of the structure. In this paper, an analytic extraction method of global modes of composite flexible structures is presented, and the nonlinear dynamic model and the state-space model of the system can be obtained by the global mode discretization. Adopting the Cartesian coordinates to describe the motion of the system, establishing the motion equations of the system, and combining with the partial differential equation of the flexible part, the ordinary differential motion equation of the rigid body, the matching condition of force, moment, slope of the deflection curve and displacement at the interface, and the boundary condition of the system, the frequency equation of uniform form is given by using the separating variable method. Consequently, the natural frequencies and the global mode representation of the analytic function of the system are obtained. The global mode extraction method presented here not only facilitates the parametric analysis of the natural frequencies and global modes of composite flexible structures, but also provides an effective way to establish the low dimensional nonlinear dynamic model and the state space model of the composite flexible structure, which is of great significance for the study of nonlinear dynamic responses and the design of active vibration control of this kind of structures.

    Hao Li, Fagang Zhao, Xubin Zhou
    2019, 51(2):  354-363.  DOI: 10.6052/0459-1879-18-266
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    A quasi-zero stiffness (QZS) vibration isolator has zero stiffness at its equilibrium position, and is efficient in isolating the low amplitude micro vibrations. Therefore, the QZS vibration isolators have excellent potential in applying on the micro vibration isolation of space structures, e.g. satellite structures. Normally, a QZS vibration isolator composes of a positive stiffness element and a negative stiffness element. In many concepts of QZS vibration isolators, the negative stiffness elements are inefficient in weight and volume, because they are normally combined by several components, and external restrains or forces are needed to stress certain components. As a result, the volume and weight of the QZS vibration isolators are unacceptable in some applications, such as space technology and aviation technology. In order to improve the weight and volume of QZS vibration isolators, in this study a novel QZS vibration isolator is put forward by applying the bistable composite laminates as negative stiffness element. The system of this QZS vibration isolator is greatly simplified because of the inherent negative stiffness of bistable laminates. The principle of this novel QZS vibration isolator is illustrated, and the performance of which is analyzed by finite element method. A prototype of the novel QZS vibration isolator is fabricated and is tested in experiment. Experimental results indicate that the acceleration transmission rate of the proposed QZS vibration isolator is much improved comparing with a linear spring isolator. Nevertheless, the tested results of the isolator are not as good as predicted via the finite element analysis. The in practice performance of the proposed QZS vibration isolator is analyzed and discussed. Finite element analysis illustrates that both manufacturing error and assembly error have significant negative influence on the practical performance of the proposed QZS vibration isolator, and the robustness of the isolator should be improved in the future work.

    Zhongwen Pan, Jianwei Xing, Lei Wang, Shenyan Chen
    2019, 51(2):  364-370.  DOI: 10.6052/0459-1879-18-285
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    Whole-satellite vibration isolation is an effective measure to improve the satellite vibration environment. Traditional Whole-Satellite vibration isolation schemes mainly insert flexible and high-damping structures between satellite and rocket. Due to the series of flexible components, the scheme achieves vibration reduction, and also causes a significant decrease in the modal frequencies of satellite branches (satellite, satellite brackets, transition brackets) and the entire launch vehicle with a remarkably increase in satellite vibration displacement. The former seriously affects the flight stability of launch vehicle, especially the stability of final stage, while the latter greatly reduces the dynamic clearance between satellite and fairing, which may lead to collision between satellite and fairing in severe cases. In order to solve the problem of series whole-satellite vibration isolation, this paper presents a whole-satellite vibration isolation scheme with parallel dampers in the original main bearing structure (transition support). This scheme does not change the form and connection relationship of satellite branch structure, and does not affect the strength and stiffness of satellite branch main bearing structure. According to the characteristics of flexible spacecraft, a multi-degree-of-freedom system dynamics model is established. The effects of different damping characteristics on the transmission characteristics near the resonance frequencies of the system are analyzed by simulation. It is concluded that increasing damping can effectively improve the vibration transmission characteristics near the resonance frequencies of the system. A viscous damper and its mounting bracket are designed according to the external excitation characteristics of a launch vehicle, the structural form of transition support and vibration reduction requirement of satellite. By evenly distributing eight vibration reduction units in the transition support, a whole satellite vibration isolation scheme with Parallel bearing and vibration reduction is constructed. Finite element analysis and experimental results show that the variation of satellite branch frequencies is less than 5% and the transmission characteristics at resonance frequencies are improved by 30%~40% compared with the non-vibration state.

    Xingtian Liu, Shuhai Chen, Jiadeng Wang, Junfeng Shen
    2019, 51(2):  371-379.  DOI: 10.6052/0459-1879-18-302
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    In vibration isolation field, nonlinear vibration isolation system catch more attention than linear system because of the better vibration isolation performance. In this paper, a novel nonlinear vibration isolation system with geometric nonlinear friction damping is proposed by add two friction damper that perpendicular to the movement direction of the isolated object. The absolute and relative displacement transmissibility of such kind of vibration isolation system are studied in this paper. Different from the friction damper which usually assuming that the friction force is constant, the friction force studied in this paper is proportional to the displacement of the isolated mass by configuring two linear friction dampers perpendicular to the moving direction of the mass. The mathematical model of the friction damping and the forced vibration of the system are established. The dynamic equation is solved by using Harmonic Balance Method (HBM) subsequently by making some simplification. The result solved by HBM is verified numerically. The performance of the nonlinear vibration isolation system is compared with that of a linear one by the performance index defined by absolute and relative transmissibility. The geometric nonlinear friction can offer small or large friction damping depends on the relative displacement, therefore, the nonlinear friction force can improve the transmissibility for both absolute and relative displacement at resonance and the higher frequencies region if the damping values are chosen carefully which surpass a traditional Kevin vibration isolator model. Meanwhile, the nonlinear vibration isolation system can enlarge the application region for different excitation amplitude and avoid the system failure though the responses of the isolated mass is amplified at low frequency. The vibration isolation system with the configuration of the friction damper proposed is very suitable for both resonance and higher frequencies vibration control. The conclusions given are of importance when design and choosing the friction damping parameters.

