力学学报

WALL-MODEL FOR LARGE-EDDY SIMULATION AND ITS APPLICATIONS

Wu Ting, Shi Beiji, Wang Shizhao, Zhang Xing, He Guowei

Large-eddy simulation (LES) is an important method to investigate unsteady turbulent flows. The cost of the wall-resolved LES is comparable to that of direct numerical simulation, which prevents the applications of the LES to wall-bounded turbulences at high Reynolds numbers. The grid length would be of the order of the viscous length to resolve the near-wall flow structures, which causes the prohibitive computational cost of the wall-resolved LES. Wall-models circumvent the flow details near the wall to avoid resolving all the flow structures near the wall, which significantly reduce the computation cost and have been successfully combined with the LES for turbulent flows. We discuss the basic idea of wall-models for LES and review the wall-stress models with implementation details. The construction and characteristics of the equilibrium models and the two-layer models are discussed in detail. The limitations of the wall-stress models and their improvements to account for the non-equilibrium effects are also discussed. We review the state of the art of the wall shear stress models and provide a hierarchical diagram for the current models. Finally, we present the applications of the Werner-Wengle model to the LES of flows over periodic hills.

2018, 50(3): 453-466. doi: 10.6052/0459-1879-18-071

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A REVIEW OF ORIGAMI AND ITS CREASE DESIGN

Li Xiao, Li Ming

Origami is to fold a two dimensional paper into the three dimensional structure without cutting and adhesion. With the merits of simple design, rapid forming and wide range of applications, origami has the promising applications in the fields of deployable structures, structural assembly and self-forming. Firstly, this paper reviews several typical origami applications, such as buckling-induced microscale three dimensional structures, foldable solar panels and DNA spiral assembled structures; Then, we define the classifications of origami according to different criteria, such as the number of curved creases, relative motion, the assumption of rigid folding surface, the number of used papers. Since the crease design problem is the key issue of origami, we focus on the origami crease design, including summarizing the basic principles of the crease design, addressing several typical crease design samples such as Miura, waterbomb, Yoshimura and diagonal crease designs. Furthermore, we introduce the distinctive features and geometrical relations of the typical crease design. For the recent innovative crease design methods, the improvement of the classic crease design, establishment of the crease design database, use of topology optimization method and the recent crease design algorithms are briefly discussed. Finally, we prospect the future research orientations of origami based on current research progress of origami, including the transformable structures, four-dimension origami, multi-material origami and multi-scale origami.

2018, 50(3): 467-476. doi: 10.6052/0459-1879-18-031

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THE INVERSE PROBLEM OF THERMAL CONTACT RESISTANCE BETWEEN ROUGH SURFACES

Yu Yuanfeng, Li Zewei, Zheng Xiaoya

When two solid surfaces are in contact, it leads to non-uniform contact because of surfaces roughness. This causes constriction of heat flux and forms thermal contact resistance. The theoretical research is mainly focused on the positive problem, but there are few studies on the inverse problem. The inverse problem of thermal contact resistance is to obtain thermal contact resistance by a part of the boundary temperature, heat flux and some of the measured point temperature. The research has been applied in many fields, such as aerospace, mechanical manufacturing, microelectronics and other fields. It is a fast and effective method to determine thermal contact resistance in engineering field. In this paper, the inverse problem of thermal contact resistance with 2-D coordinate variation was solved by the boundary element method (BEM) and the conjugate gradient method (CGM). In order to verify the accuracy and feasibility of the method, according to the measured point temperature and the assumed thermal contact resistance, the temperature and the heat flux of the interface could be obtained, and then calculated and compared with the value of actual thermal contact resistance. The results show that the actual thermal contact resistance can be accurately obtained by using the BEM and CGM without the measurement error. But there exists the measurement error, the calculated result will be extremely sensitive to the measurement error, and the error of inversion result will be amplified due to the measurement error. In order to deal with this ill-posed problem, the least-squares method (LSM) was used to correct the calculated results. The results show that it can avoid some points deviating from the actual value in the inverse problem, and obviously improve the accuracy of calculations.

