力学学报

ARTIFICIAL NEURAL NETWORK-BASED SUBGRID-SCALE MODELS FOR LARGE-EDDY SIMULATION OF TURBULENCE

Xie Chenyu, Yuan Zelong, Wang Jianchun, Wan Minping, Chen Shiyi

Large eddy simulation (LES) is an important method to investigate different types of complex turbulent flows, which has been widely applied to the turbulent flows in aerospace, combustion, acoustics, atmospheric boundary layer, etc. Large eddy simulation effectively solves the large-scale motions of turbulence and models the effects of small-scale dynamics on the large-scale structures by using subgrid-scale (SGS) models. Traditional SGS models only use the single-point information based on some simple forms of analytical functions to approximate the SGS terms. Thus, traditional models exhibit quite large relative errors in the a priori study, and have excessive dissipations in the a posteriori study. Recently, machine learning approaches have been widely used to develop turbulence models, including the Reynolds-averaged Navier-Stokes (RANS) models and LES models. In this paper, we review the recent developments of artificial neural network (ANN) methods for SGS models in LES of turbulence. We discuss three different ANN-based SGS models, including artificial neural network mixed model (ANNMM), spatial artificial neural network (SANN) model and deconvolutional artificial neural network (DANN) model. Due to the strong data interpolation capability of artificial neural networks, the new SGS models exhibit improved accuracy in both a priori study and a posteriori study. In the a priori study, the new SGS models can predict the SGS stress much more accurately than the traditional SGS models: the correlation coefficients predicted by new SGS models can be made larger than 99%. In the a posteriori study, the new SGS models can give better predictions on turbulence statistics and instantaneous flow structures, as compared to a variety of traditional SGS models including the implicit LES (ILES), dynamic Smagorinsky model (DSM), and dynamic mixed model (DMM). It is shown that artificial neural network-based methods have strong potentials for the developments of advanced SGS models in the LES of complex turbulence.

2021, 53(1): 1-16. doi: 10.6052/0459-1879-20-420

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2021, 53(1): 17-18. doi: 10.6052/0459-1879-20-417

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ADVANCES IN KEY MECHANICAL PARAMETERS FOR RELIABILITY ASSESSMENT OF HIGH-SPEED TRAIN BEARINGS

Wang Xi, Hou Yu, Sun Shouguang, Li Qiang, Ren Zunsong

Bearing is the key component of the traction transmission and wheelset systems of high-speed train. It is possible to experience fatigue damage or failure under the influence of traction motor torque, gear meshing and random wheel-rail excitation during the train operation, which seriously threatens the operation safety of high-speed train. The special complex service conditions of high-speed trains in China require higher fatigue performance and reliability for bearing components, however, the fundamental theory and key technology of fatigue performance and reliability are the weak links in the forward design and development of bearing in China. The research on bearing reliability assessment plays a significant connecting role in solving the bottleneck problem of bearing reliability research. The method and technology of reliability assessment for high-speed train bearings aim to obtain the key mechanical parameters for bearing reliability assessment in service environment, and further to promote the fundamental theory research on bearing fatigue performance and reliability under complex internal and external excitations. Therefore, the key is to identify what mechanical parameters are required for reliability assessment of high-speed train bearings and how to obtain them in such a complex service environment. In this article, the complex service environment and main failure modes of high-speed train bearings during the train operation are firstly reviewed. Then, the key mechanical parameters required for the reliability assessment of high-speed train bearings are proposed and analyzed, in which the important roles of internal rolling-sliding behavior and load distribution on bearing reliability assessment and condition monitoring are emphasized. From the aspects of calculation methods and measurement technologies, the advances to obtain those two key mechanical parameters (i.e. the rolling-sliding behavior and load distribution in bearings) are systematically reviewed. Finally, several open problems in the research of reliability assessment of high-speed train bearing are addressed for future studies.

2021, 53(1): 19-34. doi: 10.6052/0459-1879-20-200

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RESEARCH, DEVELOPMENT AND PROSPECT OF CHINA HIGH-SPEED TRAIN

Ding Sansan, Chen Dawei, Liu Jiali

For more than ten years, based on the long-term technology accumulation and independent research and development of the high-speed railway equipment represented by the high-speed train, multiple generations of the advanced high-speed train products had been successfully developed through the technology introduction, digestion and innovation, independent promotion and innovation, comprehensive innovation and continuous innovation. Through the continuous technological innovation, important technology breakthroughs had been made in the series key technologies of the high-speed train, and the independent research and development capabilities had been formed, which continuously improve the safety, reliability, economy, environmental protection and intelligence of the high-speed train. China high-speed trains have excellent comprehensive performance indicators, such as the operating speed, comprehensive comfort, safety, reliability, energy conservation, environmental protection, etc. Some performance indicators have reached the international advanced level. In the present paper, the development achievements and major technology breakthroughs of China high-speed trains, including Hexie EMU, Fuxing EMU, intercity EMU and advanced EMU products, were firstly systematically reviewed. Then the key technology challenges that faced during the research and development of the high-speed train were analyzed, including the complex environment adaptability, complex coupled effect of the large system, safe and reliable design, intelligent application, etc. The research progresses and major technology breakthroughs of the key technologies of the high-speed train, such as the prognostic and health management (PHM) technology, lightweight vehicle body technology, passive safety protection technology, carbon fibre reinforced plastics (CFRP) applications, aerodynamic shape design technology, high-speed bogie technology, noise control technology, traction and brake technology, etc. were systematically outlined. Finally, the future developments of the key technologies of the high-speed train, such as the dynamic technology, structural safety technology, passive safety protection technology, fluid-structure coupled technology, traction and brake technology, intelligent control safety technology, prognostic and health management technology, comprehensive energy saving technology, etc. were further prospected.

