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2021 Vol. 53, No. 6

Display Method:
Luo Kai, Wang Qiu, Li Yixiang, Li Jinping, Zhao Wei

High speed and shock compression behind the bow shock of an aircraft head result in very high temperature, which would subsequently lead to a conductivity plasma flowfield around the vehicle. The plasma gas provides a direct working environment for the application of magnetic field. The magnetohydrodynamic (MHD) flow control, which uses the magnetic field to alter the trajectory of ions or electrons, can improve the aerodynamic characteristics of hypersonic vehicles effectively. It has potential prospects on aerodynamic force control and aerodynamic heating management. Besides, the development of superconducting materials and electromagnetic technology contribute to a great upsurge of MHD flow control research significantly. Although research work has been carried out in the field of MHD flow control at home and abroad, its experimental investigation is still challenging. And for the measurement of pressure and heat flux, there is no systematic conclusion because of the limited test conditions and measurement techniques. The results of different researchers may be different from each other and from the theoretical results and numerical simulations. Thus, the influence on the shock stand-off distance, pressure and heat flux under MHD flow control deserves an in-depth investigation. Besides, the numerical simulations and theoretical methods do also need reliable experimental data for variation. The aim of this review paper is to summarize and discuss the developments on MHD flow control technology based on high temperature real gas effect, including the experimental technique, numerical method, and the influence rules and dynamics mechanism of MHD flow control. Its development trend is also discussed and prospected in the paper.

2021, 53(6): 1515-1531. doi: 10.6052/0459-1879-21-067
Zhang Zhen, Ye Shuran, Yue Jieshun, Wang Yiwei, Huang Chenguang
Solving the Reynolds-averaged Navier-Stokes (RANS) equation remains an effective and practical approach in engineering applications, but the uncertainty of Reynolds stress modeling will lead to discrepancies in the prediction accuracy of this approach. With the development of artificial intelligence, the data-driven method of turbulence model combined with machine learning algorithm is more effective than the original RANS model, however, the stability and prediction accuracy of the data-driven method could still be further improved. In the present paper, a fully connected neural network is constructed to predict the eddy viscosity, and this neural network is called as Eddy Viscosity Neural Network (EVNN). Additionally, a tensor-based neural network (TBNN) is also applied to predict the higher-order eddy viscosity relationship between the unclosed quantity and the analytical quantity, and the basis tensors are used to ensure the Galilean invariance. Finally, the closed-loop accuracy of the predicted flow field is realized through multiple modifications. For the method above, the neural network which is combined by EVNN and TBNN, is trained by using the high-fidelity data generated by the large eddy simulation (LES) and the baseline data obtained by the RANS simulation. Compared with the high-fidelity LES results, the results of the modified model exhibit significantly higher accuracy in the posterior velocity field, the mean pressure coefficient, and the mean friction coefficient than the original RANS model. It can be found that the implicit treatment of the linear part of the Reynolds stress can enhance the numerical stability, and the modification of the nonlinear part of the Reynolds stress can better predict the anisotropic characteristics of the flow field. Furthermore, the prediction accuracy is further improved through the multiple modification strategy. Therefore, the combined neural network and multiple modification strategy developed in this paper, have strong potentials in data-driven turbulence modeling and engineering applications in the future.
2021, 53(6): 1532-1542. doi: 10.6052/0459-1879-21-073
Jiang Hao, Wang Bofu, Lu Zhiming
It is a challenging and important issue to establish a nonlinear dynamic model of system by use of limited data. The data-driven sparse identification method is an effective method developed recently to identify the governing equations of the dynamic system from data developed in recent years. In this paper, governing equations for different flows are identified by data-driven sparse identification methods. Partial differential equation functional identification of nonlinear dynamics (PDE-FIND) scheme and least absolute shrinkage and selection operator (LASSO) scheme are used to identify the governing equations of two-dimensional flow past a circular cylinder, liddriven cavity flow, Rayleigh-Bénard convection and three-dimensional turbulent channel flow. An over-complete candidate library is constructed by direct numerical simulation flow field data in the process of identification. Variables in the library are retained up to second order, variable derivatives are retained up to second order, and nonlinear terms are retained up to fourth order. By comparing the results from the two methods, we find both methods show good performance in identifying governing equation with no nonlinear terms, i.e., vorticity transport equation, heat transport equation and continuity equation. PDE-FIND scheme correctly identified the governing equations and Rayleigh number and Reynolds number for the flow field. But LASSO scheme failed to identify the governing equations which contain strong nonlinear terms, i.e., Navier-Stokes equations. This is because grouping effect may occur among the items in the candidate library and only one item in the group is chosen in such case in LASSO scheme. So PDE-FIND scheme is more effective than LASSO scheme in sparse identification of strongly nonlinear partial differential equation. It is also found that selecting data from regions with abundant flow structures can improve the accuracy of data-driven sparse identification results.