2018, 50(3): 479-486. doi: 10.6052/0459-1879-18-076

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MODELING OF ELECTROMIGRATION FAILURE PREDICTING FOR FCBGA SOLDER BUMP UNDER MULTI-PHYSICAL FIELD LOADS

Zhang Yuanxiang, Liang Lihua, Zhang Jicheng, Chen Junjun, Sheng Yufeng

With the rapid development of microelectronics packaging technology, more attention has been paid to the electromigration (EM) failure on solder bump. The electric-thermal-structural multi-physical coupled analysis for flip chip ball grid array (FCBGA) packaging is performed in this paper based on FEM and submodeling technique. The simplified method of package model is introduced in detail. The current density distribution, temperature distribution and stress distribution of the key solder bump is investigated. It is found that the current crowding effect is easily generated at the location where electrons enter the bump from Cu metal layer, and the temperature gradient of the whole key solder bump is small. This paper presents the atomic density integral (ADI) method which considers four driving forces for electromigration such as electron wind force, stress gradient, temperature gradient and atomic density gradient. According to ADI method and the failure rule on void formation and diffusion, the electromigration void evolution process of the key solder bump is simulated with different mesh density. In can be found that the ADI method is stable and almost independent on the mesh density. The EM void location and time to failure (TTF) of key solder bump in FCBGA package is also simulated in the real service condition by ADI method. And the effect of solder material and Cu metal layer on EM failure is investigated in detail. We can see that the TTF of lead-free solder (Sn3.5Ag) is about 2.5 times than leaded solder (63Sn37Pb) because the TTF is determined to increase exponentially with the activation energy. And the EM failure is also influenced by the effective charge number. The adjustment of Cu metal layer structure will change the current flow direction and the stress distribution of the solder bump, which will affect the time to failure of solder bump.

2018, 50(3): 487-496. doi: 10.6052/0459-1879-18-077

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Fei Qingguo, Jiang Dong, Chen Sufang, Qin Furong

To obtain accurate elastic parameters and coefficient of thermal expansion (CTE) of braided composites at high temperature, An approach for identifying thermal-related parameters based on homogenization theory is proposed. Firstly, on the basis of the finite element model of unit cell, the thermo-elastic parameters of the braided composites are predicted, basing on the theory of homogenization and thermos elasticity, and by applying the periodic displacement and temperature boundary conditions. Secondly, considering the errors in the equivalent process causing by the uneven distributed stress, the thermal modal frequencies of the refined model are taken as the supplementary information to further identify the thermo-elastic parameters, as a calibration of the predicted parameters. Based on the finite element unit cell model of two-dimensional braided structure, this paper carries out equivalent prediction and identification, to verify the validity and accuracy of the proposed method. after comparing the error of the thermal mode of equival model and identification model, it is shown that the proposed method based on equivalent prediction and parameter identification can accurately identify the macro-thermo-elasticity related parameters of braided composites at high temperature.

2018, 50(3): 497-507. doi: 10.6052/0459-1879-18-078

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A GENERALIZED THERMOELASTIC PROBLEM WITH NONLOCAL EFFECT AND MEMORY- DEPENDENT DERIVATIVE

Zhang Pei, He Tianhu

The existing generalized thermoelastic theory is mainly applicable to obtain the dynamic responses of the problems in which the time scale is extremely short while the spatial scale is still macro-scale. Nevertheless, when the characteristic length scale of elastic body is also of micro-scale, the dynamic responses of the elastic body will take on intense size-dependent effect, and the existing generalized thermoelastic theory will be no longer suitable for such problems. In present work, based upon the generalized thermoelasticity with nonlocal effect and memory-dependent derivative, the dynamic response of a finite thermoelastic rod fixed at both ends and subjected to a moving heat source is investigated. The corresponding governing equations of the problem are formulated and the initial conditions as well as the boundary conditions are specified. Then, the governing equations are solved by means of Laplace transform and its numerical inversion. In calculation, first, the influence of the time-delay factor on the distributions of the considered physical quantity was examined. Then, the influence of the time-delay factor on the distributions of the considered variables under two kinds of kernel functions (i.e. normalized form and unmodified form) was compared. Last, the influence of the nonlocal factor on the dimensionless temperature, displacement and stress is considered and illustrated graphically. The results show that: with the increase of the time-delay factor, the heat wave propagation velocity becomes smaller, the peak values of the physical quantities become larger, and the influence of the time delay factor on the considered variables is more significant in the case with the kernel function modified by normalized condition than that with unmodified kernel function; The non-local parameter barely affects the distribution of the dimensionless temperature, slightly affects the distribution of the dimensionless displacement, while markedly affects the peak values of the dimensionless stress.

