力学学报

RESEARCH PROGRESS AND OUTLOOK OF FLOW FIELD CREATED BY DIELECTRIC BARRIER DISCHARGE PLASMA ACTUATORS DRIVEN BY A SINUSOIDAL ALTERNATING CURRENT HIGH-VOLTAGE POWER

Zhang Xin, Wang Xunnian

Flow control technology using dielectric barrier discharge plasma actuators which are driven by a sinusoidal alternating current high-voltage power is an active flow control technology based on plasma actuation and has some advantages, such as short response time, simple structure, low consumption power, and no need for additional air source devices. It has broad application prospects in lift enhancement and drag reduction, vibration suppression and noise reduction, assisted combustion and anti-icing. In view of the three problems that most of the power consumed by the plasma actuator has not been exploited, the whole evolution process of the induced flow field has not been fully understood, and the evolution mechanism of the induced flow field is not clear, the present manuscript summarizes the research progress of the induced flow field of the plasma actuator from the three aspects which include the spatial structure, the space-time evolution process and the evolution mechanism of the induced flow field of the plasma actuator. For flow structures of the induced flow field, the turbulent characteristics of induced wall jet under high voltage excitation are found, and the correlation mechanism between coherent structure in the vicinity of wall and non-dimensional actuation parameters is analyzed; The potential energy of the plasma actuator is excavated from the aspect of the acoustic energy induced by the plasma actuator, and the new phenomenon of "the ultrasound and the acoustic streaming flow created by the plasma actuator" is found, and the novel mechanism of acoustic excitation created by the plasma actuators is proposed; In the aspect of the spatial-temporal evolution process, the complete evolution process of the flow field induced by the plasma actuator from the thin wall jet to the "arch" jet, then to the starting vortex, and finally to the quasi-steady wall jet is uncovered; In terms of the evolution mechanism, the evolution mechanism of the induced flow field is proposed based on the acoustic characteristics. In addition, to break through the bottleneck of flow control technology using plasma actuators and open up the innovation link of "concept innovation - technology breakthrough - demonstration and verification", a few opening issues on the flow field generated by the plasma actuators are presented.

2023, 55(2): 285-298. doi: 10.6052/0459-1879-22-377

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STATIC AEROELASTIC ANALYSIS BASED ON PROPER ORTHOGONAL DECOMPOSITION AND SURROGATE MODEL

Li Kai, Yang Jingyuan, Gao Chuanqiang, Ye Kun, Zhang Weiwei

The static aeroelastic problem is concerned with those physical phenomena which involve significant mutual interaction between elastic and aerodynamic forces, which has dramatical influence on the overall flight performance and security of the aircraft. The computational fluid dynamics (CFD) and computational structural dynamics (CSD) coupling method is an essential and accurate tool to account for the impact of static aeroelastic problems in the design of the advanced aircraft. However, aerodynamic loads based on CFD simulation require a large computational cost and time, which cannot meet the need of the design stage. Therefore, many aerodynamic reduced order models based on CFD have been proposed in order to maintain a balance between the computational accuracy and efficiency. Then, an efficient and accurate steady aerodynamic reduced order model for the static aeroelastic analysis is developed in this work, using proper orthogonal decomposition (POD) and Kriging surrogate model to replace the CFD simulations and couple the finite element analysis (FEA). Compared with the conventional static aeroelastic analysis with the modal method, the proposed approach can deal with more complex static aeroelastic problems and predict the aerodynamic distribution loads in the static aeroelastic deformation. Then, the performance of the proposed approach is evaluated by a transonic flow with multiple Mach numbers and angles of attack past a three dimensional HIRENASD wing configuration, which is initiated by Aachen University's Department of Mechanics to provide a benchmark test case for computational aeroelastic code validation. Results demonstrate that the relative error for the static displacement at the wing tip (Y/b = 0.99) of the CFD/CSD coupling method and the proposed approach is within 5%. In addition, the error for predicting aerodynamic distribution loads in the position of static equilibrium is within 5% and the computational efficiency is improved by the proposed approach at least 6 times for the static aeroelastic analysis.

2023, 55(2): 299-308. doi: 10.6052/0459-1879-22-523

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EXPERIMENT INVESTIGATION OF OBLIQUE DETONATION WAVE STRUCTURE INDUCED BY HYPERSONIC PROJECTILES

Shang Jiahao, Hu Guotun, Wang Qiu, Wang Yejun, Zhang Kun, Xiang Gaoxiang, Zhao Wei, Wei Bingchen