2021, 53(6): 1543-1551. doi: 10.6052/0459-1879-21-052
Tu Jiahuang, Hu Gang, Tan Xiaoling, Liang Jingqun, Zhang Ping
The numerical computation of vortex-induced vibration of three circular cylinders in a tandem arrangement with two degrees of freedom has been carried out. The effects of Reynolds number, natural frequency ratio and reduced velocity on the dynamic response and spectral characteristics of three tandem cylinders were analyzed. The results indicate that the Reynolds number and natural frequency ratio have little influence on the amplitude and fluid force coefficient of the upstream cylinder. The frequency locked region of the midstream cylinder increases with the increasing of Reynolds number. The dynamic response of the midstream cylinder is greatly affected by the wake of the upstream cylinder, whereas the effect of natural frequency ratio is small. Meanwhile, when the reduced velocity is small, Reynolds number and natural frequency ratio have great influence on the fluid force coefficient. In addition, the amplitude and the fluid force coefficient of the downstream cylinder are greatly affected by Reynolds number and natural frequency ratio. Reynolds number, natural frequency ratio and reduced velocity have great influence on the main peak amplitude, spectrum component and fluctuation of fluid force coefficients PSD curve. The fluctuation of the PSD curve becomes intense, giving rise to the movement trajectory of cylinder from "8" shape to irregular shape. As natural frequency ratio increases to 2.0, the P$+$S mode is found in the wake of the upstream cylinder, which leads to the occurrence of asymmetric motion, and the equality of main peaks of the PSD curve of the lift and drag coefficients. Finally, the variation of average power value of excitation load with reduced velocity is similar to that of corresponding structural dynamic response. In the same reduced velocity range, the strength of structural vibration response is directly proportional to the average power value of displacement. When analyzing the power spectral density of lift coefficient in different intervals, the vibration frequency ratio has more influence on the structural vibration response.
2021, 53(6): 1552-1568. doi: 10.6052/0459-1879-21-036
Liu Jubao, Wang Ming, Wang Xuefei, Yao Liming, Yang Ming, Yue Qianbei
When the computational fluid dynamics discrete element method (CFD-DEM) is used for solid-liquid two-phase coupling analysis, the selection of particle calculation time step directly affects the accuracy and efficiency of the coupling calculation. For this reason, each target particle is selected as the research object, and interpolation function is introduced to calculate the motion displacement of the time step, and a variable spatial search grid is constructed. An improved particle collision search algorithm (modified discrete element method, MDEM) was proposed by selecting possible collision particles to build a search list and using reverse search Method to judge collision particles. The algorithm in particle group and fluid coupling calculation, the particle counting the initial time step selection particle collision time without limit, realization of automatic adjustment and correction by large step, calculated by the real-time update of fluid particles and fluid coupling conditions, time step, the granular computing time step selection, as a result of low computational efficiency, selection is too large too small to solve the problem of false negatives, particle collision of particles and fluid coupling numerical simulation provides a effective calculation method. Through the numerical simulation of two particles and multiple particles, the relative errors of the collision forces, collision positions and times between particles obtained are all less than 2% compared with the theoretical calculation results. Compared with the traditional DEM collision search algorithm, the three calculation time steps selected do not affect the calculation accuracy, and the calculation efficiency is higher. Through the coupling numerical simulation of multiple particles and fluid, using the traditional CFD-DEM method, the precise solution can be obtained only when the particle calculation time step is 10$^{-6}$ s or smaller, while the precise solution can be obtained by using the proposed method to take 10$^{-4}$ s, which avoids the problem of missed decision caused by particle collision with the increase of time step, and the calculation time is reduced by 16.7%.
2021, 53(6): 1569-1585. doi: 10.6052/0459-1879-21-002
Yu Yaojie, Liu Feng, Gao Chao, Feng Yi
Recently, the flux reconstruction (FR) method has attracted more and more attentions for its simplicity and generality. However, it is still computationally expensive and time consuming when simulating the complex flow problems by FR method. There is a huge demand for developing appropriate efficient implicit solvers and parallel computing techniques for FR. This paper proposes an implicit high-order flux reconstruction solver on GPU platform based on the block Jacobi iteration method. As it is inefficient to solve the large global linear system resulting from spatial and implicit temporal discretization of FR directly. A block Jacobi approach is used to change the characteristics of the lift-hand matrix of the global linear system and this avoids the dependence of neighboring elements. Therefore, only the diagonal blocks of global matrix need to be stored and calculated. Then, the problem of solving the huge global linear system is transformed into solving a series of local linear equations simultaneously. Finally, these small local linear equations would be solved by the LU decomposition method in parallel on GPU platforms. Two typical cases, including subsonic flows over a bump and a NACA0012 airfoil, were simulated and compared with the multi-grid explicit Runge-Kutta scheme. The numerical results demonstrated that the present implicit method can reduce the iterations significantly. Meanwhile, the implicit solver has shown at least 10x speedup over the multi-grid Runge-Kutta scheme in all cases.