2018, 50(3): 508-516. doi: 10.6052/0459-1879-18-079

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EFFECT OF AGING ON STRUCTURE AND STRESS RELAXATION OF PP/SSFs COMPOSITES

Zhu Zhenhua, Shao Baijun, Wang Jun, Shao Yu, Chen Jiankang, Zhang Minghua

Conductive polymer composites, with good flexibility, adjustable conductivity, easy forming and low production cost, can be used as functional material in many fields for its antistatic properties, electromagnetic shielding/microwave absorbing properties, and pressure/temperature sensitivity. However, in the process of processing, storage and use, due to comprehensive influence of many factors, aging will inevitably occur which will lead to deterioration of the properties. In this paper, PP/SSFs (stainless steel fibers) conductive composites were prepared by melt-blending and injection molding. The specimens were subjected to accelerated hygrothermal aging and UV aging. Stress relaxation curves, resistivity and crystallinity were experimentally measured. Micromorphology and elemental distribution of specimens before and after aging have been observed and dectected by scanning electron microscope (SEM) and energy spectrometer (EDS). The results show that the stress relaxation curves display three-stages in characteristics. And the stress reduces after hygrothermal aging due to the breaking and cross-linking of molecular chain caused by aging. The initial resistivity of PP/SSFs composites decreases with the increase of filler content, while it will increased with aging time. Due to the piezoresistive effect of the conductive polymer, the resistivity of the specimens decreases significantly with the increase of initial load, and then it tends to a stable value and fluctuation in a smaller range. The results of SEM/EDS analysis show that with the increase of aging time, the oxygen content on the specimens surface increases, and it will decreases with distance (depth) to the surface of specimen. XRD results show that the crystallinity of composites decreased with the increase of SSFs content and aging time. The present research will provide an experimental basis for the study of aging properties of conductive polymer composites.

2018, 50(3): 517-526. doi: 10.6052/0459-1879-18-080

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ACCURACY ANALYSIS AND IMPROVEMENT OF VISCOUS FLUX SCHEMES IN UNSTRUCTURED SECOND-ORDER FINITE-VOLUME DISCRETIZATION

Wang Nianhua, Li Ming, Zhang Laiping

Due to the widespread applications of unstructured second-order finite volume schemes in computational fluid dynamics (CFD) simulations, studying the discretization accuracy of second-order finite volume schemes is of practical value. Two primary factors that affecting accuracy of viscous flow simulation, including cell gradient reconstruction and interface gradient calculation method, are considered in this paper. Firstly, the odd-even decoupling problem in the discretization of viscous flux is analyzed theoretically and verified by the method of manufactured solutions (MMS) based on the scalar diffusion equation. Modification of interface gradient is proposed to eliminate the decoupling problem and the computational accuracy of the diffusion equation is improved greatly as a result. Then, the effects of cell gradient reconstruction and interface gradient method on the accuracy of viscous flow simulation are studied by the MMS method based on the diffusion equation. Results of MMS grid convergence tests show that cell gradient reconstruction and interface gradient method determine the accuracy of viscous flow simulation together. Finally, grid convergence tests are carried out for three realistic viscous flow cases, i.e., the laminar flat plate, the turbulent flat plate and the 2D airfoil near wake in NASA Turbulence Modeling Resource website. The numerical results verify the conclusions obtained by MMS tests, and the viscous flux discretization schemes are obtained with better performance in accuracy and grid convergence property.