2021, 53(1): 35-50. doi: 10.6052/0459-1879-20-225

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RESEARCH PROGRESS IN AERODYNAMIC OPTIMIZATION OF HIGH-SPEED TRAINS

Sun Zhenxu, Yao Yongfang, Guo Dilong, Yang Guowei, Yao Shuanbao, Zhang Ye, Chen Dawei, Li Guibo, Shang Keming, Jia Ling

With the increase of running speed, high-speed trains have higher requirement for aerodynamic shape. The pursuit of excellent performance and beautiful aerodynamic shape tends to be an important direction in the development of new high-speed trains. Based on the current aerodynamic study of high-speed trains, aerodynamic shape optimization can be divided into two categories: shape modification optimization based on flow mechanism and shape optimization based on optimization algorithms. After a brief review of the current domestic and foreign work on these two optimization approaches, this paper focuses on a series of aerodynamic shape optimization work done by the author's team in recent years. In terms of the modification optimization based on the flow field mechanism, this paper focuses on the research and development of the appearance of the two main models, namely "CRH" and "Fuxing" , to discuss the idea of the modification optimization. It mainly discusses the optimization design of air conditioning cover, pantograph installation platform, windshield and bogie apron, which have obvious influence on the train resistance, and introduces the improvement of aerodynamic performance of these components compared with the previous models. In the shape optimization method based on an optimization algorithm, according to the aerodynamic shape optimization process, taking the streamline of high-speed train head as the main optimization object, we introduce our series of work from three aspects: high-speed train parameterization method, surrogate model development and the improvement of the optimization algorithm. Among them, high-speed train parameterization methods mainly include local function method, modified vehicle modeling function method, and category/shape function method; in the development of the alternative model, the optimization alternative model and Kriging model based on cross-validation are introduced; on the improvement of the optimization algorithm, the improved non-inferior classification multi-objective particle swarm optimization algorithm and continuous domain chaotic ant colony algorithm are introduced. Based on the improvement of the above three aspects, the application cases of the developed aerodynamic shape optimization strategy in typical engineering are further introduced.

2021, 53(1): 51-74. doi: 10.6052/0459-1879-20-205

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SENSITIVITY ANALYSIS AND OPTIMIZATION ON PARAMETERS OF HIGH SPEEDPANTOGRAPH-CATENARY SYSTEM

Wu Mengzhen, Liu Yang, Xu Xianghong

With the improvement in the speed of high-speed trains, thedynamic interaction between pantograph and catenary, a basic mechanicalproblem, has attracted more attention. Good pantograph-catenary relationshipis a basic premise to ensure the security and efficiency of the trainoperation, the stability and reliability of the current collection andreduce the wear of the contact line and pantograph slide. The couplingperformance of the pantograph-catenary system mainly depends on its kineticparameter. In this paper, the stochastic statistical characteristics of thecontact force of the pantograph-catenary system are adopted as theoptimization objective function, and the sensitivity analysis andoptimization design of pantograph dynamic parameters are carried out.Firstly, a dynamic model of 2D stitched catenary and three lumped parameterpantograph is established, and the validation of dynamic analysis of themodel is verified according to British Standard EN50318:2018. Secondly,based on dynamic simulation of the high-speed pantograph-catenary system, adynamic sensitivity analysis on three lumped nine dynamic parameters ofDSA380 high-speed pantograph is carried out, and the sensitivity level ofthe parameters is determined. The sensitivity level of the equivalent massof the pantograph head is the highest, followed by the equivalent damping ofthe lower frame and the equivalent mass of lower frame and the equivalentdamping of the upper frame are the third. Finally, the effect of jointvariation in equivalent stiffness and equivalent damping of the pantographhead on the pantograph-catenary coupling dynamic performance is studied, anda dual-parameter optimization scheme of equivalent stiffness and equivalentdamping of the pantograph head is proposed to improve the current collectionquality pantograph-catenary system. It is suggested to reduce the equivalentdamping of pantograph head and increase the equivalent stiffness ofpantograph head at the same time, and the dual-parameter optimization schemecan achieve a better quality of the pantograph-catenary system than thesingle parameter optimization scheme