2021, 53(6): 1586-1598. doi: 10.6052/0459-1879-20-404
Ren Yanlin, Liu Zhaomiao, Pang Yan, Wang Xiang
The metal droplet deposition manufacturing technology adopts a point-by-point stacking method, which provide an unsupported manufacturing method for oblique column deposition with high flexibility. In this paper, a lattice Boltzmann model is established for simulating the continuous deposition process of the oblique column, and the horizontal displacement of the droplet on the solidification surface is studied. According to the charging and discharging process of surface energy, the deposition process is divided into four stages: falling, rapid expansion, slow expansion, and rebound. The forces on the deposited droplet are analyzed by the trend of surface energy, the gravitational potential energy, the kinetic energy, and the viscous dissipation. The internal flow of droplet is sliding in the expansion stage and rolling in the rebound stage. The internal flow of the droplet shows sliding state in the expansion stage and rolling state in the rebound stage. The acceleration of the deviation mainly occurs in the expansion stage, while the deviation distance occurs in the rebound stage. Combined with the forces in the expansion stage, it is concluded that the main driving forces of displacement are gravity and capillary force. With the increase of the droplet axial distance, the acceleration in expansion stage is shortened, and the peak of velocity is increased, so that the horizontal deviation is first increased and then decreased. This staged feature stems from the competitive relationship between the acceleration period and the maximum speed in the deviate motion. Under different deposition heights and solid-liquid wettability, the deviation distance maintains the same trend. Under a certain axial distance, the deviate distance decreases with the increasing solid-liquid wettability, or the increasing deposition height. The evolution tendency of the horizontal deviation distance is fitted, and the scanning step is optimized to realize the uniform deposition of the inclined column whose inclination angle is consistent with the theoretical result.
2021, 53(6): 1599-1608. doi: 10.6052/0459-1879-21-022
Han Mingjie, Peng Zhilong, Yao Yin, Zhang Bo, Chen Shaohua
The controllable interface adhesion of attachment and detachment has important application requirements in climbing devices, adhesion switches and mechanical grippers. In present paper, the influence mechanism of external magnetic field and film's initial curvature on the interfacial adhesion of a magnetic sensitive film/substrate is studied. The peel-test of the magnetic sensitive thin film with initial curvature on a substrate as well as the corresponding theoretical study are respectively carried out. Both the experimental and theoretical results indicate that the interfacial adhesion force of the magnetic sensitive thin film/substrate increases with increasing the initial curvature of the film, and the external magnetic field can enhance the interfacial adhesion force. Compared with the steady-state peel-off force of a flat thin film that is independent on the bending stiffness, the bending stiffness would decrease the steady-state peel-off force of the film with initial curvature. The interface effective adhesion energy is further considered from the energy point of view, which can disclose the comparing mechanisms of the film's bending energy, the potential energy of external magnetic field and the adhesion energy. Lastly, based on the experimental and theoretical results, a simply mechanical gripper controlled by both the magnetic field and film's initial curvature is proposed, which can continuously realize the gripping, transport and release of an object. The results obtained in the present paper can not only be helpful for understanding the interface reversible adhesion mechanism actuated by multi-field, but also provide a novel approach to design functional devices with controllable interface adhesion.
2021, 53(6): 1609-1621. doi: 10.6052/0459-1879-21-091
Ding Yifan, Wei Dean, Lu Songjiang, Liu Jinling, Kang Guozheng, Zhang Xu
Particle reinforced copper matrix composites have high strength, elastic modulus, excellent electrical and thermal conductivity and wear resistance, they are widely used in aerospace, rail transit, equipment manufacturing and other fields. In particle reinforced composites, the dislocation movement is prevented by small dispersed particles in the alloy, thus effectively improving the mechanical properties of metallic materials and enhancing their service safety. In this paper, the three-dimensional discrete dislocation dynamics (3D-DDD) method was used to simulate the compression of particles reinforced copper matrix composites micro-pillar. The influence of the dislocation-precipitate interaction on the mechanical response of the material was analyzed to reveal the microscopic mechanism of the precipitation strengthening. In this study, the precipitate was regarded as a spherical particle with an impenetrable surface. The dislocation bypass mechanism was used to simulate the interaction between the precipitates and the dislocations. By changing the relative distance of dislocation slip plane against the center of spherical particle, it is found that when the distance is zero, the yield strength and the subsequent strain hardening rate are the highest. As the slip plane is far away from the center of spherical particle, the yield strength and the strain hardening rate decreases. The study also found that the higher the Schmid factor, the lower the yield strength and the lower strain hardening rate. In the simulation of multiple dislocations, it was found that the reaction of dislocations in same slip planes and the interaction of dislocations in different slip systems may be responsible for the reduction of the yield strength and the strain hardening rate.