By taking advantages of rapid heat release, high specific impulse and simple combustion chamber structure, oblique detonation plays an important role in hypersonic air-breathing propulsion systems, which has been attracted more attentions in recent decades. However, due to the existence of technical difficulties, such as high-speed test environment generating, fuel and oxidant mixing, and high-temperature combustion flow-field structure measurement, the ground experimental research about oblique detonation wave at home and abroad is still limited at present. Thus, it’s difficult to support the development of oblique detonation engines. To study the wave structures and dynamic characteristics of the self-sustained propagating oblique detonation wave, investigation on oblique detonation induced by a hypersonic projectile launching has been conducted based on a two-stage light-gas gun device. The spherical projectile with a diameter of 30 mm is launched into a test chamber, in which fills with stoichiometric hydrogen/oxygen combustible mixture to induce the initiation of the detonation wave. In this work, two different shadowgraph techniques have been employed to record the structures of shock induced by the projectile. Three kinds of shock structures have been observed with different projectile velocities and filling pressure: shock induced combustion, detonation wave initiated by the projectile and steady oblique detonation wave around the projectile. A decrease in the filling pressure results in increasing length of transverse wave and unsteady flow structure of detonation wave. The measured oblique detonation wave angle agrees well with the theoretical result. The discrepancy of the shock wave angle between experiment and theory exists due to large angle of attack of the projectile, which is caused by aerodynamic instability. The propagation velocity of the oblique detonation wave is determined by oblique detonation wave angle at various points of detonation wave. Moreover, it shows that the detonation propagation velocity decays to the CJ detonation velocity as moving away from the projectile, and thus accelerate the attenuation of propagation velocity of the oblique detonation wave.

2023, 55(2): 309-317. doi: 10.6052/0459-1879-22-536

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IMPACT OF RUDDER GEOMETRY ON THE WAKE EVOLUTIONS OF PROPELLER-RUDDER INTERACTION

Zhang Weipeng, Ren Jianxin, Guo Hang, Wang Zibin, Hu Jian

The evolutions of propeller wake can be impacted by interaction between the propeller and rudder which results in turbulence enhancement in the propeller wake. The turbulence in the propeller wake worsens vibrations and noise on vessels. The intensive research aimed on the wake evolution in the propeller-rudder interaction brings sights on the control of propeller wake and relief of vibrations and noises. Hence, the rudders with different chord and profile are employed to investigate the impact of rudder geometry on the evolutions of propeller wake. Large eddy simulation method is used to simulate the turbulence in the flow field. The propeller vortices obtained with different rudder chords and profiles are compared in present study. The impact of trapezoidal rudder on the propeller wake evolution are studied based on the research aimed on the impact of rudder chords and profiles on the propeller wake. The distributions of turbulence kinetic energy in the interaction between the trapezoidal rudder and propeller are also researched in present study. Results show that both of rudder chord and rudder profile can impact the evolutions of propeller wake. Larger chord and thicker profile of the rudder enhance the span-wise displacement of propeller tip vortices. Thinner profile leads to more intense displacement of propeller hub vortex. The vortex trajectory and pressure fluctuations on the rudder surface indicate that trapezoidal rudder enhances the span-wise displacement occurring in anti-direction of rudder tapering. This enhancement takes asymmetry to the propeller wake around the rudder and in the downstream. The turbulences in the propeller wake can be related to the collisions between the propeller vortices and rudder, between the propeller vortices and rudder trail vortex, between the propeller tip vortices and hub vortex. The more intense span-wise displacement of propeller wake induced by trapezoidal rudder brings earlier enhancement on turbulence in the propeller wake.

2023, 55(2): 318-329. doi: 10.6052/0459-1879-22-552

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EFFECTS OF WAVY ROUGHNESS ON THE STABILITY OF A MACH 6.5 FLAT-PLATE BOUNDARY LAYER

Wang Haopeng, Yuan Xianxu, Chen Xi, Liu Shuyi, Lai Jiang, Liu Xiaodong

Transition from laminar to turbulent flow of the hypersonic boundary layer can increase the wall friction coefficient and heat conduction coefficient by 3 ~ 5 times, which has a significant influence on flight performance and safety of hypersonic vehicles. Wavy roughness is a possible passive control method to delay hypersonic boundary layer transition, and is thus of engineering significance. In this paper we investigate the effort of finite-length wavy roughnesses with different locations and heights on the stability of a Mach 6.5 flat-plate boundary layer using direct numerical simulation and linear stability theory (LST). DNS is employed to obtain the laminar base flow, and to study the linear evolution of fixed-frequency disturbances parametrically introduced upstream by blowing and suction. The effects of the relative position of the fast/slow mode synchronization point and the wavy roughness are revealed. It is found that when the wavy roughness is placed upstream of a disturbance’s synchronization point, the disturbance is damped compared to the smooth surface case; when the disturbance’s synchronization point is within or slightly downstream of the wavy roughness, the disturbance is generally enhanced. The effects of heights of wavy roughnesses are also considered. For the wavy roughness with small heights compared to the boundary layer thickness, the effect of wavy roughness is positively correlated with the height of the wavy roughness, while the effect is weakened by the higher wavy roughness. Linear stability theory can predict well the effects of wavy roughness on high-frequency disturbances, but exhibits large discrepancies with DNS in predicting the behaviors of moderate and low-frequency disturbances. This indicates that the receptivity process and the strong non-parallel effect in the vicinity of the wavy roughness neglected by LST should play an important role.