2021, 53(1): 75-83. doi: 10.6052/0459-1879-20-207

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FATIGUE STRENGTH AND RESIDUAL LIFETIME ASSESSMENT OF RAILWAY AXLES SUBJECTED TO FOREIGN OBJECT DAMAGE

Wu Shengchuan, Luo Yan, Wang Wenjing, Li Yongheng, Hu Chunming

As the key load-carrying component of high-speed vehicles, theaxle bears various loads from both body and track, the service performanceis directly related to the high-speed railway safety. On account of the fatigue crack is often concealed and sudden,the train derailment caused by axle fracture is catastrophic. Therefore, itis very important for the safe and reliable operation of high-speed railwayto ensure that the axle does not break suddenly during operation. Foreignobject damage (FOD) larger than millimeter frequently happens during therunning of high-speed railway axles, causing damage to the surface integrityof the axle, which significantly induces the safety problem. In the present study, by using a commercial compressed-gasdevice, foreign object damage was prepared on alloying steel specimens fromhigh-speed railway hollow axles. The damage features were thenobserved using the stereomicroscopy and scanning electronic microscopy (SEM). Thefatigue S-N curves and fatigue limits were acquired for smoothed and FODedspecimens under high cycle fatigue (HCF) experiments. In view of the loadvariation, surface quality and size between the small-sizedspecimens and full-scale axles, the fatigue properties of FODed specimenswere modified to deserve the fatigue performance of full-scale axles.Through the fracture surface analysis, it was found that the multicrack initiations occurred in the FOD crater, and the cracks propagatedcontinuously in different planes to converge into a semi-elliptic crack.Besides, theoretical fatigue limits from Peterson formula and ElHaddad model under two impact velocities (100 m/s and 138 m/s) were moreconservative than those of experimental value and also far from standard value, showing an over dangerous design. Finally, the service life of FODed axlescalculated by the modified Miner formula can satisfy the 25years design lifetime of high-speed hollow axles.

2021, 53(1): 84-95. doi: 10.6052/0459-1879-20-228

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RESEARCH ON SERVICE SIMULATION MODELING AND CALCULATION METHOD OF HIGH-SPEED TRAIN

Zhang Weihua

The appearance of high-speed railway makes wheel-rail transportation technology reaches a higher level. The increase of train speed puts forward higher requirement of traction power and dynamics performance. Moreover, the coupling effects between train and track, high-speed flow and other operation environments are intensified, which directly affect the operation quality and safety. In the initial development stage of high-speed train, the research focuses on how to ensure the high-speed, smooth and safe operation of the high-speed train. With the continuous increasing of running speed, the coupling effects between different subsystems of high-speed train become intense and can't be ignored. The service simulation of the train is more and more important. Today, the service simulation, health management and fault prognosis and early warning of high-speed train become the research hotspot. To master the global dynamic behavior of the system and to understand the micro-local vibration is the research direction of the system dynamics. Based on the requirement of high-speed train service simulation, this paper presents a modeling and calculation approach for long train formation based on the cyclic variable method, which can realize the simulation of any train formation and obtain the service status of vehicles in different train formation positions. A method of modeling the track and calculating the vehicle-track coupling interaction based on the sliding window method is proposed to obtain the service state of trains running on any long-term line. A method of long-term service calculation based on time-varying parameters is also proposed to perform the service simulation of trains in different service states and service time. Hence, the service simulation of train can be realized in different life-cycle based on the simulation frame proposed in the paper. Besides, this method can also be applied in simulations of the high-speed maglev train and even the high-speed evacuated tube train in the future.

2021, 53(1): 96-104. doi: 10.6052/0459-1879-20-234

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MOVING MODEL ANALYSIS OF THE SLIPSTREAM OF A LONG GROUPING HIGH-SPEED TRAIN

Guo Yi, Guo Dilong, Yang Guowei, Liu Wen

The slipstream is the air flow induced by the high speed train passing by, which continues to be an important aspect of aerodynamic performance and a critical factor of safe operation. In this paper, a 1:8 scaled eight-group type model of a high-speed train was measured on the moving model rig, and the characteristic of the flow around high-speed train can be observed. The long group type model can break through the limitation of the reduced length to wide ratio in the moving model experiment. The slipstream of a high-speed train has a stable local peak in the nose and a remarkable unsteady characteristic in the area of body and wake of the high speed train which indicated by the ensemble average profile and the ensemble standard deviation profile of the slipstream. The slipstream profile indicated that fluctuation of the flow around the eight-group high-speed train appeared at the second coach, the velocity rose vibrationally and reach the local maximum at the seventh coach. But the perturbation caused by bogie cabins and inter carriage gaps did not appear in the slipstream profile. The experimental results in the wake of slipstream were decomposed by Proportional Orthogonal Decomposition (POD). It is found that the fluctuating energy intensively appeared in the near-wake region, and appeared in the trailing area of body secondly. Conditional averaging was applied to analyzing the experimental results of slipstream in the moving model experiment. The condition of the conditional averaging was the distance between the peak location of slipstream profile and the tail of the high speed train model. The result of conditional averaging of slipstream indicated that the relative position between the slipstream measurement probes and the wake vortices may impact the peak of slipstream profile in the wake of the train when the vortices generated.