    Fluid Mechanics
    Chao Shang, Juancheng Yang, Jie Zhang, Mingjiu Ni
    2019, 51(2):  380-391.  DOI: 10.6052/0459-1879-18-307
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    The eutectic alloy GaInSn which is liquid at room temperature has a great importance in application where the special heat transfer requirements because of its excellent heat conductivity. However, the corresponding flow characteristics in GaInSn will naturally be different from conventional fluid due to the high surface tension. In present paper, we carry out studies on the spreading, recoiling and rebounding phenomenon after the impacting of GaInSn droplets on metal foam surface. The high-speed camera is used to capture the droplet contours projected by the backlight during the moving of droplets. Through the image process method, the spreading factor, height of droplet contour in the center line and the oscillation characteristic of droplet after rebounding are obtained. Results show that at the early stage of the droplet impact, the spreading characteristic of GaInSn droplet with high surface tension is proportional to the square root of the normalized time, which is consistent with that from conventional liquid, while relates with the non-dimensional pole size of foam surface during the following spreading process. The maximum spreading factor of GaInSn droplets spreading on small non-dimensional pole size of foam surface is larger than that on smooth nickel surface, and decreases with the increase of the non-dimensional pole size of foam surface. During the rebounding process, the shape oscillation can be divided into three modes due to the difference in pore structure of surface: the regular oscillation in horizontal direction and vertical direction, the oscillation in horizontal direction and vertical direction with rotation and the rotation oscillation. Finally, the traditional theoretical formula used to predict the oscillation frequency of droplets or bubbles has been extended to cases with irregular oscillation in droplet shape through the fitting of present experimental data and analysis.

    Qiaozhong Li, Mufeng Chen, You Li, Xiaodong Niu, Khan Adnan
    2019, 51(2):  392-404.  DOI: 10.6052/0459-1879-18-278
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    An Immersed boundary-simplified thermal lattice Boltzmann method(IB-STLBM) for fluid-structure interaction problem with heat transfer is developed in this work. In the IB-STLBM, an effective simplified thermal lattice Boltzmann method without the evolution of distribution is used for the intermediate flow field. Different from the stander thermal lattice Boltzmann method, STLBM directly updates the macroscopic variables instead of the distribution functions, which offers several distinct benefits:lower cost in virtual memories, simpler implementation of physical boundary condition and higher numerical stability. In addition, from the mesoscopic view, the existence of solid boundary in the field is considered as an interference of system, which breaks the original equilibrium state of fluid particle, and a non-equilibrium state occurs on the fluid-structure interaction physics boundary. On this basis, in the present IB-STLBM, fluid-structural interaction duo to Immersed boundary appearance in the fluid can be expressed by the non-equilibrium distribution function, which is calculated by the popular non-equilibrium bounce-back boundary condition of the LBM. Hence, the solution procedure of present IB-STLBM can satisfy the non-slip boundary by a simpler way. Numerical experiments for the forced convection over a stationary heated circular cylinder and natural convection in a square cavity with a circle particle are presented to verify the stability, the capability and the flexibility of IB-STLBM for fluid-structure interaction problem with heat transfer. In the case of a stationary heated circular cylinder, quantitative and qualitative comparisons are carried out with previous study. The results of the drag coefficient and the avenge Nusselt numbers on the cylinder are in accordance with the results of previous study. From the case of natural convection in a square cavity with a circle particle, some interesting phenomena can be found. First, the temperature field is clearly stirred by the suspended particle. Second, the temporal trajectories of the particle exhibited regular changes. Third, the particle enhances heat transfer and the average Nusselt numbers periodically oscillate with time.

    Wenlai Cai, Yajun Huang, Weiyang Liu, Haoyu Peng, Zhigang Huang
    2019, 51(2):  405-414.  DOI: 10.6052/0459-1879-18-297
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    Dielectrophoresis field flow fraction (DEP-FFF) is an efficient method for the separation of micro particles, in which the particles in micro channels are polarized and controlled to separate via a non-uniform electric field. The separation of flexible particles in DEP-FFF are influenced by many complex factors including multiphysics effects, multiphase flows and particle deformation. It is difficult to simulate the process with a single calculation method. In this paper, a finite element-lattice Boltzmann coupling method is introduced to solve this problem. The lattice Boltzmann is a mesoscopic method, in which the micro volumes of a fluid are represented with small particles. The Boltzmann transport equation for fluid dynamics is solved on discrete lattice, such that the multiphase flows and large deformation problems can be easily handled. Due to these advantages, the particle deformation in the DEP-FFF process can be readily handled by the lattice Boltzmann method. On the other hand, the simulation of the total DEP-FFF process requires the solution of the Navier-Stokes equation, dielectrophoresis force equation and particle trajectory equation. The computational burden will be very severe if only the lattice Boltzmann method is employed. By computing the dielectrophoresis force with finite element method, the computational efficiency is significantly improved. The finite element-lattice Boltzmann coupling method is applied in the simulation of the particle separation process within a typical DEP-FFF chip. Analyzing the dielectrophoresis force on the particles produced by the non-uniform electric field, the relationship between the dielectrophoresis force and the change rate of electric field is revealed. The trajectories of the particles under different electric conditions are traced to validate the efficiency of the DEP-FFF method. Most importantly, the deformations of the particle under the non-uniform electric filed are analyzed. It is found that the change of the particle trajectory is controlled by the dielectrophoresis force and thus the non-uniform electric field, while the deformation of the particle is mainly related to the shearing effect of the flows. The finite element-lattice Boltzmann multiscale coupling method introduced in this paper provides an effective solution for the calculation of complex micro flows.