2021, 53(6): 1622-1633. doi: 10.6052/0459-1879-21-028
Wang Yishu, Shen Chaomin, Liu Sihong, Chen Jingtao
The macroscopic mechanical behaviour of granular materials is closely related to the fabric anisotropy of the contact networks. The interparticle contact system can be divided into different sub contact networks according to whether the contacts slide or not, rotate or not and the magnitude of interparticle contact forces. It is generally accepted that the mechanism of force transfer of different sub contact networks varies, which would result in the different contribution to the macroscopic mechanical responses. Based on the discrete element method (DEM), a series of conventional triaxial tests for granular materials with different rolling resistance coefficients $\mu_r$ are carried out. The evolutions of the fabric tensor of different sub contact networks during shearing process are analyzed. The influence of rolling resistance coefficients on the evolution of contact normal and normal contact force anisotropy indexes of different sub contact networks is explored. The numerical results demonstrate that the evolutions of fabric tensors of rolling and non-rolling contacts are not independent and are affected by the sliding between particles. The non-sliding and the strong force related contact networks are the main force transfer structures of the granular system. The contact normal and normal contact force anisotropy indexes of the non-sliding contact networks increase with the increase of $\mu_r$, and the contribution of the non-sliding contact networks to the macro stress decreases with the increase of $\mu_r$. For the strong force contact networks, the contact normal anisotropy index increases with the increasing $\mu_r$ while the normal contact force anisotropy index has no obvious change with the increase of $\mu_r$. The contribution of strong contact network to the macro stress is the same under different $\mu_r$.
2021, 53(6): 1634-1646. doi: 10.6052/0459-1879-21-090
Lü Aizhong, Liu Yijie, Yin Chonglin
The stress state at a point in the material can be represented by three principal stresses $\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$. When it is specified that the principal stress is positive in pressure, the shrinkage deformation occurs along the direction of the maximum principal stress $\sigma_{1}$. If both the intermediate principal stress $\sigma_{2}$ and the minimum principal stress $\sigma _{3}$ are far less than $\sigma_{1}$, the lateral extending deformation will occur along the direction of $\sigma_{2}$ and $\sigma_{3}$. When the lateral extending deformation reaches a certain limit, the extending tension failure will occur in the direction parallel to $\sigma_{1}$. There is still a lack of research on how to establish the strength criterion of this kind of extending tension failure, the maximum tensile strain theory (the second strength theory) is sometimes used to explain the extending tension failure, but it is difficult to apply it to the triaxial stress state. In this paper, $\varepsilon_{1}$, $\varepsilon_{2}$ are used to represent the maximum tensile strain and the intermediate tensile strain respectively. Based on the maximum strain theory, the failure will occur if $\varepsilon_{1}$ reaches the uniaxial tensile yield strain. The extension failure criterion will be established herein when the sum of $\varepsilon _{1} +\varepsilon_{2}$ reaches the critical value $\varepsilon_u$ and it can be proved that $\varepsilon_{1} +\varepsilon_{2}$ actually denotes the extension rate of the $\sigma_{1}$-plane. When $\sigma_{3} <\sigma_{2} \ll \sigma_{1}$, most rocks have the characteristics of brittle failure, so the rock material in prefailure stage can be assumed as linear elastic that satisfies the generalized Hooke's law. Thus, the strength criterion expressed by $\varepsilon_{1}$ and $\varepsilon_{2}$ can be expressed by $\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$. In this process, the rock's characteristics of different elastic parameters and strength under tension and compression can also be considered, and the failure state of uniaxial tension and uniaxial compression can be used to determine $\varepsilon_u$. Regardless of whether $\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$ are compressive stress or tensile stress, or there is tension and compression in $\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$, corresponding strength criteria can be established based on $\varepsilon_{1} +\varepsilon_{2} =\varepsilon_u$. The established criterion can reflect the effect of intermediate principal stress $\sigma_{2}$ on the strength. It can also be proved that: like yielding which will happen under the hydrostatic tension but not under the hydrostatic compression; compression failure can increase the plastic volume, and the results can better reflect the actual situation than Mohr-Coulomb criterion. The established strength criterion is verified by experimental data under tension-compression stress state and the theoretical calculation results are in good agreement with the existing test data. Through the proposed strength criterion and the test results of disc splitting, a more reliable uniaxial tensile strength of rock can be obtained.
2021, 53(6): 1647-1657. doi: 10.6052/0459-1879-21-026
Long Long, Zheng Yuxuan, Zhou Fenghua, Ren Huilan, Ning Jianguo
When a half-infinite beam is subjected to a constant bending moment, if the initial bending moment at the free end is suddenly released, a series of unloading flexural stress waves will be excited. This paper studies the propagation characteristics of the excited flexural stress waves using Timoshenko and Rayleigh beam theories. The Laplacian transform method is used for derivation and analysis. The analytical image function solutions of the unloading flexural waves in Timoshenko and Rayleigh beams in the frequency domain are derived, the numerical inverse Laplacian transform method is used to give the quantitative solutions of wave propagation in the time domain, and the changes over time of the deflection, the shear force and the bending moment at each point in the beam are studied. The calculation results reveal that: Unlike the simple Euler-Bernoulli beam, the introduction of the rotary inertia effect leads to a strong localization effect during the propagation in both Timoshenko and Rayleigh beams. Especially the values of the bending moment at each point in the beam are different related to distance from the free end, and the peak values change over time. The peak values of the bending moment in a Rayleigh beam firstly increase with the distance from the free end, then decrease, and finally reach an asymptotic value; the peak values of the bending moment in a Timoshenko beam generally monotonously increase over time to the same asymptotic value, which is identical with the value of the peak bending moment in a Euler-Bernoulli beam, being 1.43.The introduction of the shear effect further reduces the flexural stress wave speed, and also makes the maximum value of the peak bending moment in a Timoshenko beam smaller than that in a Rayleigh beam. For studying the flexural fracture process of a brittle thin beam, the Timoshenko beam theory can better predict the location of the secondary fracture, and the corresponding fragmentation size is about 7 times beam cross section thickness.