2021, 53(1): 105-114. doi: 10.6052/0459-1879-20-226

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RESEARCH ON LOAD TEST SPECTRUM OF EMU CAR BOGIES BASED ON DAMAGE CONSISTENCY

Zou Hua, Wu Qifeng, Sun Shouguang

The load situation of the EMU car bogie frame is complex, and it contains multiple basic load systems under actual operating conditions. Therefore, the damage of the local position of the bogie frame is the accumulation of the corresponding damage of several load systems at that location; the experimental spectrum of the bogie frame is to assess the life of the EMU frame. The bogie frame test spectrum is the key means to assess the life of EMU frame, and how to prepare the test spectrum without measured load is the research goal. In this paper, firstly, the linear assumption, the stability assumption and the typical assumption are researched and confirmed; Then, based on the only dynamic stress data of the long-term measured line, the typical stress of the bogie frame is compiled into a stress spectrum; the load system of the frame is established according to the stress characteristics, and the load stress transfer relationship under each load system is calibrated in the test bench; the maximum calibration coefficient of typical measuring points in the region is taken as the load stress transfer coefficient of the region; then, based on the damage consistency principle, the optimization function is established, and the load stress transfer coefficient matrix obtained is substituted into the optimization function, and a method for deriving the experimental load spectrum from the measured dynamic stress data of transmission lines is established. The test results prove that the method has high accuracy, and the assessment of key parts of the structure has achieved full coverage of typical areas; under the operating conditions of the Chinese line, compared with the international general specifications, this method can achieve damage reproduction in all typical areas. Compiling experimental spectrum is more applicable to the assessment of bogie frame.

2021, 53(1): 115-125. doi: 10.6052/0459-1879-20-214

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DYNAMIC AND STATIC AIR TIGHTNESS ANALYSIS METHOD AND THEIR APPLICATION IN EMU

Li Ming, Zhang Lei, Liu Bin, Kong Fanbing

With the increase of running speed, the external disturbance of high speed EMU becomes more and more severe. In particular, when the EMUs pass through the tunnel and meet in the tunnel, the violent transient pressure generated by the external surface of the EMU is transmitted into the compartment, which will cause ear discomfort to drivers and passengers. Aiming at studying the influence of the airtight performance of EMU during operation on the pressure fluctuation and the passengers ride comfort, this article adopted the analysis method with combination of the dynamic and static test, combining with the time constant model and the equivalent leakage area model, through the internal and external arrangement of air pressure fluctuation monitoring sensors in different vehicles, carried out the aerodynamic load test before and after the operation of the EMU maintenance (Level IV) . According to the specific structural characteristics of different parts, different types of gas leakage testing equipment were developed to test and study static air tightness of different vehicles. The dynamic and static hermetic performance analysis model was established and the related air indexes were obtained, then the influence law of the condition of tunnel, speed and other factors on the interior pressure fluctuation and dynamic airtight performance was summarized. At the same time the leakage and the leakage area of the typical air tight parts were analyzed, and the effect of air sensitive parts sorting and optimized scheme were put forward. The method and relevant research data proposed in this paper have certain reference significance for the design scheme and repair program optimization of key components.

2021, 53(1): 126-135. doi: 10.6052/0459-1879-20-230

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PLASMA-BASED FLOW CONTROL ON PITCHING AIRFOIL AT LOW REYNOLDS NUMBER

Huang Guangjing, Dai Yuting, Yang Chao

To improve the poor aerodynamic performance of pitching airfoils at low Reynolds number, the paper developed a control strategy based on the dielectric barrier discharge (DBD) plasma control. The 2D quasi direct numerical simulation method was applied to solve the unsteady incompressible Navier-Stokes equations around an oscillating NACA0012 airfoil at low Reynolds number. Equations for plasma flow control are added to the momentum equations in the Openfoam solver as a source term. The effects of steady DBD plasma actuation on the aerodynamic force characteristics of an oscillating NACA0012 airfoil are investigated. The DBD plasma actuators are located at the leading edge and trailing edge of the upper and lower airfoil surfaces, respectively. And four open-loop control strategies for the actuators were proposed. The flow control effects of these control strategies with different Reynold numbers, reduced frequency and the positions of plasma actuators are compared. The mechanisms of plasma flow control is analyzed by the flow field structures and dynamic pressure distribution. Results indicate the effect of control strategy B (switch on actuator located on the upper surface at negative angle of attack, and switch on actuator located on the lower surface at positive angle of attack) is best when the plasma actuators located at leading edge of airfoil, and control strategy C (switch on actuator mounted on the upper surface during counterclockwise rotation stage, switch on actuator mounted on the lower surface during clockwise rotation stage) has best effect when the plasma actuators located at the trailing edge of airfoil. When the plasma actuators located at leading edge, the flow control effect will decrease as the reduced frequency increases, and it also increase airfoil's drag. For the trailing edge plasma cases, the pressure drag may decrease, which is better than the leading edge plasma cases. Meanwhile, the trailing edge DBD plasma control has good effect of enhancing lift and reducing drag for all the calculated reduced frequency ranges (5.01~11.82). The lift enhancement effects of DBD flow control are good at different Reynolds numbers. However, due to the flow viscosity effect enhancement, the drag reduction effects of DBD flow control become worse with decreasing Reynolds numbers.