2018, 50(3): 527-537. doi: 10.6052/0459-1879-18-037

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AN IMPROVED GHOST-CELL IMMERSED BOUNDARY METHOD FOR SOLVING SUPERSONIC FLOW PROBLEMS

Zhang Yang, Zou Jianfeng, Zheng Yao

An improved ghost-cell immersed boundary method proposed in this paper, coupled with a high order finite difference solver, is applied to simulate the supersonic compressive flows around the complex obstacles.The main improvement of this algorithm is the treatment of the solid boundary that both ghost points inside the solid domain and forcing points inside the fluid domain due to the extension of the boundary are chosen to reconstruct the flow information considering the effect of solid wall on fluid.This brings refined boundary with discrete points and strengthens the wall conditions, which plays the role of local mesh refinement.The fluid points are limited in a certain source space as the interpolating points of the inverse distance algorithm, which effectively avoids the fact that the interpolating points are too few to possibly lead to coincide with the forcing points.Two problems of two dimensional shock reflection (Ma=2.81) and three dimensional flow around the smooth sphere (Ma=1.2) demonstrate the significant improvement of the numerical accuracy compared to the general ghost cell method. The results reveal the instability mechanism of the free shear layer as a result of the interaction between the shear layer, the compression wave system and the wake. The thickness and Reynolds fluctuation of the shear layer experience three regimes of linear growth, large amplitude oscillation and small amplitude fluctuation, resulting in an exponential growth of wrinkling factor.The turbulent structure near the shear layer shows obvious anisotropy because the streamwise Reynolds normal stress is dominant and a spatial hysteresis exists in the effect of the tail shock on Reynolds normal stresses in different directions.

2018, 50(3): 538-552. doi: 10.6052/0459-1879-17-424

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THE CHARACTERISTICS OF WATER FLOW DISPLACED BY GAS IN NANO ARRAYS

Song Fuquan, Hu Xiao, Zhu Genmin, Zhu Weiyao

The two-phase flow characteristics of water flow displaced by gas at nanometer scale have a wide application in the development of nano-fluidic chips and shale gas. In this paper, experiments of water flow displaced by gas and single-phase flow was carried out to study the flow characteristics of water flow displaced by gas at nanoscale of alumina membranes with diameters of 292.8 nm, 206.2 nm, 89.2 nm, 67.0 nm and 26.1 nm. The experiments show that there are three flow stages for water flow displaced by gas at nanoscale: firstly, the flow rate increases slowly with increasing the driving pressure in the first stage, and the gas flux is decreased about one order of magnitude when compared with gas single-phase flow; secondly, gas flux increases rapidly with increasing the driving pressure as water in nano arrays are largely driven out in the second stage; thirdly, gas flow characteristics are consistent with the single-phase flow when water in nano arrays are all displaced out in the third stage. The analysis results show that due to the “pinning" effect of capillary pressure at the gas-liquid interface and the interaction of solid-liquid interface, gas flux increase slowly in the first stage of water flow displaced by gas. And the larger driving pressure is required to increase the gas flux in nano arrays, which is the main reason of the nonlinear flow characteristics. Once the “pinning" effect is destroyed, the gas will enter the pipeline to promote the movement of the interface, which will change the capillary curvature between capillary column and liquid column. As a result, the capillary force reduces rapidly with the increase of displacing pressure and gas flux will increase sharply, which is the main reason of the sudden change of water flow displaced by gas in the second stage.

2018, 50(3): 553-560. doi: 10.6052/0459-1879-17-343

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THERMAL STABILITY OF SUPERCAVITATING JET IN A COMPRESSIBLE ROTARY GAS

Lü Ming, Ning Zhi, Yan Kai

Thermal stability of liquid jet is the deeper discussion to jet stability, which can improve our understanding to the mechanism of breakup and atomization of liquid jet. Also, Study on the thermal stability of liquid jet has an important value in theory and engineering. Based on the jet stability theory, under the conditions of gas rotation, fluids compressibility and supercavitation, this paper gives the mathematical model describing the thermal stability of supercavitating jet in a compressible rotary gas, and the corresponding numerical method for solving the mathematical model is proposed and verified by the data in reference. Then, this paper analyzes the effects of gas-liquid temperature differences and temperature gradients on jet instability, and studies the thermal stability of supercavitating jet. The results show that the maximum disturbance growth rate, the dominant frequency and the maximum disturbance wave numbers increase linearly with the increasing of gas-liquid temperature differences. The existence of temperature gradient inside the jet makes the instability effects of temperature differences on jet more obvious. The temperature gradients will inhibit the effects of supercavitation on jet instability, while gas-liquid temperature differences will promote the effects of supercavitation on jet instability.