2021, 53(6): 1658-1670. doi: 10.6052/0459-1879-21-106
Zhang Yi, Xue Shifeng, Han Limei, Zhou Bo, Liu Jianlin, Jia Peng
The damage constitutive model is of great significance for studying the fracture and failure behavior of materials, but very few studies have been conducted to characterize damage evolution in polymeric materials quantitatively. In this study, notched round bar specimens with four different notch radii, made from high density polyethylene (HDPE) are stretched under uniaxial tension until fracture to obtain load-displacement curves and true stress-strain curves. The constitutive equations for HDPE materials under different stress states are determined through a combination of experimental testing and finite element (FE) simulation. The FE model, which can successfully regenerate the experimentally determined load-displacement curves, is then applied to establish the relationship between notch radius and stress triaxiality. A two-stage test method is proposed to quantify the variation of elastic modulus in HDPE specimens under uniaxial tension. The damage evolution equations for four types of HDPE specimens are established based on the degradation of elastic modulus. In addition, microstructure evolution in HDPE specimens under different stress states has been analyzed using interrupted tests and scan electron microscopy (SEM). The results show that the smaller the notch radius, the higher the stress triaxiality. Additionally, damage initiates earlier and develops fasters in HDPE specimens with higher stress triaxiality. From the microstructural point of view, higher stress triaxiality facilities the initiation and evolution of cavities in HDPE specimens, while suppresses the formation of fibrillar structures. A new approach for the identification of parameters in damage evolution models has been proposed base on the information of fracture strain, stress triaxiality and damage evolution equations determined from experimental testing and FE simulation. The constitutive equation and damage evolution model determined using the proposed methods are applied to simulate the deformation and fracture behavior of HDPE plate subjected to punch loading. The simulation results are in good agreement with the punch test results.
2021, 53(6): 1671-1683. doi: 10.6052/0459-1879-21-101
Feng Qingsong, Yang Zhou, Guo Wenjie, Lu Jianfei, Liang Yuxiong
The energy method is widely used in structural dynamicsanalysis with its advantage of converting the boundary value problems fordifferential equation into the functional extreme value problem, and hasalso been introduced into periodic structure band gap computation in recentyears. However, it is difficult to construct the displacement function whenusing traditional energy methods (such as the Rayleigh-Ritz method) foranalysis because of the certain complexity in boundary conditions of theperiodic structure. Additionally, the wave number term is contained in thedisplacement function so that the mass and stiffness matrix need to berecomputed continuously in the process of calculating the band gap ofscanning wave number, which leads to a large amount of calculation. For thatreason, this paper improved the traditional energy method by introducingartificial spring model to simulate various boundary conditions includingperiodic boundaries so that boundary constraints could be transformed intothe elastic potential energy of artificial springs and only the periodicboundary elastic potential energy in energy distributions contains the wavenumber term, by which the corresponding stiffness matrix only needed to berecomputed in the scanning process of wave number and other mass andstiffness matrices need to be calculated only once and then significantlyreduced the computational burden. The research results show that the methodin this paper is accurate and reliable. The calculation efficiency of thismethod is advantageous compared with the traditional energy method. Theadvantage of calculation efficiency of this method is more obvious comparedwith the traditional energy method in the situation that the mass andstiffness matrix promote in dimension, or the scanning points of wave numberincrease. In addition, the artificial spring model is more flexible andconvenient to use, and can be further adopted to band gap analysis of morecomplex periodic composite structures.