2021, 53(1): 136-155. doi: 10.6052/0459-1879-20-183

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RESEARCH ON THE INFLUENCE OF FREE SURFACE ON THE FLOW CHARACTERISTICS OF SUBMARINE WAKE

Guo Chunyu, Xu Peng, Han Yang, Wang Chao, Guo Xinyu, Kuai Yunfei

The flow characteristics around the submarine will affect the maneuverability of the submarine, especially when the submarine is near the water surface, the existence of the free surface will increase the complexity of the wake field of the submarine. In order to explore the influence mechanism of free surface on the flow characteristics of submarine wake when the submarine near the free surface, the research on the flow characteristics of submarine wake is carried out with the help of large-scale underwater three-dimensional particle image velocimetry technology. Firstly, the accuracy of the test method in this study is verified by the standard model experiment of DTMB in USA; Then, the wake field of the submarine is measured by the model test, and the axial velocity and pulsating velocity of the propeller disk under different submergence depths and different speeds are obtained. At the same time, the wave and the velocity field of the longitudinal section which can not be measured by the model test are supplemented by numerical simulation, and the influence mechanism of the free surface on the flow characteristics of the wake field is expounded from the wave point of view. The results show that: When the submarine near the water surface, with the increase of Fr, the upper isopleth of the axial velocity at the propeller disk tends to be flattened; and compared with the 4D submergence depths, the local maximum value of pulsating velocity appears in the 1.5D submergence depths, and the structure of pulsating velocity moves down as a whole. When the free surface exists, the velocity of flow field between the hull and the free surface increases obviously, especially in the area of the propeller disk. With the increase of Fr, the height of the free surface of the propeller disk decreases gradually, which leads to a larger fluid velocity and the squeeze phenomenon of wake field on propeller disk.

2021, 53(1): 156-167. doi: 10.6052/0459-1879-20-279

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ANALYSIS OF HYDRODYNAMIC INSTABILITY AND NONLINEAR EVOLUTION CHARACTERISTICS OF TWO DIMENSIONAL FLOW IN CONSTANT CURVATURE BEND

Li Bin, Xu Haijue, Bai Yuchuan, Ji Ziqing

In recent years, the study of meandering river has shifted from linear characteristics to instability and nonlinear characteristics. Many researchers see the meandering river as an unstable system, for which they thought that the meandering river is mainly affected by the instability of the field flow and corresponding boundary. Aiming at the instability and nonlinear characteristics of the dynamics of the flow in meandering river, we make up the nonlinear evolution equations of flow disturbance amplitude and disturbance angle of constant curvature bend under the condition of weakly curve meandering, which were established by using the weakly nonlinear theory and perturbation method. In this paper we study the characteristics of disturbance development by considering different curvatures firstly, then discuss the spatial and temporal distribution characteristics of disturbed flow field under the influence of a series of curvatures, and expounds the influence of curvatures on the flow stability of curved river bend, in the end, we analyze the motion characteristics of disturbed vortex in disturbed flow field. We find that the increase of meandering bend curvature ratio will improve the stability of flow in the meandering bend, which is corresponding the others researchers' results. The disturbance amplitude and the disturbance angle of the flow decay faster with the increase of meandering curvature ratio, in the term of the symmetry of the disturbance velocity, which will become weaker with the increase of meandering curvature ratio and the incline to the convex bank of the bend when the meandering curvature ratio is larger. The flow dynamic of the meandering bend near the neutral state has the characteristics of convective instability and nonlinear attenuation. The research results in this paper provide a new idea for constructing a nonlinear interaction model of the nonlinear flow dynamics and the geometric nonlinearity of the meandering bed in the future research.

2021, 53(1): 168-183. doi: 10.6052/0459-1879-20-191

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STUDY ON THE VISCO-HYPERELASTIC BEHAVIOR OF POLYSILOXANE RUBBER

Huang Ruiyu, Yu Peishi, Liu Yu, Tian Changlu, Chang Jinyuan, Wang Pengfei, Zhao Junhua