2018, 50(3): 561-569. doi: 10.6052/0459-1879-17-403

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INFLUENCE OF LADDER TYPE ACCELERATING SECTION ON ATOMIZATION CHARACTERISTICS OF PRESSURE SWIRL ATOMIZER

Liu Zhaomiao, Wang Kaifeng, Wang Zhilin, Zheng Huilong, Zhang Tan, Kang Zhenya

Swirl atomizer inner core is the most important swirling component of the pressure swirling atomizer, the geometric topology of the swirl atomizer inner core directly affects the spray characteristics of pressure swirling atomizer.The current smooth acceleration section of the swirl atomizer inner core has lower flow efficiency.In order to reduce the energy loss, the swirl atomizer core accelerating section with ladder type has been designed to make spray medium pre-swirl and enhance the swirl strength in this paper, the lower part rotates 15° relative to the upper part, and the direction of the rotation is the same as the direction of the swirling slots of the atomizer. Spray flow rate, spray Sauter mean diameter(SMD), spray cone angle and droplet velocity were experimentally investigated by making use of particle dynamics analysis system(PDA) and charge coupled device experimental system(CCD) before and after the structure improvement of the acceleration section, and the axial and radial distributions of SMD and droplet velocity were also analyzed. Under the pressure ranges from 0.08 MPa to 0.46 MPa, the ladder type acceleration section has the better pre-swirl effect. The flow characteristics of the atomizer were increased by 48% to 51.8%; the axial and radial velocity of the spray were increased by 31.4% to 32.8% and 1.6% to 16.8%, respectively.The spray cone angle was reduced by 4.21° to 6.57°, and the SMD at downstream of the spray was decreased by 9.2% under higher pressure conditions.Compared with the smooth accelerating section, the application of ladder type accelerating section is beneficial to improve the quality of atomization.

2018, 50(3): 570-578. doi: 10.6052/0459-1879-18-006

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A SEMI ANALYTICAL METHOD TO SOLVE J-INTEGRAL FOR MODE-I CRACK COMPONENTS

He Yi, Cai Lixun, Chen Hui, Peng Yunqiang

The J-integral to characterize the singular level of the stress and strain field at the crack tip is definite and rigorous and is a basic parameter of elastoplastic fracture mechanics. The calculation of J-integral mainly depends on the plastic factor method and the finite element method at present. For theoretical predicting and testing of material fracture toughness, it is important and difficult to obtain analytical expressions about J-integral-load and load-displacement relations of cracked components. The most widely used test for structure integrity evaluation with J-integral is the ductile fracture toughness of type-I cracked specimens. Here, based on the Chen-Cai energy equivalence hypothesis, a unified characterization method of J-integral-load and load-displacement relation is proposed for six Mode-I cracked components which are commonly used in fracture toughness test under the plane strain condition. Then, the undetermined parameters of the engineering semi-analytical formulas of the J-integral-load and the load-displacement relations are obtained by a small amount of finite element analysis. The results show that the J-integral-load and load-displacement relation predicted by the unified semi-analytical formulas are in good agreement with those from finite element method. The engineering semi-analytical J-integral-load formula, which contains the elastic modulus, stress strength coefficient and strain hardening exponent of materials, can be widely adapted for different materials. And the J-integral value corresponding to arbitrary load points can be easily obtained by the formula. The presented novel method is convenient to establish the engineering semi-analytical formulas of J-integral-load and load-displacement relations for various type-I cracked components or specimens.