2023, 55(2): 330-342. doi: 10.6052/0459-1879-22-327

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INFLUENCE OF EXPANSION STERNS ON THE FLATTING TRAJECTORY CHARACTERISTICS OF A TRANS-MEDIA VEHICLE DURING HIGH SPEED WATER ENTRY

Liu Xiyan, Luo Kai, Yuan Xulong, Ren Wei

The expansion stern is an important factor affecting the flatting trajectory and its stability of a trans-media vehicle during high speed water entry and turning flat process. In this paper, based on the fluid volume multiphase flow model and dynamic mesh technology, the coupling calculation method of multiphase flow field and trajectory of the trans-media supercavitating vehicle entering water at high speed is established. The accuracy and applicability of the numerical calculation method are verified by the experiments. Through the numerical simulation study on the high speed water entry and turning flat process of the trans-media vehicle, the influence of the expansion stern on the cavity development morphology, hydrodynamic characteristics and trajectory characteristics of the vehicle during the water entry and turning flat process is obtained, and the influence of the cone angle of expansion sterns on the flatting trajectory during high speed water entry is analyzed. The results show that when the vehicle without the expansion stern entering water and turning flat under the different preset rudder angles, the angle of attack increases continuously, eventually leading to the divergence of the flatting trajectory. After the vehicle with the expansion stern entering water, the recovery moment is formed when the expansion stern is wetted, and the stable flatting trajectory is obtained. The vehicles with different expansion stern cone angles (1.5°, 6°, 8°) have formed three different kinds of trajectory characteristics: stable planing, single-sided tail-slapping and double-sided tail-slapping, and all of them can achieve stable flatting trajectory. The principle of stable planing trajectory is the dynamic balance under the coupling effect of the preset rudder angle and expansion stern planing. This trajectory has the smallest comprehensive drag coefficient, the highest flatting efficiency and the smallest dynamic load, which is an ideal flatting trajectory form for the trans-media vehicle during high speed water entry.

2023, 55(2): 343-354. doi: 10.6052/0459-1879-22-427

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SIMULATION OF DYNAMIC WETTING EFFECT DURING GAS-LIQUID SPONTANEOUS IMBIBITION BASED ON MODIFIED LBM

Zhang Shengting, Li Jing, Chen Zhangxing, Zhang Tao, Wu Keliu, Feng Dong, Bi Jianfei, Zhu Shang

Gas-liquid spontaneous imbibition in microchannels is a widely occurring physical phenomenon in nature and many industrial fields. The dynamic contact angle is the key factor affecting the whole gas-liquid imbibition process. In this work, we use a modified pseudopotential multiphase flow lattice Boltzmann method (LBM) to capture the real-time contact angle during gas-liquid spontaneous imbibition in microchannels and analyze the dynamic characteristics of the contact angle and its effects on the imbibition length. Firstly, we coupled the Peng-Robinson (PR) equation of state to the original pseudopotential multiphase flow LBM, improved the fluid-fluid interaction force and fluid-solid interaction force formats, and added the external forces to the LBM framework by using the exact difference method. Then, the accuracy of the model was verified by calibrating the thermodynamic consistency of the model and simulating interfacial phenomena such as interfacial tension and static equilibrium contact angles. Finally, based on the established simulation method, the spontaneous gas-liquid percolation process in the microchannel is simulated in the horizontal direction. The results show that the contact angle in the imbibition process is dynamic and varies greatly in the early stage of imbibition due to the inertia force. With the further increase of the imbibition distance, it gradually decreases and tends to the static equilibrium contact angle. The contact angle in the imbibition process is related to the microchannel size and the static contact angle. As the width of the microchannel increases, the difference between the dynamic contact angle and the static contact angle in real-time increases; as the static contact angle increases, the difference between the dynamic contact angle and the static contact angle in real-time increases. In addition, the Lucas-Washburn (LW) equation, which ignores the dynamic contact angle, predicts the position of the meniscus is different from the simulated results. The real-time dynamic contact angle data obtained from the simulations can be directly applied to correct the LW equation, and the corrected LW equation predicts the position of the meniscus in general agreement with the simulated results.

2023, 55(2): 355-368. doi: 10.6052/0459-1879-22-409

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EFFECTIVE PRESSURE AND GENERALIZED EFFECTIVE BIOT STRESS OF POROUS CONTINUUM IN UNSATURATED GRANULAR MATERIALS

Li Xikui, Zhang Songge, Chu Xihua

The definition of effective pressure with associated formula of the Bishop parameter for unsaturated porous medium proposed in the frame of the theory of macroscopic porous continuum has been controversial for a long time. This also affects the correct prediction of directly related generalized Biot effective stress. Based on the Voronoi cell model described with the discrete system composed of solid particles, binary bond liquid bridges and liquid films, the present paper presents the definitions of effective internal state variables at local material points in unsaturated porous continua with low saturation, i.e. effective pressure and generalized Biot effective stress. Using the proposed Voronoi cell model, their expressions are formulated with the information of hydro-mechanical meso-structure and moso-response evolved with incremental loading process exerted on the representative volume element (RVE) of unsaturated granular material. With the derived effective pressure formula, it is demonstrated that the effective pressure tensor of unsaturated porous continuum is anisotropic. It has not only an anisotropic effect on hydrostatic components, but also an effect on shear stress components, of generalized Biot effective stress tensor. It is demonstrated that the fundamental defect of both the generalized Biot theory and the so-called bivariate theory lies in that it is assumed that effective pore pressure tensor representing the hydro-mechanical effect of two immiscible pore fluids on the solid skeleton of unsaturated porous continua is isotropic. In addition, the Bishop parameter introduced as the weighted factor to define the isotropic effective pore pressure tensor is assumed not related to the matrix suction with very important effect on the hydro-mechanical response occurring at local material points over unsaturated porous continua. The derived formulae of both generalized Biot effective stress and effective pressure (including effective Bishop parameter reflecting the isotropic effect of effective pressure) can be upscaled to a local material point, where the RVE is assigned, in macroscopic unsaturated porous continua, for computational multi-scale methods represented by the concurrent computational homogenization method for unsaturated granular materials.