Polysiloxane rubber is a kind of typical polymer material which is usually colorless and transparent. The molecular structures of Polysiloxane rubber consist of Si——O bonds as the main chain and organic groups directly connected to the silicon atoms, respectively. Owning to the outstanding hyperelastic property derived from the intertwined molecule chains, the polysiloxane rubber is widely used for fabrication of damping structures and stretchable electronics. In engineering application it is crucial to precisely describe the visco-hyperelastic behavior of materials under dynamic and large deformation for the design of polysiloxane rubber based damping structures and flexible electronic devices. Therefore, the visco-hyperelastic property of polysiloxane rubber is systematically investigated in this work. For the first step, the hyperelastic behavior and viscoelastic effect are decoupled to propose the basic forms of the visco-hyperelastic constitutive model. Secondly, the hyperelastic model of the material is established based on quasi-static uniaxial tension, uniaxial compression and planar tension tests, respectively. Then, the strain rate effect is quantified by Hopkinson pressure bar tests, based which the viscoelastic model is established. Accordingly, the visco-hyperelastic constitutive model is finally proposed by combing the two decoupled models. Besides, the proposed visco-hyperelastic constitutive model is used to simulate the drop-weight impact behavior of polysiloxane rubber specimens by finite element method. The well agreement between the simulations and tests show that the viscoelastic constitutive model established in this paper can effectively predict the mechanical behavior of the polysiloxane rubber under impact load, which provides a theoretical and applied basis for the optimal design of polysiloxane rubber based shock absorption structure and flexible electronic devices.

2021, 53(1): 184-193. doi: 10.6052/0459-1879-20-287

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LOW-VELOCITY IMPACT RESPONSES OF FG-GRC SANDWICH BEAMS WITH VISCOELASTIC CORES

Jin Qiduo, Ren Yiru, Hu Xuan, Jiang Hongyong

The dynamic snap-through and oscillation behaviors are studied of a post-buckled functionally graded graphene reinforced composite (FG-GRC) beam with a viscoelastic core under low-velocity impact. The modified Halpin Tsai meso-mechanical model is used to predict the material properties of FG-GRC. The Hertz point contact model is used to calculate the contact force between the impactor and the post-buckled beam. Considering the axial prestress, the constitutive relations of the composite layer and the Kelvin type viscoelastic constitutive model of the damping layer are proposed. A generalized higher-order shear deformation zig-zag beam theory is utilized to model the nonlinear displacement fields. Based on the Hamilton energy variational principle, the governing equations of dynamics are derived. Through two-step analysis, the post-buckling equilibrium paths are obtained as the initial state condition for the impact problem analysis. Further, combined with the fourth-order Runge Kutta method, the two-step perturbation-Galerkin method is extended to simulate the time history curves of the contact force and the dynamic response curves of the post-buckled beams. Compared with the results based on other beam models, the correctness of the material model, theoretical model and computation method is validated. The dynamic characteristics of bi-stable large amplitude vibration of the post-buckled beams under single and two collisions are studied. The effects of axial load, impact velocity, viscoelastic damping characteristics and impactor materials on the contact force and the deflection time history curves of the post-buckled beams are discussed. The results suggest that the contact force is only sensitive to the impact velocity. A certain structural collision parameter design can change the response of the post-buckled beam from single potential energy trap motion to double trap large oscillation, and the contact force is approximately unchanged. The results of this work can be of reference significance for the design of bi-stable energy capture system with collision.

2021, 53(1): 194-204. doi: 10.6052/0459-1879-20-248

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A TRIANGULAR ELEMENT DISCRETIZATION FOR COMPUTING DISPALCEMENT OF AN ARBITRARILY SHAPED THERMAL INCLUSION

Hou Jiahui, Li Pu, Li Jianglin, Jin Xiaoqing

Inclusion models have been widely used to explore the micromechanical properties of fiber-reinforced composite materials. The composite materials usually contain irregularly shaped inclusions, which can severely affect the mechanical properties of the materials. Abundant research has demonstrated that the stress localizations as well as the sites of crack initiation are predominantly detected in the neighborhood of nonmetallic inclusions. Previous studies on polygonal inclusion mainly focused on the stress/strain solutions under uniform eigenstrains, while the analyses on displacement are limited. Based on the method of Green's function and contour integral, this work presents a closed-form solution for a line element along the boundary of a two-dimensional thermal inclusion. The proposed method of solution is effective for determining the displacement of an arbitrarily shaped inclusion subjected to any distributed dilatational eigenstrain. In the case of uniform eigenstrain, only the boundary of the inclusion needs to be discretized into line elements; therefore, the proposed method analytically yields the closed-form solution for the displacement of an arbitrary polygonal inclusion subjected to uniform thermal eigenstrain. When the eigenstrain is non-uniformly distributed in the inclusion, the resulting displacements may be evaluated by discretizing the thermal inclusion into a system of triangular elements. It is known that the stress and strain fields exhibit singularities at the vertices of a polygonal inclusion. Such singularity issue can be intractable in numerical evaluations of the stresses/strains in the vicinity of the vertices, leading to a commonly seen yet tricky phenomenon of numerical instability. In contrast, the present work shows that the displacement is continuous and bounded at the corners of the polygon. Other than the merit of numerical discretization, the derived closed-form solutions may be conveniently programmed on a personal computer, while the corresponding algorithm seems to be straightforward, facilitating a high accurate and expeditious evaluation of the displacements. Benchmark examples demonstrate the computational efficiency and numerical robustness of the proposed method.