2018, 50(3): 579-588. doi: 10.6052/0459-1879-18-026

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CONSTITUTIVE MODEL FOR SAND BASED ON THE CRITICAL STATE

Yao Yangping, Zhang Minsheng, Wan Zheng, Wang Naidong, Zhu Chaoqi

The mechanical properties of sand are influenced by void ratio and compression pressure. Based on the sand critical state line characteristics, this paper describes the isotropic compression line by means of the linear relation in e-(p/p_a)^ξ space. A reference compression curve which is more suitable for describing the isotropic compression of sand is proposed by comparing the relationship between two different compression curve functions and critical state line functions, and the isotropic hardening rule based on the reference compression line is given. A yield surface function suitable for describing the mechanical properties of sand is proposed and a method for determining the yield surface shape parameter μ using isotropic compression and equal p paths is given. To get the potential strength M_f and the characteristic state stress ratio M_c, describe the sand compression and shear characteristics, the compression curve corresponding to stress ratio is taken as the reference curve of sand. The correlation between the current stress ratio and the reference curve of state parameter is proposed based on the isotropic compression and constant p path. Consequently, a smooth transition from reference compression curve to critical state line for the reference curve of state parameter is achieved. The established 11 parameters of the sand constitutive model can all be obtained through routine geotechnical tests or experiences. The sand constitutive model established in this paper describes well the compression and shear characteristics of Toyoura sand in different void ratios and pressures based on the model prediction, isotropic compression tests, triaxial drained and undrained tests of Toyoura sand.

2018, 50(3): 589-598. doi: 10.6052/0459-1879-17-334

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ACCURATE COMPUTATION ON DYNAMIC SIFS USING IMPROVED XFEM

Wen Longfei, Wang Lixiang, Tian Rong

Compared to the standard extended finite element method (XFEM), the improved XFEM overcomes, in theory, the linear dependence and the ill-conditioning issues, and improves in magnitude of orders the efficiency of linear system solve. In particular, in dynamic crack propagation problems, thanks to the exclusion of the extra dofs on crack tip enriched nodes, the new method eliminates the issue of energy inconsistency or the inconservitive energy transfer caused by dof dynamics, and provides more accurate dynamic stress intensity factors (DSIFs) with much less numerical oscillation. To the best of our knowledge, numerical solution on DSIFs for crack propagation under dynamic loading remains engineeringly unsatisfied. In this paper, the extra-dof free XFEM is extended to implicitly dynamic crack propagation problems-still a remaining difficulty for the current XFEMs. The implicit Newmark algorithm is used for time discretization. A dynamic interaction integral method is employed for DSIFs for both stationary and moving cracks under dynamic loading. Compared with the interaction integral method for static cracks, the dynamic method considers the effects of crack growth speed and inertia terms. The paper investigates in detail the influences of element size, mass matrix formulation, time step size, crack tip enriched zone size, inertia term, crack growth speed, and J-domain mesh/cell sizes of the interaction integral. Numerical tests show satisified accuracy and efficiency of the new method for dynamic crack problems. In particular on the challenging benchmark problem "Mode I semi-infinite stationary and then moving crack", the new improved XFEM provides the best DSIFs up to the time of publication.

2018, 50(3): 599-610. doi: 10.6052/0459-1879-18-030

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ICM METHOD FOR FAIL-SAFE TOPOLOGY OPTIMIZATION OF CONTINUUM STRUCTURES

Peng Xirong, Sui Yunkang

Aimed at the topology optimization of continuum structures considering the fail-safe principle, for the purpose of overcoming the shortcomings of the topologies obtained by the traditional topology optimization being too sensitive to local damages for the lack of reasonable redundancy components, the fail-safe design is achieved. At first, four concepts are clarified: the structural local failure mode, the structural local failure region, structural failure case, and the pre-estimation distribution of structural failure cases. Secondly, based on the ICM (independent continuous mapping) method, a minimizing structural volume model with structural performance constraints is established for the fail-safe topology optimization problems of continuum structures. While establishing the objective function, minimizing the maximum of structural volumes of all structural failure cases is converted into minimizing the structural volume of the ground structure without failure regions. Therefore, the difficulty of dealing with multi-objective optimization is avoided. While establishing the approximation functions of constraints, mechanical property constraints of all of the structural failure cases are taken into account. The problems with a single load case or multi-load cases can be solved by the presented model. At last, optimization problems with displacement constraints are taken as examples. The optimization model is established and the solution method is also presented. Some examples with displacement constraints under a single load case or multi-load case are presented to verify the validity of this method. The results show that the optimal topologies obtained by this method are more complex and has a greater volume than that obtained by the topology optimization without fail-safe. Namely, optimal topologies have more redundancy, which is the result of considering the fail-safe principle. The proposed research is an important progress for the design of vehicles serving for aviation, aerospace, water or land fields and other engineering structures undergoing accident damages, war wounds or terrorist attacks.