2023, 55(2): 369-380. doi: 10.6052/0459-1879-22-407

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LARGE DEFORMATION AND FRACTURE ANALYSIS OF THIN PLATE BENDING BASED ON PERIDYNAMICS

Shen Guozhe, Wang Ruiyang, Xia Yang, Zheng Guojun

Thin plate structures are widely used in the fields of automobiles, ships, and aerospace because of their excellent load-bearing performance, light weight and easy processing. However, in practical applications, thin plate structures often produce large displacement, rotation and even cause crack initiation and growth under small loads, and then the overall structure fractures. Therefore, it is of great engineering practical significance to establish a crack growth and fracture simulation model of thin plate structures in the process of large deformation. In this paper, a peridynamic (PD) and classical continuum mechanics (CCM) coupling model for geometrically nonlinear deformation and fracture analysis of thin plate structures is established. First of all, the updated Lagrangian formula is used to obtain the expression of virtual strain energy density increment of thin plates at each increment step in large deformation analysis under von Karman's hypothesis. Then, the PD constitutive parameters of geometrically nonlinear micro-beam bond are obtained by using the virtual work principle and homogenization hypothesis. After that, the virtual strain energy density increments of the PD model and CCM model for geometrically large deformation thin plate were respectively established, and the geometrically large deformation PD-CCM coupling model of the thin plate was established. Finally, the progressive fracture process of the thin plate structure under the action of lateral deformation is simulated, and the simulation results are highly consistent with the experimental results, which verifies the accuracy of the proposed geometrically nonlinear PD-CCM coupling model. It is shown that the proposed geometrically nonlinear PD-CCM coupling model is simple and efficient without restriction on material parameters and consideration of boundary effects, and can be well used to predict local damage and structural fracture of thin plate structures during geometrically large deformations. It is beneficial to the fracture safety evaluation and theoretical development of thin plate structures.

2023, 55(2): 381-389. doi: 10.6052/0459-1879-22-519

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TURE MODE II CRACK SIMULATION BASED ON A STRUCTURED DEFORMATION DRIVEN NONLOCAL MACRO-MESO-SCALE CONSISTENT DAMAGE MODEL

Ren Yudong, Chen Jianbing, Lu Guangda

The fracture problem in which the crack deformation mode under mode II loading is also mode II is called the true mode II fracture problem. It is challenging to accurately and quantitively capture the whole process of true mode II fracture. In this paper, a structured deformation driven nonlocal macro-meso-scale consistent damage model is adopted to simulate the true mode II fracture problem. The nonlocal strain of a material point pair is decomposed into elastic strain and structured strain based on the theory of structured deformation. Then the structured positive elongation quantity of the material point pair can be evaluated by using the Cauchy-Born rule and the structured strain. In the present paper, the structured strain is taken as the deviatoric part of the nonlocal strain. When the structured positive elongation quantity of a material point pair exceeds the critical elongation quantity, mesoscopic damage starts to emerge at the point-pair level. The topologic damage can be obtained by weighted summing of the mesoscopic damage within the influence domain, then it is embedded into the framework of continuum damage mechanics through the energetic degradation function bridging the geometric damage and energetic damage for numerical solution. Further, the Gauss-Lobatto integration scheme is adopted in this paper to evaluate the nonlocal strain of point pairs, which reduces the number of integral points to 4 and thus considerably reduces the computational cost of preprocessing and nonlinear analysis. The reason for adopting the deviatoric strain as structured strain is revealed based on the analysis of the strain field at the crack tip under mode II loading. Numerical results for two typical true mode II fracture problems indicate that the proposed model can not only well capture the crack deformation pattern of true mode II cracks, but also quantitatively characterize the load-deformation curves without mesh size sensitivity. Problems to be further investigated are also discussed.

2023, 55(2): 390-402. doi: 10.6052/0459-1879-22-280

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PERIDYNAMIC METHOD FOR THE INTERFACE IN THE REINFORCED CONCRETE

Lu Dechun, Gao Yixin, Wang Guosheng, Song Zhiqiang, Du Xiuli

The peridynamic (PD) method has been widely used to study the cracking and failure of reinforced concrete structures. The control equations and material parameters of the traditional PD method are determined based on the energy equation of homogeneous materials. When dealing with the interaction between different materials, the mechanical behavior of their interfaces cannot be reasonably reflected in the traditional PD method. In order to solve this problem, the interaction model of material points in the interface region of the PD method is proposed by analyzing the bond-slip mechanism of the interface of reinforced concrete. Then the bond-based PD method considering the interface bond of reinforced concrete is developed based on the proposed interaction model. Based on the energy density equivalent principle of the bond-based PD and continuum mechanics, the method to determine the interface micro elastic parameters of the PD is proposed. According to the stress distribution law of concrete between steel ribs, the equivalent relationship between the point radius of interface material and the radius of restricted wedge is obtained. Based on the slip deformation corresponding to the peak stress of the interfacial bond slip curve, a method for determining the critical tensile constant of the interface is presented. So far, the PD method for the interface in the reinforced concrete has been established. By comparing with the pull-out test of two groups of reinforced concrete members, the developed interface PD method of the reinforced concrete is verified, and numerical tests of reinforced concrete members under different conditions are carried out. The results show that the developed PD can reasonably reflect the influence of rebar diameter, anchorage length, concrete strength and rib spacing on the bond behavior of reinforced concrete interface, which well reflects the rationality and superiority of the proposed method, which reflects the rationality and superiority of the proposed method.