2021, 53(1): 205-212. doi: 10.6052/0459-1879-20-240

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DYNAMIC MODELING AND COMPUTATION FOR FLEXIBLE MULTIBODY SYSTEMS BASED ON THE LOCAL FRAME OF LIE GROUP

Liu Cheng, Hu Haiyan

The main content of the dynamics of flexible multibody systems focuses on the dynamic modeling, computation and control of complex systems composed of flexible components, which are subjected to the relative overall motion and connected by kinematical constraints. Compared with the computational structural mechanics, the multibody dynamics issues have high geometrically nonlinear, which is not only deduced by the large rotation caused from the large deformation of flexible components, but also is deduced by the overall rigid body motion. Under the concept of the local frame of Lie group (LFLG), the topic that how to develop a new modeling and computational method for flexible multibody dynamics is discussed. The major studies of this paper include the following aspects: the modelling methods of beam elements and plate/shell elements based on the LFLG, the long-time integration algorithm for the flexible multibody systems including collision problems, the parallel algorithm for multibody systems based on the domain decomposition method, and several numerical examples to verify the feasibility of the proposed method. The unique feature of the new method can eliminate the geometrically nonlinear of the overall rigid motion for flexible components. Therefore, the generalized inertial forces and internal forces as well as their Jacobian matrices are invariable under the arbitrary rigid body motion. The proposed method can motivate the integration of the modeling method of the flexible multibody dynamics and the computational structural dynamics with large deformation components and is expected to promote the development of the next-generation software of multibody system dynamics.

2021, 53(1): 213-233. doi: 10.6052/0459-1879-20-292

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GENERALIZATION OF KIRCHHOFF KINETIC ANALOGY TO THIN ELASTIC SHELLS

Xue Yun, Chen Liqun

The Kirchhoff kinetic analogy is generalized from thin elastic rods to thin elastic shells. The generalization makes thin shell deformations physically correspond and mathematically equivalent to rigid body motions. Hence theories and methods of rigid body dynamics can be applied to investigate deformations of thin elastic shell, and also provide a novel discretization for continuous thin elastic shells. An orthogonal spatial axis system is established along the coordinate lines of the middle surface under the straight normal assumption. The moving of the axis system along the coordinate lines in unit velocity forms its "angular velocity", which is the curvature-twist vector with two independent variables. The curvature-twist vector along two coordinate lines expresses the deformation and the configuration of a thin elastic shell. It is demonstrated that curvature-twist vectors are compatible, and curvature-twist vectors and tangential vectors of middle surface are compatible. Nonholonomic constraints and differential equations of middle surfaces are established in the Euler angles and the Lam$\acute{e}$ coefficient form. The strain, the stress and the internal forces are formulated in the curvature-twist vectors and the Lam$\acute{e}$ coefficients. The equilibrium partial differential equations are presented with distributed internal forces intensity of thin elastic shells. The forms of the equations are similar to the Euler equations of rigid body dynamics and Kirchhoff equations of thin elastic rods. The fact means that the Kirchhoff kinetic analogy of thin elastic rods is generalized to thin elastic shells. The analogy relations between thin elastic shells and dynamics of rigid body or thin elastic rods are concluded. Finally, an example is given to show the application of this method. The proposed analogy leads to novel views and approaches to model and to analyze deformation of thin elastic shells. It is possible to generalize further the analogy for dynamics of thin elastic shells.

2021, 53(1): 234-247. doi: 10.6052/0459-1879-20-266

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NONLINEAR THERMAL ANALYSIS FOR THE INTER-SHAFT BEARING UNDER THE DYNAMIC LOAD

Gao Peng, Hou Lei, Chen Yushu

As an important supporting part between the higher pressure rotor and the lower pressure rotor in a dual-rotor system, inner and outer races are rotating with the lower and higher pressure rotors, the heat transfer of the inter-shaft bearing is more prominent. This paper studies the nonlinear thermal behaviors of the inter-shaft bearing under the nonlinear dynamic load. The dynamic load of the inter-shaft bearing is defined based on the dynamic responses of the dual-rotor system, where the nonlinear factors of the inter-shaft bearing such as the radial clearance, the fractional exponential nonlinearity and the parameter excitation are taken into consideration. Thus the nonlinear behaviors such as the jump and the bi-stable phenomena happen to the dynamic load. According to Palmgren's empirical formula, a heat transfer model of the inter-shaft bearing under the dynamic load is established with considering the viscosity-temperature relationship of the lubricant. Steady-state temperatures of the inter-shaft bearing are obtained by the numerical integration. It shows that the nonlinear thermal behaviors of the inter-shaft bearing such as the jump and the bi-stable phenomena are caused by the nonlinear behaviors of the dynamic load. Furthermore, effects of the rotation speed ratio, the unbalances, the inter-shaft bearing's radial clearance, Hertz contact stiffness and roller number on the temperatures and the nonlinear thermal behaviors of the inter-shaft bearing are analyzed. The results show that the unbalances, the radial clearance and the stiffness only affect the nonlinear thermal behaviors of the inter-shaft bearing; the rotation speed ratio and the roller number have a magnificent influence on both. This discovery implies that the dynamic load is more appropriate to describe the actual load of the inter-shaft bearing than the static load. The thermal behaviors of the inter-shaft bearing become nonlinear, which is much more complicated than before, due to nonlinear dynamic characteristics of the dual-rotor system.