2018, 50(3): 611-621. doi: 10.6052/0459-1879-17-366

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DISCRETE ELEMENT SIMULATIONS OF THE HIGH VELOCITY EXPANSION AND FRAGMENTATION OF QUARTZ GLASS RINGS

Xiong Xun, Li Tianmi, Ma Qiqi, Fang Jisong, Zheng Yuxuan, Zhou Fenghua

The mechanical behavior of quartz glass rings under internal velocity impact is simulated by using discrete element method (DEM) based on the flat-jointed bond model. The microscopic mechanical parameters of the quartz glass ring were determined by comparing the standard uniaxial compressive/tensile and three-point bending numerical test results with the experimental results. Using these material parameters, the fragmentation processes of quartz glass rings under different impact velocities were numerically simulated. The numerical results showed that: the failure time of the quartz glass ring corresponded to a rebounding of the radial velocity, macroscopically this timing is coincident with the rapid drop of average stress. This radial velocity rebounding is attributed to the unloading waves incited from the brittle cracking of the tensile specimen, and can be used in the numerical analysis as the failure point. Detailed numerical tests and analysis showed that: (1) The fracture strain of quartz glass ring increases with the increase of strain rate, a phenomenon consistent with experimental observations for ductile materials; (2) The average mass of the quartz glass ring decreases with the increasing strain rate; (3) The average fragment size in the simulation was consistent with the theoretical and experimental data in other papers. An experiment device of liquid-driven expanding ring was used to conduct preliminary tests. The morphology and the number of fragments recovered from real tests are consistent with the numerical simulations.

2018, 50(3): 622-632. doi: 10.6052/0459-1879-17-410

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A CALCULATION MODEL FOR TANGENTIAL CONTACT DAMPING OF MACHINE JOINT INTERFACES

Wang Wen, Wu Jiebei, Gao Zhiqiang, Fu Weiping, Kang Weichao, Liu Yanpeng

This paper is focusing on the problem of tangential contact damping to study when two rough surfaces contact under combined normal force and tangential force. Firstly, according to the KE model, the tangential contact behaviors of a single asperity in the elastic, elastic-plastic, and plastic deformation stages were analyzed, and then the stick-slip characteristics of asperity in the three deformation stages can be obtained. Secondly, according to GW statistical model, a statistical model of a mechanical interface tangential damping was built based on a type of “asperity-based” model of including asperity elastic, elastic-plastic and plastic deformation mechanism, which considered the asperity stick-slip tribology behavior in the three different deformation mechanisms. Finally, the effects of the normal preload of mechanical interface, vibrational frequency and tangential dynamic displacement amplitude on the mechanical interface tangential damping were respectively discussed. These conclusions can be obtained that: the tangential contact damping coefficient increases with the increase of the normal load on the mechanical interface, whereas decreases as the tangential excitation frequency and the tangential dynamic displacement amplitude increase. For the high frequency and bigger amplitude, the tangential contact damping coefficient of joint surface is almost independent of tangential relative displacement amplitude and vibration frequency. In order to verify the veracity of the proposed model, a tangential damping experiment of joint surface was established under a dynamic tangential force, and the results show that the simulation results of the proposed theoretical model are mainly consistent with the experimental results in the change rule and the order of magnitude, which proves that the tangential damping of the proposed model is correct and effective.

2018, 50(3): 633-642. doi: 10.6052/0459-1879-17-425

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ANALYSIS OF FLEXURAL VIBRATION OF V-SHAPED BEAMS IMMERSED IN VISCOUS FLUIDS

Hu Lu, Yan Han, Zhang Wenming, Peng Zhike, Meng Guang

V-shaped beams have been widely used in atomic force microscope (AFM) and micro-nano mechanical sensing applications.The structure is usually used for sophisticated detection, sensing and performance characterization in viscous fluids, thus making it complex to study the vibration characteristics of the structure by considering the fluid-structure interaction between the complicated geometry and viscous fluids.It is of fundamental importance to investigate the vibration characteristics of V-shaped beams submerged in viscous fluids owing to the fact that the vibration characteristics will directly affect the dynamic properties of the applications.In this paper, an underwater vibration model is developed to depict the dynamic characteristics of V-shaped beams immersed in viscous fluids by taking into account the fact that the cross-section and bending stiffness of the V-shaped beam are variable along the beam axis.A complex hydrodynamic function in terms of the gap to width ratio and the frequency parameter is developed to describe the hydrodynamic loading where the complex hydrodynamic function is derived from the modified hydrodynamic function based on the gap to width ratio in beam