    Fengxian Fan, Zhiqiang Wang, Ju Liu, Huateng Zhang
    2019, 51(2):  415-424.  DOI: 10.6052/0459-1879-18-262
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    When a narrow tube inserted into a static container filled with particles is subjected to vertical vibration, the particles rise in the tube and finally stabilize at a certain height. As this phenomenon much resembles the capillary effect of liquid, it is termed as granular capillarity. To explore the particle-scale dynamical behaviors and their mechanisms associated with the process of granular capillarity, the motion of particles was modeled based on the discrete element method (DEM). Using this model, the dynamical processes and behaviors of particles in the granular capillarity were numerically investigated. The entire process of the granular capillarity obtained by experiments in literature was numerically reproduced and the evolution of the height of the granular column in the tube with time was shown. The results show that depending on the parameters of the granular system, the granular capillarity process under the simulation condition exhibits three phases characterized as periodic rising, period-doubling rising, and period-doubling steady-state in turn. During the period-doubling rising phase the velocity of capillary rise decreases gradually and a smooth transition to period-doubling steady-state phase is observed. On this basis, the evolutions of particle velocity filed as well as the particle packing fraction in the tube were analyzed. Furthermore, the distributions of the percentage of particles transported from the container into the tube in the granular capillarity process were revealed. It is found that the particle velocities at different heights are unsynchronized, as a result, velocity wave appears in the tube with the vibrational motion of the tube. The propagation of the velocity wave causes alternative expansion and compression of particles in the tube, giving rise to the periodical change of particle packing density. Moreover, higher percentage of particles transported from the container into the tube is observed in the region closer to the tube wall in the rising phase, while granular convection that occurs in the upper layers of the granular column leads to a reversing distribution of percentage of particles transported from the container into the tube in the steady-state phase.

    Yuanping Huo, Junfeng Wang, Ziwen Zuo, Hailong Liu
    2019, 51(2):  425-431.  DOI: 10.6052/0459-1879-18-256
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    A detailed visualization study on the evolution of Liquid bridge formation and fracture from a capillary is reported. By means of high-speed microscopy with high time-space resolution, special attention has been paid to the formation dynamics of the liquid bridge in the dripping mode, the change of interface structure and the fracture dynamics behavior of hydraulic bridge are studied, and the action rule of time characteristic number, electric Bond number and half-moon angle on liquid length and fracture order of liquid bridge is obtained. The results show that the fracture length of liquid bridge depends on the ratio of viscosity to surface tension, but is little affected by the relaxation time of charge. Under low voltage condition, the change of liquid bridge relative length for each experiment medium is not obvious, while the relative length of liquid bridge grows rapidly during high voltage condition. With the continuous increase of electric Bond number, the change of liquid bridge length is more obvious under the higher Bond number, and a mutation zone occur which shows the transition of the atomization model, this means the mutation of liquid bridge is a transition signal of atomization modes. With the changes of the formation angle of liquid bridge upstream and downstream, the transition behavior of jet flow in different physical media varies greatly. In the case of ethyl alcohol, the increase in the number of electric bonds causes the dropping mode to first transition to the spindle mode, while in the case of biodiesel, the pulsation mode rather than the spindle mode will first appear after the dropping mode. It is of great significance to reveal the transition law of charged micro fluidic atomization model and enrich the theory of electrostatic atomization.

    Weilin Chen, Chunning Ji, Dong Xu
    2019, 51(2):  432-440.  DOI: 10.6052/0459-1879-18-208
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    Vortex-induced vibrations of an elastically mounted circular cylinder will be altered through influencing the development of the boundary layer of the surface and the vortex shedding by the added smaller cylinders. The excitation or suppression of vortex-induced vibrations can be obtained by changing the arrangement and number of the small cylinders. In the former, more fluid energy can be transformed into mechanical energy or electricity while the latter can be applied to protect the structures. Numerical simulations of a transversely vibrating cylinder with two small cylinders behind were conducted, where the Reynolds number is 100, based on the main cylinder, the mass ratio is 2.0 and the reduced velocity is 3~11. The diameter ratio between the small and the main cylinder is 0.125 and the gap ratio is 0.125. Results indicate that the small cylinders can change the vibration of the main cylinder significantly in the simulated control angle range of 30°~90°. When the control angle is small (30°), the small cylinder suppresses the vibration of the main cylinder. The response can be divided into two branches, i.e. VIV-and galloping-branch, at the control angle of 45°~60°. The vibration amplitude increases monotonically with the increasing reduced velocity in the galloping branch. When the control angle is large (75°~90°), the promotion from the small cylinder decreases with the increase of the control angle. Furtherly, mechanisms of the small cylinders are explained by combining vortex shedding and pressure distribution around the cylinder of different instants in one period. Analysis of the energy coefficient indicates that the energy transferred from the fluid to the main cylinder decreases with the reduced velocity, which is caused by the variation of vortex structures.