2021, 53(1): 248-259. doi: 10.6052/0459-1879-20-261

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MECHANOTRANSDUCTION OF THE CELL AND ITS PRIMARY CILIUM IN THE MICROFLUIDIC CHANNEL

Li Chaoxin, Wu Xiaogang, Sun Yuqin, Qin Yingze, Duan Wangping, Zhang Meizhen, Wang Yanqin, Chen Weiyi, Wei Xiaochun

Cells usually live in a complex physiological environment. The primary cilium, which is a an important organelle of the cell, is attached to the cell surface and is regard as an important mechanical signal sensor to help living cell receive various external mechanical signals, the primary cilium is considered to be closely related to physiological activities such as metabolism, development, division and proliferation of the living cell. In order to study the mechanotransduction behavior of the living cell and the primary cilium growing on its surface in a microfluidic environment, this paper established the adherent cells within a rectangular microfluidic control channel model system, cells with poroviscoelastic properties are in a culture solution driven by the pressure gradient and electric field driven loads. The mechanical signal responses of cytoplasm and nucleus of cells such as the stress, strain, pore fluid pressure and pore fluid velocity under oscillatory laminar flow were investigated, as the mechanical signal's receptors of the living cell, the primary cilium's biomechanical behavior was quantitatively investigated. The results show that the mechanical response of the living cell under an oscillating laminar flow field has the same oscillating law as the synchronous external the pressure gradient and electric field driven loads. The permeability of the living cell is one of the most important physical parameters affecting the cell's poroviscoelastic behavior. Primary cilium is the main mechanoreceptor organelle. The living cell can adjust their mechanical sensitivity (stress-affected zone) by changing the length and diameter of its primary cilium. With the increase of the length of the primary cilium, the flexural rigidity of the primary cilium decreases, but the sensitivity increases. The establishment of the model provides a basis for further research on the microscopic mechanisms of cell growth and differentiation under the loading of microfluidic shear stress, and also provides theoretical technical support for testing the microstructure mechanical properties of the cell anticipates (protein chains such as primary cilium).

2021, 53(1): 260-277. doi: 10.6052/0459-1879-20-283

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SENSITIVITY RESEARCH ON MODELS OF EARTH ENTRY AND IMPACT EFFECTS BY ASTEROIDS

Dang Leining, Liu Sen, Bai Zhiyong, Shi Yilei

Asteroid impact on Earth is one of the potential threats to human beings. Engineering models of Earth entry and impact effects by asteroids have been developed in order to estimate ground hazard by planetary defense communities nowadays. However, there are large uncertainties in input parameters of these models, which not only brings trouble to use of the model, but also greatly affects results of hazard estimate. Ranges of input parameters are analyzed, of Which baseline values are taken as maximum probability values or recommended values in literatures. Furthermore, by changing one or more input parameters based on ranges and baseline values, AICA (Asteroid Impact Consequence Analysis) code developed by authors of this paper, are used to study sensitivity of output parameters, such as energy deposition, airburst altitude, radius of 4psi overpressure and 3rd degree burn, to input parameters. The results are given for stony asteroids with diameter of 60~300~m and entry velocity of 12~40~km/s. It is indicated by results that airburst altitude of asteroid trends to decrease, with increase of size, strength at 1st breakup and mass fraction of debris cloud, and with decrease of entry velocity and ablation coefficient. Drag coefficient of asteroid and fragment, as well as strength scaling exponent, has little effect on airburst altitude and ground damage range. Radius of overpressure and thermal radiation damage generally increases with increase of size and entry velocity. If mass fraction of debris cloud is less than 50%, airburst altitude and ground damage range will fluctuate. But a large value for mass fraction of debris cloud, such as 80%, is reasonable according to analysis of many meteor events at present. Luminous efficiency only affects damage range of thermal radiation. Under the computational condition in this paper, radius of 3rd degree burn is less than that of 4-psi overpressure, indicating that the main type of ground hazard is overpressure caused by airburst.

2021, 53(1): 278-292. doi: 10.6052/0459-1879-20-057

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THEORY AND APPLICATIONS OF INCOMPATIBLE AND HYBRID ELEMENT METHOD——IN MEMORY OF PROF. WU CHANGCHUN

Huang Yingqing, Xiao Qizhi, Feng Miaolin, Chen Haibo

This memorial paper gives an overview of Prof. Wu Changchun's main contributions to computational mechanics, especially his pioneering work on the incompatible and hybrid element method and its applications. The general formula for the incompatible shape functions and the optimization design method for hybrid stress elements proposed by Prof. Wu are still important means to develop high performance finite elements and are cited by peers constantly.

2021, 53(1): 293-297. doi: 10.6052/0459-1879-20-381

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2021, 53(1): 298-299.

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