2023, 55(2): 403-416. doi: 10.6052/0459-1879-22-470

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A NEW HELICAL TUBE MODEL FOR THE ELASTICITY OF RUBBER-LIKE MATERIALS

Wei Zhigang, Chen Haibo, Luo Zhonglong, Hu Wenfeng

One of the biggest challenges for soft materials is to establish statistical mechanical models to correctly describe the relationship between its microstructure and macroscopic mechanical properties, and the statistical models for rubber-like materials still have some imperfections. Based on the macroscopically isotropic, continuous uniform and incompressible properties of rubber-like materials, combined with a non-Gaussian statistical model for molecular chains, a new elastic model for rubber material is proposed. The force transfer path between the corresponding points on the representative volume element is described by a subnetwork constrained to a region as a spiral helical tube, whose surfaces all deform affinely with the macroscopic deformation. The sub-network consists of molecular chains or chain segments linked end-to-end with random orientation and length. Hence, the constitutive model describing the macroscopic mechanical characteristics of the material is derived from the entropy of the subnetwork. A large number of test data were used to fit the constitutive model, which show that the model has very good accuracy. Especially, the proposed model with two parameters show very high reliability that it gives good predictions of the three basic test with the parameters derived from data-fitting with uniaxial tension data only. With the proposed curved affine tube confinement, this model can explain the incompressible properties of the material from the microstructure scale, overcome the shortcoming of straight tube model, and build a new model for the correlation between the stochastic at the micro scale and the uniform at the macro scale.

2023, 55(2): 417-432. doi: 10.6052/0459-1879-22-435

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TOPOLOGICAL OPTIMIZATION DESIGN METHOD OF LAYER-WISE GRADED LATTICE STRUCTURES WITH HIGH LOAD-BEARING

Huang Kaixuan, Ding Zhe, Zhang Yan, Li Xiaobai

With the rapid development of additive manufacturing technology, lattice structures have attracted extensive attention due to their excellent mechanical properties, such as high specific strength and high specific stiffness. However, the designs of lattice structures are mostly based on the assumption of uniform distribution, resulting in a relatively poor load-bearing capacity. This paper proposes a layer-wise graded lattice structure design method based on a topology optimization technology. Firstly, an explicit description model of lattice geometric configuration is established by using the level set function, and a shape interpolation technology is employed to generate the graded configurations of lattice cells. Secondly, a prediction model of macro effective mechanical property for these graded lattice cells is constructed based on the Kriging metamodel, achieving the essential relationship between the effective density of macro element and the effective mechanical property of micro lattice cell. Then, with the maximum stiffness of lattice structures as the optimization objective, the allowable material usage amount and structural system equilibrium equation as the constraint conditions, a layer-wise graded topology optimization model of lattice structures is established, which is solved numerically by using the OC algorithm. The numerical results indicate that the proposed method can realize the optimal layer-wise graded design of lattice structures, which not only fully improve the load bearing performance of lattice structures, but also ensure the geometric connectivity between different graded lattice cells. Finally, the quasi-static compression simulation analyses of the layer-wise graded lattice structures, the traditional uniform lattice structures and the linear graded lattice structures are carried out and discussed. The simulation results show that, compared with the traditional uniform lattice structures and the linear graded lattice structures, the loading capacity of the layer-wise graded lattice structures is significantly improved. The proposed method provides a theoretical reference for the design of high loading lattice structures.

2023, 55(2): 433-444. doi: 10.6052/0459-1879-22-363

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BIONIC MECHANISM AND LARGE-DEFORMATION MODELING OF RIGID-FLEXIBLE COUPLING STRUCTURE INSPIRED BY CHICKEN NECK

Qu Yipeng, Sun Xiuting, Xu Jian

It is observed that the necks of birds generally have the characteristics of rigid-flexible coupling and variable stiffness, which can cause large head deformation with the body movement when the bird moves as walking or flighting. In the fields such as robotics and aerospace, structures with the characteristics of large deformation, variable stiffness and rigid-flexible coupling are generally required to achieve relevant functions. Inspired by the structure of the bird neck, this paper proposes a kind of rigid-flexible coupling structure imitating the chicken neck which clarifies its bionic mechanism, and establishes the mechanical model for flexible large deformations. Firstly, it discovers that bionic structure must have the characteristics of high-degree of freedom and rigid-flexible coupling based on the biological anatomical structure of the chicken neck. A bionic single standard unit is constructed according to the characteristics of the chicken neck skeleton and a model of spring connection between nodes is constructed according to the connection mode of muscles, thus a bionic rigid-flexible coupling structure is established by combining these two elements. Then, this paper describes the distribution and function of the elastic elements between nodes by defining the connectivity matrix, with which the force balance equation of any standard rigid section under any movement is obtained. Finally, several representative working conditions are selected for simulation, which verifies the accuracy of the established theoretical modeling method by the comparation with finite element analysis, and the nonlinear variable stiffness characteristics of the structure are displayed; The relations between deformations under four typical plane bending conditions and corresponding muscles force generation are obtained. The analysis on the bionic rigid-flexible coupling structure clearly shows the characteristics of bionic mechanism of chicken neck, which gives the theoretical calculation model for large deformations, representing the nonlinear stiffness characteristics. It also explains the deformation mechanism of the chicken neck.