2021, 53(6): 1684-1697. doi: 10.6052/0459-1879-21-007
Chen Zhankui, Luo Kai, Tian Qiang
To perform efficient dynamic computation of a tensegrity structure and to consider local dynamic buckling of the flexible bars during large overall motions of the structure, the reduced-order dynamic model of a slender bar under compression is proposed in this research. The model is a five-node discrete one with lumped parameters of axial stiffnesses, torsional stiffnesses and lumped masses that are achieved by the equivalent analysis of the static and dynamic characteristics of the continuous bar. First, the expressions of the axial and torsional stiffnesses are deduced by the equivalent analysis of the static behaviors such that the discrete model can predict accurately the pre-buckling and buckling of the bar and approximate its post-buckling. Second, the expressions of the lumped masses are deduced by the equivalent analysis of the kinetic energy such that the linear motion of the bar can be accurately described. Third, the distributed parameters of the torsional stiffnesses and lumped massed are determined by the equivalent analysis of the natural modes of transverse vibration. The appropriate combination of their values can largely reduce the relative errors of the first two natural frequencies up to less than 1%. Fourth, the transient dynamics equations of tensegrity structures are established in the frame of global coordinates, and the method of static condensation is used to enhance the computational efficiency of the iterative solution. Last, the simulation and experimental tests are carried out and the results are compared for the quasi-static compression, modal analysis and impact dynamics of a spherical tensegrity structure. The effectiveness of the proposed reduced-order dynamic model is verified for modeling statics, natural vibration and transient dynamics of tensegrity structures. And the influence of the variation of structural parameters on the mechanics of tensegrity structures is analyzed. The proposed modeling and computation method is expected to be applied for dynamic analysis and control of complex tensegrity systems, such as planetary probes with soft landing, large-scale deployable space structures and lattice materials.
2021, 53(6): 1698-1711. doi: 10.6052/0459-1879-21-056
Gao Shan, Shi Donghua, Guo Yongxin
Hamel's field variational integrators are numerical schemes for classical field theory. It reduces computational cost caused by geometrical nonlinearity and exhibits a long-term energy stability and momentum-preserving property numerically. In the framework of one-dimensional field theory, taking geometrically exact beam as an example, this paper investigates theoretically discrete momentum conservation law of Hamel's field variational integrator. The major studies of this paper include the following aspects: The dynamical model of geometrically exact beam is established by using moving frame methods, dynamical equations of geometrically exact beam are obtained by variational principle, a momentum conservation law is then obtained through its dynamical equations and Noether theorem; For discrete model of geometrically exact beam, a discrete momentum conservation law is given by utilizing Hamel's field variational integrator of geometrically exact beam and discrete Noether theorem, and then the first order approximation of discrete momentum is proposed. Hamel's field variational integrators use system's symmetry to simplify the geometrical nonlinearity. It locates discrete convective velocities, discrete convective strain and configurations at different nodes on the spatial-temporal grid, thus leading to a series term in the expression of discrete momentum. This paper discusses the relation between the expression of continuous and the corresponding discrete one. Analytical and numerical examples are proposed to verify the conclusion. The proposed proof above is also applicable to the case in classical field theory and motivates further investigation of structure-preserving properties of Hamel's field variational integrator.
2021, 53(6): 1712-1719. doi: 10.6052/0459-1879-21-092
Dai Han, Zhao Yanying
Compared with the traditional dynamic vibration absorber, negative stiffness dynamic vibration absorber has better damping capacity and wider effective damping frequency bandwidth. The time-delay feedback control is coupled into negative stiffness dynamic vibration absorber system to further reduce the amplitude of the resonant peak and increase the bandwidth of the effective damping frequency. In the present paper, the time-delay feedback control dynamic vibration absorber system with negative stiffness is designed by equal-peak optimization. The optimal design criteria are as follows: the peak values of the first and the second resonance peaks are equal; two objectives are considered at the same time, one is to optimize the maximum resonance peak amplitude to be less than the anti-resonance peak amplitude of the passive negative stiffness absorber system, and the other is to optimize the difference between the resonance peak and the anti-resonance peak to be less than the passive absorber system. Then, the equal-peak optimum design of the control system is carried out by designing and adjusting the negative stiffness coefficient, the damper coefficient of vibration absorber and the time-delay feedback control coefficient. Finally, the effect of structural parameters on effective damping frequency bandwidth is analyzed under the condition of reducing amplitude of resonant peak. A set of structural parameters are selected and compared with two typical models based on the results of equal-peak optimization. In order to quantitatively compare the reduction effect of different models, the amplitude reduction percentage is defined. It is found that the percentage amplitude reduction is over 40% in the effective damping frequency band. The results show that the percentage reduction of the resonance peak amplitude also approximates to 40% by optimizing the structural parameters and adjusting the gain coefficient and time delay. In addition, the amplitude-frequency response curve has wider effective damping frequency bandwidth and a lower difference between the amplitude of the resonance peak and the amplitude of the anti-resonance peak by adjusting gain coefficient and time delay.