    Yu Han, Zhijun Liu, Yunfeng Wang, Yao Luo, Fengxia Liu, Xiaojuan Wang, Wei Wei, Xiaofei Xu
    2019, 51(2):  441-449.  DOI: 10.6052/0459-1879-18-269
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    Multiphase microfluidics based on droplets or bubbles is one of the important branches in the microfluidic technology with rapid development in recent years. In this study, an experimental study of gas-liquid two-phase flow regimes and impact factors was conducted in a T-junction microchannel based on high-speed microscope photography and digital image processing technology. Surfactant-added sodium alginate aqueous solutions were selected as the liquid phase, and air was the gas phase. The transition process of the gas-liquid two-phase flow in the T-junction microchannel was studied, and then the bubble flow was classified according to the frequency of bubble generation and the aspect ratio of the generated gas slug in the microchannel. Under the current feeding mode, bubble flow and stratified flow were observed, and the bubble flow could be divided into dispersed bubble flow, short-slug bubble flow and long-slug bubble flow according to the frequency of bubble generation and the aspect ratio of the generated gas slug. Based on the force analysis, the formation mechanisms of the three types of bubble flow were observed as shearing, shearing-to-squeezing and squeezing. The effects of liquid viscosity and surface tension coefficient on the operating range of different types of bubble flows were investigated. It is indicated that liquid viscosity has a greater influence on the operating ranges of bubble flow than that of the surface tension coefficient. The dimensionless correlations of the bubble flow regime transition boundaries were proposed to achieve the controllable operation of the microbubble generation process.

    Jiaxing Lu, Yingjie Wei, Cong Wang, Lirui Lu, Hao Xu
    2019, 51(2):  450-461.  DOI: 10.6052/0459-1879-18-288
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    Water-entry process of parallel moving bodies widely exists in air-to-sea combat modes,such as airborne projectile elimating mines and air-dropped torpedo saturation attack, which has a strong engineering application background. In order to study the cavity evolution characteristics in the water-entry process of parallel cylinders, experimental study on the water-entry process of parallel cylinders is carried out used optical measurement method based on high-speed photography technology. The countor of cavity are identified and extracted with image processing technology. And by comparing the cavity countor between single cylinder and double cylinders with different Froude number at the time of water entry (Fr0), the cavity evolution characteristics in the water-entry process of parallel cylinders and the effect of Fr0 are analyzed. The experimental results show that the whole cavity shows good mirror symmetry, while the inside and outside cavity of the cylinder has obvious asymmetry. When the Fr0 is low, the cavity closure mode is pinch off, and the closure point moves backward with the increase of Fr0. And when Fr0 reaches critical value, the closure mode transits to surface closure and the closure point moves forward with the increase of Fr0 insteadly. Under the positive impact of Fr0 and the negative impact of ambient pressure and splashing and rolling, the peak value and time length of cavity expansion and outward offset of cavity center at different depth increase first and then decrease with the increase of Fr0. Due to the different dominant impact at different depths, the critical points of Fr0 at which the peak and time trends change are different.

    Solid Mechanics
    Zeqi Tong, Yang Liu, Shutian Liu
    2019, 51(2):  462-472.  DOI: 10.6052/0459-1879-18-323
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    As one of the main thin-walled energy absorption structure in automobile, the top-hat beam draws great attention and its performance improvement is a concerning issue. Research indicates that the energy absorption performance of thin-walled structures can be improved by the wall thickness optimization. However, complicated thickness distribution would cause manufacturing difficulties. Thus, it is urgent to develop a design optimization method of structural thickness distribution based on specific manufactory process technology. In this paper, a design optimization method is proposed for maximizing the energy absorption of top-hat beam under transverse crash manufactured by variable gauge rolling technology. This top-hat beam is made of tailor rolled blanks, and can be classified as uniform thickness sections and transition sections. Through adjusting the length and thickness of the uniform section, and the description of the transition section, the performance of the structure can be optimized. To find the optimal structure parameter, we use the hybrid cellular automata to determine the optimization direction. To meet the variable gauge rolling constraint, the structure is filtered in the iteration. Based on this method, we studied an example of top-hat beam and found its optimized section length, thickness and transition description, which shows the effectiveness of this method.

    Zhigang Wei, Haibo Chen
    2019, 51(2):  473-483.  DOI: 10.6052/0459-1879-18-303
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    The constitutive relation of rubber-like materials is important for scientific study and engineering application. However, the fitting ability and reliability of the existing models don't satisfy the requirement. To solve this problem, a new incompressible isotropic constitutive model for the elasticity of the rubber-like materials was proposed in this paper. The form of the constitutive model was studied and a new model was proposed based on plane stress deformation state. This model is an isotropic incompressible model which is defined in terms of the first and second principal stretches and is applicable to describe the elasticity of rubber-like materials in general deformation state. The deformation rules of the material subjected to a lateral constraint was studied and the constraints which this model should satisfy were studied. With a proposed function for stress-strain relation of rubber-like materials under plane stress deformation, a method and a function was proposed to extend the function for plane stress deformation states to a general one for arbitrary three-dimensional deformation states. Thus, a new general incompressible isotropic elastic constitutive model for rubber-like materials was derived. The model was fitted to five groups of test data which all include three types of test and a biaxial test data which covers a broad range of deformation state. The results show that this model fits the test data very well and has a better reliability than the existing models. Besides, the model can predict the material's response well even with a type of test data such as the uniaxial tension test.