2023, 55(2): 445-461. doi: 10.6052/0459-1879-22-553

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INVESTIGATION OF STABILITY AND BIFURCATION CHARACTERISTICS OF WHEELSET NONLINEAR DYNAMIC MODEL

Wang Peng, Yang Shaopu, Liu Yongqiang, Liu Pengfei, Zhao Yiwei, Zhang Xing

To explore the lateral instability of the wheelset system, the gyroscopic effect and the influence of the primary suspension damping are considered, a dynamic model of the wheelset system with a nonlinear wheel-rail contact relationship is established, and the hunting stability, Hopf bifurcation characteristics, and migration transformation mechanism are investigated. The hunting instability critical speed of the wheelset system is obtained through the stability criterion. The central manifold theorem is used to reduce the dimensions of the wheelset system. Then the reduced wheelset system is simplified using the normal form method to obtain a one-dimensional complex variable equation with the same bifurcation characteristics as the wheelset system. The expression of the first Lyapunov coefficient of the wheelset system is derived theoretically, and the Hopf bifurcation type of the wheelset system can be judged according to its sign. The influence of different parameters on the Hopf bifurcation critical speed of the wheelset system is discussed, and the distribution law of supercritical and subcritical Hopf bifurcation regions of the wheelset system in two-dimensional parameter space is explored. Three typical Hopf bifurcation diagrams of the wheelset system are obtained by numerical simulation, which verifies the correctness of the distribution law of the supercritical and subcritical Hopf bifurcation regions of the wheelset system. The results reveal that the critical speed of the wheelset system decreases with the increase of the equivalent taper, increases with the increase of the longitudinal stiffness and longitudinal damping of the primary suspension, and first increases and then decreases with the increase of the longitudinal creep coefficient. The change of system parameters will change the type of Hopf bifurcation of the wheelset system, that is, the subcritical and supercritical Hopf bifurcations migrate and transform each other. The distribution law of the Hopf bifurcation domain of the wheelset system in two-dimensional parameter space has a certain guiding significance for wheelset parameter matching and optimization design.

2023, 55(2): 462-475. doi: 10.6052/0459-1879-22-469

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STUDY ON ISOGEOMETRIC ANALYSIS FOR LARGE-AMPLITUDE PROPELLANT SLOSHING AND SPACECRAFT COUPLED DYNAMICS

Yu Jiarui, Yue Baozeng, Li Xiaoyu

With long mission cycles and complicated space missions, modern spacecraft usually need to carry a lot of liquid propellant. Large-amplitude sloshing of liquid propellant in storage tanks will seriously affect the attitude stability and control accuracy of the spacecraft, which is an important problem for the modeling of the spacecraft coupled dynamics system and the accurate control of orbit and attitude. In this paper, a new computational fluid dynamics method for the numerical simulation of large-amplitude liquid sloshing is proposed. The modeling and spatial discretization of the whole gas and liquid mixed fluid system in the tank are carried out by using isogeometric analysis. The pressure-modified fractional step method is used for the time discretization of the governing equations. By decoupling the pressure and velocity variables, the implicit equations are transformed into the explicit equations to improve the computational efficiency. For the common liquid sloshing problem, a simple and efficient mass correction method is proposed to eliminate the liquid mass error caused by the evolution of level set function. Based on the numerical method of isogeometric analysis for liquid sloshing, the coupled dynamics system of liquid-filled spacecraft with solar panels is modeled and the motion of the coupled spacecraft is simulated. The liquid sloshing momentum equation is transformed and introduced into the spacecraft dynamics equations. The numerically stable rigid-liquid coupled dynamics equations of spacecraft affected by liquid sloshing are established. The modeling of solar panels is based on the Kirchhoff-Love plate theory and the vibration of solar panels is solved by modal analysis. By comparing the numerical simulation results with the analytical results, the correctness of the proposed method is proved. Besides, the motion of rigid-liquid-flexible coupled spacecraft is simulated. It is found that liquid sloshing has a significant effect on the amplitude and frequency of spacecraft attitude change and structural vibration.