2021, 53(6): 1720-1732. doi: 10.6052/0459-1879-21-074
Ji Wenchao, Duan Lixia, Qi Huiru
The pre-B?tzinger complex is essential for the generation of the respiratory rhythm of newborn mammals and it is the center for the generation of the respiratory rhythm. The function of the memristor is similar to the plasticity of neuronal synapses, which can be used to simulate magnetic flux. In this paper, by adding stimulation current and magnetic flux-controlled memristor to the Butera dynamics model, we mainly investigate the influences of these two factors on the mixed bursting firing pattern of a single pre-B?tzinger neuron. Timescale analysis of variables is carried out by dimensionless methods. The results indicate that the model contains three different time scales. The dynamic mechanism of mixed bursting is studied through fast-slow decomposition and bifurcation analysis. Both the stimulation current and the magnetic flux can affect the number of somatic part of mixed bursting. Decrease the values of stimulation currentand magnetic flux, the number of somatic bursts will also decrease accordingly, and the stimulation current and magnetic flux can make the firing patterns of the somatic bursts transit from "fold/homoclinic" bursting to "Hopf/Hopf" bursting via "fold/homoclinic" hysteresis loop. Two-parameter bifurcation analysis in ($h$, [Ca]) plane shows that with the gradual increase of calcium ion, the trajectory of the full system crosses back and forth between the fold bifurcation and homoclinic bifurcation curve, which implies the dynamic mechanism of mixed bursting mainly rely on these two bifurcations. The number of transitions between the fold bifurcation and homoclinic bifurcation curve of the full system trajectory corresponds to the amount of somatic bursts in the mixed bursting.
2021, 53(6): 1733-1746. doi: 10.6052/0459-1879-21-071
Nie Shaojun, Wang Yunpeng, Xue Xiaopeng, Jiang Zonglin
Shock tunnel is a common ground test device used for aerodynamic shape design and optimization of hypersonic vehicles. Based on detonation driven technology, shock tunnel can generate high-temperature and high-pressure driver gas in a short test time (millisecond level) to simulate hypersonic test airflow. The main diaphragm is located between the detonation driver section and the shock tube section in the shock tunnel. During the test, the diaphragm is opened under the detonation impulse pressure. The opening state and falling off state of the diaphragm have a great influence on the air quality in the shock tunnel. At the same time, the diaphragm is also a prerequisite for the formation of shock wave. In the traditional wind tunnel, aluminum diaphragm is used for testing. In the shock tunnel, a diaphragm with stronger pressure bearing capacity is needed. At this time, aluminum diaphragm is no longer applicable, and steel diaphragm is needed. Therefore, it is necessary to research the rupture characteristics of steel diaphragm in a shock tunnel. By comparing the numerical results with the experimental results, it is found that the numerical results are in good agreement with the experimental results, and the calculated results are reliable. Based on the stress-strain model of the diaphragm, a dynamic model of the diaphragm opening was established. According to the CJ detonation theory, the process of the diaphragm rupture was simulated by finite element software, and the mechanism and mechanical characteristics of the diaphragm rupture were analyzed and summarized. The control variable method was used to analyze and study the diaphragm of different thickness and groove length, and the change rule of diaphragm rupture pressure and effective diaphragm rupture time was obtained. In the shock tunnel test, the diaphragm parameters suitable for JF-12 wind tunnel were designed according to the total rupture time of the diaphragm.
2021, 53(6): 1747-1757. doi: 10.6052/0459-1879-20-341
Ma Jing, Zhao Mingxuan, Wang Haomiao, Liu Pai, Kang Zhan
Structures that contain multiple embedded components and the host material are widely used in aerospace and other fields because of their lightweight, multi-functional, and other superior performances. Most existing topology optimization studies on multi-component structures assume the interfaces between different materials to be perfectly bonded, and thus ignore the possible interfacial failure. In this paper, we propose an efficient integrated optimization method to optimize components' shapes, layouts, and the host structural topology simultaneously, while considering the interfacial behaviors to achieve the maximum structural stiffness. First, the components' shapes and layouts are described explicitly and parameterized with the superellipse model, and the corresponding level set functions are constructed; then, combining level set topological description, the cohesive zone model and the extended finite element method (XFEM), the behaviors of interfaces that are evolving during the optimization iterations are computed on the fixed grid; further, the optimization formulation considering the interfacial behavior to achieve maximum structural stiffness is established, and the optimization problem is solved with a gradient-based algorithm with analytical sensitivities that are derived with the adjoint method. In this paper, we applied the optimization framework to design the cantilever beam and MBB beam with embedded transformable components respectively. During the optimization process, we found that the initial layouts of the components have a great influence on the final design and that may lead to undesired structures. To avoid this situation, we proposed a two-stage optimization strategy-the layouts and shapes of embedded components will be optimized first, and then the collaborative optimization will be carried out. The numerical examples show that in the optimized designs, the components together with their interfaces are usually distributed in regions that are under compression, and the optimized bonding interfaces exhibit small curvature. This result avoids the interface failure and improves the structural stiffness, and illustrates the effectiveness of the proposed optimization method.