    Xiaoming Wang, Rongxing Wu, Heng Xiao
    2019, 51(2):  484-493.  DOI: 10.6052/0459-1879-18-334
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    A multi-axial compressible strain energy function is propose to simulate the stress-strain hysteresis loops, which produced by the Mullins effect for rubber-like materials subjected to loading-unloading cycle by a direct, explicit method. The novelty of this paper is to introduce a new variable, which captures the property of dissipation into the potential, and give out a new multi-axial strain energy function. Two properties are incorporated into the new potential: Firstly, the new variable may not affect the potential in the process of loading. Therefore, we can exactly simulate the three benchmark tests, including uniaxial tension and compression, equal-axial tension and compression, and plane strain, by explicitly giving out the appropriate formulations of shape functions; Secondly, the new variable may become active in the process of unloading. The variable may affect the potential by changing with the unloading stress, and produce different stress-strain curves in the unloading process. As a result, the hysteresis loops may be produced in the loading-unloading cycles. We give out the change rules of the shape functions in the unloading process, and predict the stress-strain relation with different unloading stress by analysis the classical test data of the Mullins effects. Numerical results for model validation are in good accord with the three benchmark tests, and the experiments with hysteresis loops producing from the Mullins effect at the end of this paper.

    Fan Peng, Shuangshuang Xie, Hongliang Dai
    2019, 51(2):  494-502.  DOI: 10.6052/0459-1879-18-264
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    The paper concerns the problem of singular stress filed in viscoelastic contact interface ends under creep loading. The local boundary conditions taking into account the contact friction are linearized by the assumptions of tiny relative slip and invariant slip direction between interfaces. The solution of stress field at the interface end in the Laplace transform domain is obtained based on the correspondence principle, and the convolution integral expressions of the singular stress field in the time domain is developed. The numerical inversion of convolution integral kernel is made by considering two types of combinations of contact materials. One is that the durable modulus has a difference in magnitude, and the other is that the durable modulus is nearly the same. The results of inversion show that kernel functions can be approximated by analytical expressions obtained by the quasi-elastic method with a good accuracy. On this basis, simplified formulas of the viscoelastic singular stress field are developed by using the integral mean value theorem and introducing the correction coefficient of each stress component. The value range of expressions for correction coefficient is investigated in combination with the examination the numerical inversion results of the kernel functions, following conclusions are drawn as follows. If the durable modulus of the two-phase contact material differs greatly, the quasi-elastic solution can be used to describe the singular stress fields near the interface end; in general, there is no uniform singular value and no uniform stress intensity factor for stress fields; when the solution of viscoelastic stress is approximated by formulas similar to the quasi-elastic solution, the error limit can be estimated. In the last part of the paper, the viscoelastic stress analysis of viscoelastic plate at support ends is performed by means of finite element simulation as plane strain problem. The example includes two types of contact interface ends, one is constructed by the viscoelastic plate and an elastic metal support, the other is formed by a viscoelastic plate and viscoelastic cushion layers. The theoretical conclusions obtained in the front part of the paper are validated by the simulation results.

    Lele Zhang, Xianglin Liu, Jinxi Liu
    2019, 51(2):  503-511.  DOI: 10.6052/0459-1879-18-413
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    Piezoelectric nanomaterials have many unique properties, such as enhanced electromechanical coupling, low power dissipation and sensitive response, etc. Also such materials can meet the demand of microminiaturization of piezoelectric devices. These advantages make them strong candidates for applications in the fields of sensing, nanoelectromechanical systems (NEMS), flexible electronic device, and so on. As one of the most important features of nanomaterials, surface effect which resulted from the high ratio of surface to volume commonly plays a dominant role in the overall mechanical properties of piezoelectric nanomaterials. Due to the presence of surface effect, the bulk stress and bulk electric displacement jump across the piezoelectric surface, thus the classical continuity conditions are invalid. In this paper, the dispersion characteristics of SH guided waves propagating in a monolayer piezoelectric nanoplate are investigated with consideration of the surface effect. A surface is regarded as a two-dimensional continuum of zero thickness which possesses own material properties, and the influences of surface elasticity, surface piezoelectricity, surface permittivity and surface density are accounted into the non-classical boundary conditions of the piezoelectric nanoplate via the surface piezoelectricity model. The analytical expressions of dispersion relations are derived, and the numerical examples are provided to discuss the impacts of surface material parameters and nanoplate thickness on the symmetric and antisymmetric modes. Analysis results show that the propagation characteristics of SH guided waves exhibit obvious size-dependence. The surface effect has a significant impact on dispersion behaviors when the nanoplate thickness is small enough, while they may become more and more negligible as the thickness increases.