2023, 55(2): 476-486. doi: 10.6052/0459-1879-22-539

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NATURAL VIBRATION ANALYSIS OF TWO-DIMENSIONAL FLEXIBLE WING BASED ON NON-UNIFORM BEAM MODEL

Huang Ke, Zhang Jiaying, Wang Qingyun

In order to improve the flight performance of the aircraft, morphing technologies are used to change aerodynamic characteristics through smooth and continuous structural deformation. Since this new concept requires changing the structural shape to obtain the best performance, its inherent dynamic characteristics will be affected and even change its aeroelastic performance. In this paper, an equivalent modelling method of the two-dimensional flexible wing with camber morphing is developed. The dynamic model of the flexible wing is established based on the hypothesis of a non-uniform beam model. The analytical solution and natural frequencies are obtained by the method of Frobenius and verified by comparison with the finite element method solution. The errors of the first four natural frequencies are within 1% and the corresponding modes are consistent. The flexible wing is prepared by 3D printing engineering plastic (ABS) and silicone rubber skin. The Young's modulus of the 3D printing material and silicone rubber are respectively measured by dynamic measurement method and tensile test. The vibration response test platform is built to carry out vibration test of the flexible wing. It is found that the fundamental frequency obtained by vibration test is consistent with the theoretical model results, and the error is less than 3% compared with the finite element method. The equivalent modelling method of a two-dimensional flexible wing is established through theoretical analysis and experimental verification. The research results will provide theoretical support for applying the flexible trailing edge structures.

2023, 55(2): 487-496. doi: 10.6052/0459-1879-22-551

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FORCE-DISTRIBUTION ANALYSIS FOR REDUNDANT CABLE-DRIVEN PARALLEL ROBOTS UNDER HYBRID JOINT-SPACE INPUT

Qin Zhiwei, Liu Zhen, Gao Haibo, Sun Guangyao, Sun Cong, Deng Zongquan

Cable-driven parallel robots (CDPRs) represent a class of particular parallel robots whose rigid links are replaced by cables, where cable can only generate pull force and cannot be compressed. The force distribution in cables is one of the core problems for redundant CDPRs. The hybrid joint-space control strategy, where the chosen redundant cables are force-controlled, whereas the remaining ones are length-controlled in the joint space, is the main type of control strategy discussed in this paper. Because different cable combinations may lead to different control effects. This study provides the selection criteria for the target force-controlled cable combination in the hybrid-input control strategy. The cable tensions in the space with tension vectors as basis for two redundancies for cable-driven parallel robots were expressed based on the equivalent transformation method of vector space basis. The acceptable cable force errors limit proposed in this paper (CFEL) were defined and calculated based on the cable tensions in the space with tension vectors to find appropriate cable combinations for the force control. To validate the analysis of the force-distribution characteristics, a hybrid-input control trajectory planning strategy was developed using multibody dynamics simulations, based on a suspended cable configuration with layouts including two redundancies, while considering the interference of cable length and cable forces. In addition, a fix-pose simulation case via hybrid-input control strategy was performed to validate accuracy of the proposed calculation method for the CFEL. Finally, we found that cable combinations play an essential role for force control as the force control errors may be significantly magnified in cable combinations with high force-distribution sensitivity characteristics. The simulation results illustrate the significance of the analysis in this paper. What’s more, the concept of CFEL proposed in this paper provides guidance for the design of cable force controllers under the control strategies of hybrid joint-space input.

2023, 55(2): 497-508. doi: 10.6052/0459-1879-22-463

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MULTI-SCALE MODELING AND SIMULATION OF SKELETAL MUSCLE BIOMECHANICAL PROPERTIES

Wang Monan, Jiang Guodong, Liu Fengjie

Aiming at the problems that there is a certain difference between the muscle fiber microstructure model and the image observed under the microscope, the microscopic component biomechanical model cannot effectively capture the mechanical behavior of skeletal muscle during shear deformation, and the high calculation cost of multi-scale numerical models of skeletal muscle. In this thesis, the mechanical properties of skeletal muscle are studied from the perspectives of experiment, multiscale modeling and simulation. Curved-edge Voronoi polygons are proposed as the cross-section of muscle fibers, and the corresponding representative volume element (RVE) is established at the microscale. A new biomechanical model (MMA model) is proposed, and the MMA model is used as the biomechanical model of muscle fibers and connective tissue, the MMA model adopts complete strain invariants$ {I}_{4}、{I}_{5}、{I}_{6}、{I}_{7} $, so that the shear behavior of skeletal muscle is reflected at the level of material properties. Combine the experimental results of skeletal muscle, the RVE models, the biomechanical models of muscle fibers and connective tissue to establish a multiscale numerical model of skeletal muscle. According to the experimental results, the parameters of the biomechanical model are determined, the multiscale homogenization method are used to realize the connection between the microscale and the macro-scale, and the macroscopic mechanical behavior of skeletal muscle is finally obtained, four deformation forms of Longitudinal stretch, stretch laterally, out-of-plane longitudinal shear and in-plane shear are performed to verify the convergence of the model. This thesis research the effects of model parameters, muscle fiber volume fraction and muscle fiber structure on skeletal muscle on macroscopic mechanical behavior. Combined with experimental data, the effectiveness of the multiscale numerical model is verified. In this paper, the multi-scale numerical model of skeletal muscle can not only be used to study the influence of microscopic factors on the macroscopic mechanical behavior of skeletal muscle, but also to study the influence of diseases on the biomechanical properties of skeletal muscle and to simulate skeletal muscle remodeling and regeneration.