2021, 53(6): 1758-1768. doi: 10.6052/0459-1879-21-010
Guo Zilong, Wang Lin, Ni Qiao, Jia Qingqing, Yang Wenzheng
Pipes conveying fluid are widely used in important engineering fields such as machinery, aviation, nuclear power and petroleum industries. In order to prevent the damage of pipeline structures due to flow-induced vibrations, it is necessary to conduct in-depth research on the stability, dynamic response and regulation of pipes conveying fluid. This paper proposes a grounded absorber model composed of an inerter, a spring and a damper in parallel, and studies the influence of this grounded absorber on the stability and nonlinear vibrations of the cantilevered pipe conveying pipe. First, a nonlinear dynamical model of the non-conservative system with a grounded inerter-based absorber is introduced based on Hamilton's principle. Then, the nonlinear governing equation is discretized using a high-order Galerkin method. Finally, the passive control effect of the cantilevered pipe under different absorber parameters is analyzed from both linear and non-linear perspectives, and the influence mechanism of the inertia coefficient and the installation position of the vibration absorber on the stability and dynamic responses of the cantilevered pipe are discussed. The results based on the linear theoretical model show that the grounded inerter-based absorber can significantly affect the critical flow velocity of the cantilevered pipe, and hence the stability of the pipe can be effectively improved by adjusting the parameters of the vibration absorber. The control effect of the inertia coefficient and spring stiffness on the stability of the system is found to be closely related to the installation position of the vibration absorber. The results based on the nonlinear theoretical model show that the nonlinear dynamic responses of the pipe conveying fluid are also significantly affected by the inertia coefficient and the position of the vibration absorber, and this effect depends on the value of the flow velocity of the pipe. Under certain parameter conditions, the vibration absorber can evolve the pipe conveying fluid from periodic motion to complex chaotic behavior. The results obtained in this paper demonstrate that by designing reasonable parameters of the inerter-based absorber, the stability of the cantilevered pipe conveying pipe can be improved and the vibration amplitudes of the pipe can be effectively suppressed.
2021, 53(6): 1769-1780. doi: 10.6052/0459-1879-21-105
Chen Shaolin, Wu Rui, Zhang Jiao, Gu Yin
When evaluating the seismic performance of a bridge across the canyon, it is necessary to consider the influence of topography effects, traveling wave effects, and soil-structure interaction effects. In this paper, the response analysis of the canyon-bridge system under the input of seismic waves is regarded as a wave scattering problem, which is the disturbance of the "free field" of the canyon site by the bridge and its adjacent irregular areas. Based on this idea, a method for seismic response analysis of canyon-crossing bridges is developed and the code is programmed. The "free field" of the canyon site is obtained as input through two-dimensional FEM, and canyon-bridge system is analyzed through partitioned method of soil-structure interaction. This method can consider the non-vertically incident seismic waves in the free field analysis to include the traveling wave effect. Therefore, the traveling wave effect, topography effect and soil-structure interaction effect can be considered together. Firstly, the method for the free field and the artificial boundary implementation are verified through a canyon site analysis. Then, by comparing the results of five calculation models,seismic response of the Mashuihe Bridge is analyzed using the proposed method, and the influence of the topography effect and the soil-structure interaction effect on the response of the bridge across the canyon is analyzed. The topography effect has obvious influence on the shear force, bending moment and axial force at the bottom of the pier, but it has less effect on displacement than shear and bending moment. The soil-structure interaction has a great influence on the bridge response, which greatly reduces the bridge response.
2021, 53(6): 1781-1794. doi: 10.6052/0459-1879-21-039
Wu Wencang, Dong Xinlong, Pang Zhen, Zhou Fenghua
Understanding the characteristics of fracture mode, fragment distribution and its controlling factor for explosively driven metal cylinders are important topics in applied physics, mechanics, weapon engineering and other fields. However, except for numerical simulation, a simple two-dimensional fragmentation model considering fracture mechanism has not put forward. In this paper, the fragmentation of TA2 titanium cylinders with varying charge were carried out experimentally. Through the analysis of macroscopic fracture and microscopic metallographic for the recovered fragments, the fracture mode and its fragmentation distribution of TA2 metal are discussed. The results show that:(1) The fragmentation of TA2 titanium alloy cylinders is all shear fracture modes under different detonation pressure of 7 $\sim$ 25 GPa, but the mechanism is different, which the fracture controlled by multiple adiabatic shear bands at higher explosion pressure; (2) different from the one-dimensional tensile fragmentation, the fragment mass distribution is modeled as an exponential distribution with $\beta = 1$ due to the insufficient fragmentation of metal cylinders. The $\beta $ can tend to be smaller when the fragmentation of explosively driven cylinders is more sufficient, which would be closer to the Poisson statistical distribution proposed by Mott and Linfoot; (3) The width distribution of cylinder fragments can be well described by the Rayleigh distribution. The normalized width distribution of fragments under different explosion pressures is similar and presents the characteristic of "quantization", which means a minimum characteristic size exists; (4) The characteristic sizes of TA2 shell fragments are much larger than that predicted by the G-K formula, as it is used to describe the distances between multiple adiabatic shear bands. Many factors affect the explosion of cylindrical shell, and the formation of each fragment is random, but the statistical regularity shows that the explosion process and fragment distribution are still predictable overall. The research provides an important reference for fragmentation characteristics, distribution, and model analysis of metal cylinders.
2021, 53(6): 1795-1806. doi: 10.6052/0459-1879-21-017