    Ting Dai, Hongliang Dai, Junjian Li, Qi He
    2019, 51(2):  512-523.  DOI: 10.6052/0459-1879-18-280
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    Functionally graded materials (FGMs) are composed of two or more discrete constituent phases with continuous and smoothly varying components. Due to the distinctive merit comparing with usual composite materials that they can reduce the stress concentration and optimize the stress distribution to make good use of each component, utilizing of FGMs helps to resolve some problems in composite materials such as low bond strength and inharmonious of properties effectively. Because of the preparation technology or for the need of special structures, micropores or pores are commonly found in various types of FGM and play an important role in the influence factors on mechanical properties of FGMs. In addition, the application conditions of FGMs are usually complex or extreme with multiple physical fields, and the mechanical responses of various FGMs under coupling multi-fields will be more complex. On micro scale, the pores in porous FGM include material pores of each components and structural gaps between different particles. These pores will affect the properties of FGM, especially under hygrothermal environments. In this paper, two kinds of micro pores (material pores and structural gaps) in FGM are both considered. An expression to characterize porosity of the whole FGM is proposed, where the porosity of each component is related to its volume fraction and the global porosity is a linear superposition. Considering temperature dependency of the component properties as well as the material properties of pore fillers (liquid water or vapor), a prediction model of the porous FGM is established. Focusing on a rotating circular plate with its thickness varying along the radial direction, and applying the current porous FGM model, governing equations of the nonlinear steady-state temperature and moisture fields as well as displacement field are derived. Solving the governing equations by the differential quadrature method (DQM), distributions of temperature, moisture, displacement and stress of the FG circular plate are obtained. In the numerical examples, analytic solution of a simplified mechanical model is carried out to verify the numerical calculation process of the current study. By changing the key parameters, influences of each porosity, gradient index and thickness change rule on the hygrothermal mechanical responses of the porous FG circular plate with variable thickness are discussed in detail.

    Wei Lu, Dong Zhao, Dongbo Li, Xiaofei Mao
    2019, 51(2):  524-539.  DOI: 10.6052/0459-1879-18-349
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    Bamboo and wood anchoring technique has been widely used in the reinforcement of rammed earth sites in recent years. However, its force transfer mechanism at the anchorage interface is still unclear, which seriously restricts the large-scale application of anchorage technology in scientific way. Relevant research results have confirmed the importance of a reasonable bond-slip model for predicting the performance of the anchorage system. Based on this, the bamboo-modified slurry-rammed earth anchoring system is taken as an example to study the whole process of force transfer in anchorage interface based on tri-linear bond-slip model considering complete debonding phenomenon. Firstly, the force transfer process of the anchorage interface was divided into six successive stages, and the corresponding interface stress, strain distribution and evolution process are analyzed theoretically, the closed form solutions of bolt axial deformation, anchorage interface slip, shear stress and shear strain were also derived. Meanwhile, the calculation method of ultimate anchorage force and effective anchorage length has been proposed. On this basis, the feature points parameters of bond-slip model were calibrated by identifying the different stages of load-displacement curve. Finally, the rationality of the analytical model was validated against two in-situ pull-out tests in rammed earth sites. The influence of anchorage length and axial stiffness of anchor bolt on the anchoring performance was emphatically analyzed in the text. The analytical model proposed by this paper has wide applicability to the analysis of the force transfer process of anchorage interface with complete debonding phenomenon, and can provide reference and guidance for the design of anchoring engineering of rammed earth sites.

    Dynamics, Vibration and Control
    Jiankang Zheng, Xiaofang Zhang, Qinsheng Bi
    2019, 51(2):  540-549.  DOI: 10.6052/0459-1879-18-241
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    Due to wide existence of multiple-time-scale problems in practical engineering, the complicated dynamic behaviors and their generation mechanism have become one of the hot topics at home and abroad. The systems with multiple time scales can often exhibit bursting oscillations with the bifurcation delay phenomenon. In order to investigate the bifurcation mechanism of bursting oscillations caused by bifurcation delay in a nonlinear system, a parametric excitation is introduced in a novel three-dimensional chaotic system. When the exciting frequency is far less than the natural frequency, the coupling of two time scales involves the vector field, which leads to the bursting oscillations. By considering the whole exciting term as a slow-varying parameter, the original system can be considered as a generalized autonomous system, which can be regarded as the fast subsystem. Upon the analysis of equilibrium points and bifurcation conditions of the fast subsystem, combining with the transformed phase portraits, the bifurcation mechanisms of bursting oscillations is presented. Four typical cases with different parameter conditions are discussed to reveal the evolution of the bursting oscillations. It is found that when the slow-varying exciting term passes across the bifurcation points, the delayed behaviors of super-critical pitchfork bifurcation can be observed. With the increase of the exciting amplitude, the occurring needed for the bifurcation delay is increased gradually. When the delayed behaviors end in different parameter regions, different types of bursting oscillations which may surround different attractors such as equilibrium points and limit cycles appear.

    Han Wu, Xiaohui Zeng, Hemu Shi
    2019, 51(2):  550-557.  DOI: 10.6052/0459-1879-18-329
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    Because of the inherent instability, EMS maglev train requires the application of active control to achieve a stable suspension. In every suspension control loop, there is inevitable time-delay, which may affect the performance of the system. When the time-delay exceeds a critical value, the maglev train will become unstable. Previous studies have proved the existence of the critical time-delay. The relationship between critical time delay in control loop and vehicle parameters (including vehicle speed, position feedback control gains, guideway parameters, and suspension parameters) is studied in this paper. A dynamic model of a maglev vehicle/guideway coupling system is established. The 10 DOF vehicle includes a carbody and four maglev frames. Each maglev frame contains four electromagnets. The guideway is modelled as a series of continuous simply supported Bernoulli-Euler beams. The vibration equation of the guideway is obtained by a modal superposition method. In order to achieve vehicle/guideway coupling, a conventional electromagnetic force model which is linearized in the neighborhood of stable suspension position is adopted. The fourth-order Runge-Kutta method is used to obtain the dynamic response of the vehicle/guideway coupling system. A proportional derivative (PD) control algorithm is used for the feedback control of the electromagnet current. To facilitate the analysis, this paper assumes that all the time-delay occurs in the control loop, and that only the position feedback control loop exists. In order to analyze the motion property when critical delay occurs, we write a simulation program. Using the program, the dynamic responses of maglev vehicle considering different position feedback control delay are calculated. The delay value which results in motion divergence is defined as critical time-delay. Based on the calculations and analysis, following suggestions to promote the stability and weaken the effect of time-delay in position feedback control loop are provided: Enlarge bending rigidity and damping ratio of the guideway; Reduce position feedback control gain; Enlarge velocity feedback control gain; Enlarge second suspension damping. In addition, in view of that the critical time-delay of a stationary vehicle is always smaller than that of a running vehicle, hence, the critical time-delay of stationary vehicle shall be considered as safety limit value.