2023, 55(2): 509-531. doi: 10.6052/0459-1879-22-496

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RESEARCH ON HETEROGENEOUS SOLID STRESS MODEL BASED ON ARTIFICIAL NEURAL NETWORK

Wu Xueyan, Li Yu, Xie Yanyan, Li Fei, Chen Sheng

The Energy-Minimization Multi-Scale (EMMS) theory has been introduced into the multiphase particle-in-cell (MP-PIC) method to establish the heterogeneous EMMS solid stress model to account for the effect of non-uniform solid distribution. However, the calculation process is very complex and also very time consuming for this heterogeneous solid stress model. The expression of the heterogeneous EMMS solid stress can be obtained by manual fitting method. However, the fitting variable describes heterogeneous solid distribution as well as the fitting function describe the shape of solid stress are required for manually fitting. Since the heterogeneous solid stress function is highly nonlinear in nature, the fitting precision is not high enough for the manually fitting model. And there is an obvious deviation between the fitting correlation and the original EMMS solid stress, because it is hard to find out an appropriate parameter to characterize the heterogeneous solid concentration distribution as well as to find out an appropriate fitting function. In order to solve the above problems, an artificial neutral network (ANN) based machine learning method was proposed to avoid the characterization of the local distribution of solid volume fraction. Subsequently an ANN solid stress model which accounts for the detailed distribution of particle concentration was proposed to improve the fitting accuracy. Firstly, a two-marker based ANN solid stress model was established based on local particle concentration and particle non-uniform distribution index. Further, particle concentrations in the current cell and its neighboring cells were arrayed to represent the particle concentration distribution, thus to establish the ANN solid stress model based on particle concentration distribution. Then, the two models are compared with the EMMS solid stress model, and the effects of grid resolution and coarse-graining ratio on the model are also tested. The simulation results predicted with ANN model agreed well with that of the EMMS solid stress model, and the dependence of simulation results on grid resolution and coarse-graining ratio was also reduced.

2023, 55(2): 532-542. doi: 10.6052/0459-1879-22-511

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EXPERIMENTS AND EFFECTIVE PERMEABILITY MODEL FOR MULTIPHASE FLOW IN ROCK FRACTURES WITH VARIABLE APERTURES

Hu Ran, Zhong Hanxian, Chen Yifeng

The effective permeability of rock fractures is a fundamental parameter for describing unsaturated flow and multi-phase flow in fractured media, and the fracture aperture is an important factor affecting this parameter. In this paper, to investigate the effect of aperture on the flow structures of water-oil multiphase flow and on the effective permeability, we develope a visualization experimental system, and perform multiphase flow experiments in fracture models replicated from real rock fractures with three different apertures. Visualization experimental results show that the flow of non-wetting phase in the fracture can be categorized as unstable bubble flow at the low flow-ratio conditions and stable channel flow for high flow-ratios. As fracture aperture increases, the flow channel of non-wetting phase becomes less branching and wider, and the effective permeabilities of the two phases both increase, during which the flow structures become stable. The visualization results also reveal the competing mechanism of fluid-fluid alternately occupying the fracture space in the slug flow structure. When the non-wetting phase fluid channel changes from continuous to discontinuous, the pressure difference between the inlet and the outlet of the fracture increases significantly; conversely, when the channel changes from discontinuous to continuous, the pressure difference decreases significantly. Finally, based on the fractal theory and the statistical model for permeability, the effective permeability model proposed for multiphase flow in rock fractures with variable apertures, and the correctness and reliability of the model is evaluated by the measured effective permeability data.

2023, 55(2): 543-553. doi: 10.6052/0459-1879-22-500

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INVESTIGATION ON PNEUMATIC EXPANSION FORMING MECHANISM OF SMALL FIN-TUBE HEAT EXCHANGER

Zheng Zhiyue, Jiang Zhansi, Ding Zeliang, Du Wangfang, Li Kai, Chen Xue

The fin-tube heat exchanger is common in the refrigeration industry. The expansion forming mechanism of the heat tube is of significant importance for refrigeration equipment, which determines its mechanical property and heat transfer performance. In this paper, a three-dimensional fluid-solid coupling model of the tube-fin heat exchanger is proposed. By using a unidirectional fluid-solid coupling transient method, the flow behaviors and deformation characteristics of the fluid and solid domains are numerically studied. Results show that the reasonable range of pneumatic expansion pressure is verified to be P = 12.5 MPa, which is consistent with the value derived from the theoretical equations. According to the variations of tube and fin stresses with time, the tube stresses at different fin-tube joints are greater than their yield limit of 66 MPa, and the fin stresses at different fin-tube joints are slightly greater than their yield limit of 132 MPa, which agree with the requirements of expansion forming process. After expansion, the average tube diameter increases with the pressure increases. The radial displacement of the heat exchanger tube is smaller in the horizontal direction and larger in the vertical direction, and the difference between maximum and minimum displacement is about 0.03 mm. The variation of the residual contact pressure with different expansion pressures was investigated, which exhibits three stages. When P < 11 MPa, the residual contact pressure increases with the expansion pressure. If 11 < P < 12.5, the residual contact pressure decreases with the increase of expansion pressure. While P > 12.5 MPa, the residual contact pressure stabilizes at 0.7 MPa. The numerical results indicate that when the expansion pressure makes the inner hole of the fin yield, increasing the expansion pressure will lead to incomplete expansion. Finally, the effect of holding time is studied, which show that changing the holding time has little effect on the expansion quality. The relevant results provide theoretical guidance for the actual engineering of the small fin-tube heat exchanger in the pneumatic expansion process.

2023, 55(2): 554-563. doi: 10.6052/0459-1879-22-482

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