    Yikun Wang, Lin Wang
    2019, 51(2):  558-568.  DOI: 10.6052/0459-1879-18-295
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    Pipes conveying fluid have been widely used in the fields of aerospace, mechanics, marine, hydraulic and nuclear engineering. The stability analysis, dynamic response and safety assessment of fluid-conveying pipes subjected to nonlinear constraints are particularly important for both engineering applications and scientific researches. Although the dynamical behaviors of fluid-conveying pipes subjected to single-point loose constraints have been discussed for four decades, the literature on the dynamics of fluid-conveying pipes subjected to distributed motion constraints is very limited. To obtain a better understanding of the dynamics of a cantilevered pipe conveying fluid subjected to distributed motion constraints, both cubic and modified trilinear spring models are employed in this study to describe the restraining force between the pipe and the motion constraints. This study is also concerned with the parametric resonance when the pipe is excited by an internal pulsating fluid. Firstly, the modified nonlinear equation of the pipe system was discretized via Galerkin's approach and solved using a fourth-order Runge-Kutta method. Via the Floquet theory, the nonlinear equation of motion was simplified to a linear one to calculate the parametric resonance regions versus the pulsating amplitude and frequency. Two representative values of mean flow velocity were employed to calculate the parametric resonance regions. Both the two values of mean flow velocity are assumed to be lower than the critical velocity for the cantilevered pipe system. Then, considering the geometric nonlinearity, the nonlinear dynamic responses focusing on the effect of external nonlinear restraining forces generated by the distributed motion constraints are discussed in detail. Results show that the stability regions of the nonlinear system agree well with that predicted by analyzing the linearized system. It is found that the distributed motion constraints would mainly affect the displacement amplitudes. Various oscillation types may arise when the pulsating frequency of the flow velocity is varied. Several bifurcation diagrams show that, however, a significant difference can be observed between the routes to chaos for the two constraint models, i.e., the pipe with a trilinear spring model can exhibit chaotic oscillations more easily than that with a cubic spring model.

    Qing Li, Likun Xing, Jiang Bai, Yuanjie Zou
    2019, 51(2):  569-576.  DOI: 10.6052/0459-1879-18-337
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    Spacecraft suffer severe acoustic environments in the course of launching along with launch vehicles. Acoustic tests should be done to check up whether the spacecraft work well while suffering acoustic environments. Response properties of structural vibrations during acoustic tests for spacecraft should be considered in the structural strength design. Moreover, they are important foundations for specifying the random vibration test conditions of the spacecraft equipment mounted on the structural boards. Therefore, it is necessary to predict the structural responses due to acoustic loads in the preliminary stage of spacecraft development. In this paper, a finite element model of a spacecraft structure is built using the commercial finite element analysis software MSC.Patran and MSC.Nastran. The sound pressure level spectrum of acoustic loads is transformed to the power spectrum density of fluctuating pressure. And then, the random vibration responses of the spacecraft structure under the acoustic loads are analyzed using the modal method. The simulation results are compared with the acoustic test results. In the simulation analysis, the effects of the damping ratio model and the fluid added mass are studied. The research shows that: using an empirical damping ratio model that the damping ratio decreases with the rising of the frequency can do a better response prediction for the medium-high frequency properties as well as for the total root mean square results; further using the virtual mass method to consider the fluid added mass effect can do a better response prediction for the power spectrum density results. The proposed simulation method in the article is convenient for modeling and efficient for computation, which is appropriate for the response prediction of structural vibrations in spacecraft acoustic tests in the preliminary stage of spacecraft development.

    Biomechanics, Engineering and Interdiscipliary Mechanics
    Dingli Zhang, Zhenyu Sun, Yanjuan Hou
    2019, 51(2):  577-593.  DOI: 10.6052/0459-1879-18-322
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    Tunnel support structure system is the key of controlling the stability of surrounding rock, which is also the basic task of tunnel design, while systemic understanding of the process and mechanism of interaction among support structures is the basis of quantitative design. This paper embarks from structural property of tunnel surrounding rock and the constitutive property of support effect, the basic function of tunnel support that "mobilizing" and "assisting" surrounding rock bearing is put forward, of which the function distribution principle and realization way are clarified, namely, through the guarantee role of advanced support, the core role of primary support and safety reserve role of secondary lining to complete. In view of three advanced failure modes including the positive extrusion, the forward type caving and posterior tilt falling of surrounding rock, the corresponding advanced support pattern and its effect evaluation method are given respectively. The primary support is the main undertaker of tunnel surrounding rock additional load, including the anchorage system and the arch and shotcrete structure, whose bearing function is carried out by "mobilizing" and "assisting" surrounding rock respectively, and also have the function of "bracing" and "protecting". The connotation of secondary lining structure as security reserve function is illuminated. The relationship between load sharing ratio and stiffness matching and support time of secondary lining structure is established, according to which the suggestive values of structure parameters and support time of secondary lining are provided. The collaborative support optimization model is set up based on the three stages of the interaction between advanced support, primary support, secondary lining and surrounding rock, whose targets are minimizing surrounding rock deformation S and optimizing synergy degreeξ. Three levels of synergy including relations between support structure system and surrounding rock, different support structures and different support structure elements are clarified. And a collaborative optimization design method for tunnel support structure is proposed.

    Shaolin Chen, Xiaofei Ke, Hongxiang Zhang
    2019, 51(2):  594-606.  DOI: 10.6052/0459-1879-18-333
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    The simulation of seismic wavefield at seafloor and seismic response of marine structures involves the coupling between seawater, saturated seabed, elastic bedrock and structure. That means, we target simulation where several types of equations are involved such as fluid, solid and saturated porous media equation. The conventional method for this fluid-solid-saturated porous media interaction problem is to use exsisting solvers of different equations and coupling method, which needs data mapping, communication and coupling algorithm between different solvers. Here, we present an alternative method, in which the coulping between different solvers is avoided. In fact, when porosity equals to one and zero, the saturated porous media is reduced to fluid and solid respectively, so we can use the porous media equation to describe the ideal fluid and solid, and the coupling between porous media, solid and fluid turns to the coupling between porous media with different porosity. Based on this idea, firstly the Biot's equations are approximated by Galerkin scheme and the explicit lumped-mass FEM is chosen, that are well suited to parallel computation. Then considering the traction and velocity continuity on the interface between porous media with different porosity, the coupled algorithm is derived, which is proved to be suitable for the coupling between fluid,solid and saturated porous media. Thus, the coupling problem between fluid, solid and saturated porous media can be brought into a unified framework, in which only the solver of saturated porous media is used. The three-dimensional parallel code for this proposed method is programed, examples for analysis of layered water-saturated seabed, water-bedrock, and water-saturated seabed-bedrock semi-infinite systems subjected to plane P-SV wave are given, and the proposed unified framework is verified through comparison between the results obtained through the proposed unified framework combined with tansmitting boundary condition and those obtained through tansfer matrix method.

    Mingqing You
    2019, 51(2):  607-619.  DOI: 10.6052/0459-1879-18-291
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    Rocks are natural materials composed of various mineral particles within fissures and pores in different sizes, those result in complicate mechanical properties. Strength criteria for rocks in engineering design and disaster prevention are still an open question. As cohesion and friction in rock do not work simultaneously, the linear Coulomb criterion proposed in 1773 is only reliable to describe pseudo-triaxial compression strength of cylindrical specimen in a small range of confining pressure. Many nonlinear criteria are merely empirical formulas but lack of physical background. The exponential criterion proposed by the author is applicable to fit the relationship between strength and confining pressure of rocks in shear failure; therefore, the cohesion and friction are analyzed in Mohr's stress space on the fitting solutions for eleven rocks. Shear stresses in rock have an upper limit, i.e. the genuine cohesion c0 of rock; and the internal friction has a peak of about 0.38 c0, by which intersection of the cohesion and internal friction is. The genuine cohesion is independent to normal stress, so the nominal cohesion of rock specimen represents the shear fracture area of intact material when rock specimen reaches its strength. The equivalent friction factor of slipping fissure decreases with the normal stress, so as the climbing angle that depends on ratio of normal stress to the genuine cohesion. Relationship between the equivalent friction factor and parameters in the exponential criterion reflects the physical background of shear fracture for rock under compressive stresses.

    Kai Long, Xuan Wang, Liang Ji
    2019, 51(2):  620-629.  DOI: 10.6052/0459-1879-18-169
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    Most existing study on topology optimization have concentrated on maximizing the system stiffness. Especially, the minimization of static compliance subject to the volume fraction is widespread in the formulation. From the engineering point of view, structural strength design is of vital importance. Past study on stress constraint have shown that an amount of numerical difficulties with the stress-constrain topology optimization exist including the so-called singularity, vast of stress constraints, highly nonlinear behavior and so on. To achieve the topological design under stress constraint requirement, the normalized stress measure using p-norm function is adopted for the reduction of stress constraints. Following the modeling manner of independent continuous mapping method, the reciprocal function of relative density is regarded as the design variables. The sensitivities of stress constraint and volume objective with respect to the design variable are derived, and their explicit expressions are formulated based on the first-order and second-order Taylor approximation respectively. By setting up the sub-problem in the form of a quadratic program, the original topology optimization problem is efficiently solved using the sequential quadratic programming approach. The difference between stiffness and strength design, as well as the effect of various upper bounds of stress value on the optimized results for stress constraint are investigated in 2D numerical examples. Through the comparison of the proposed method and traditional variable density method, the feasibility and effectiveness of the proposed optimization approach in stress constrained problems are verified. The results also demonstrate that the consideration of stress constraint in continuum structure is indispensable.

    Science Foundation
    Yihui Zhang, Xu Guo, Xue Feng, Shige Zhan, Panfeng Zhang, Kunchao Bai
    2019, 51(2):  630-634.  DOI: 10.6052/0459-1879-18-408
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    This review briefly provides a general introduction to the Eighth National Symposium on Solid Mechanics for Young Scholars hosted by Tsinghua University. It summarizes the contents of presentations delivered by the invited experts and young scholars. It discusses the recent trends, the challenges and remaining questions in the development of solid mechanics subject in the new era.