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s cross-section.Besides, the frequency response of V-shaped beams vibrating in viscous fluids is obtained theoretically.Moreover, the experimental verifications on flexural vibrations of several V-shaped beams with different geometrical sizes are carried out.It demonstrates that the experimental data is in good agreement with the theoretical results, thus validating the modified expression of hydrodynamic function and the underwater dynamic model.Besides, the effect of different fluid viscosities, angles of V-shaped beams and the scale of the geometry on the vibration characteristics of the coupling system is analyzed based on the proposed fluid-structure interaction model.

2018, 50(3): 643-653. doi: 10.6052/0459-1879-18-028

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DYNAMIC MODELING AND SIMULATION OF ROTATING FGM TAPERED BEAMS WITH SHEAR EFFECT

Gao Chentong, Li Liang, Zhang Dingguo, Qian Zhenjie

In this paper, the rigid-flexible coupling dynamics of the rigid-flexible beam system under large overall rotating motion is studied. The flexible beam is a functionally graded material (FGM) tapered beam, and its material properties are assumed to vary along the beam axis with a power law relation. The geometrical displacement relationship of the flexible FGM beam is described by the arc coordinate. The transverse bending and longitudinal stretching of the flexible beam are considered by the variables of the slope angle and the stretching strain, respectively, and the shear effect is taken into account. The assumed modes method is used to describe the deformation field, and Lagrange’s equations of the second kind are used to derive the equations to obtain the rigid-flexible coupling dynamic model considering the shear effect. Based on the new rigid-flexible coupling dynamics modeling theory, dynamics of the FGM tapered beams with different axial gradients are studied. The influences of different rotating speeds, gradient distributions and variable cross-section parameters on the dynamic characteristics of the system are analyzed by numerical simulations. The results show that the effect of shear on the deformation of FGM tapered beam with depth-span ratio is obvious. The distribution of the material gradient and the selection of the cross-section parameters will have a great influence on the dynamic responses and frequencies of the rotating FGM tapered beam. The rigid-flexible coupling dynamic model considering the shear effect is a further improvement of the previous non-shear model, which can be applied to solve the dynamic problems of the Timoshenko beam structures.

2018, 50(3): 654-666. doi: 10.6052/0459-1879-18-011

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DISCUSSION ON THE WAKE VORTEX STRUCTURE OF A HIGH SPEED TRAIN BY VORTEX IDENTIFICATION METHODS

Pan Yongchen, Yao Jianwei, Liu Tao, Li Changfeng

A flow field around a 1/30th-scale and simplified model of high speed train (HST) has been numerically calculated by the improved delayed detached eddy simulation, and the vortex structure in the near wake detailedly discussed as a focus. According to different vortex identification methods, it can be observed for the wake vortex structure that powerful vortices with high vorticity magnitude mostly appear in the vicinity of the tail; however, there are stable vortices with lower vorticity widespread in the near wake region. Based mainly on the findings and the newly-proposed definition of a vortex and physical meaning, there are conclusions given as follows. Shear deformation and high vorticity diffused play significant roles in forming those energetic vortices, due to boundary layers separated from the streamlined tail. And turbulent eddies have to be rotated and strained by the strong shears, thus resulting in prominent turbulent characteristics of the local complex flow. On the other hand, though strength of the vortices evidently drops, vortical vorticity is dominant inside the streamwise vortex cores when the strong shear strains rapidly decay. Under the circumstances, fluid particles rotate round the cores that get closer to the ground, and thus the interaction between the vortices and the ground becomes a dominant mechanism. The vortices have to be diminished at relatively low rate, but considering turbulence production, the flow mechanism can play an important role in self sustainment of turbulent eddies. As a result, the vortex structure is able to stably be in the wake flow.

2018, 50(3): 667-676. doi: 10.6052/0459-1879-17-383

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A COMBINED PARTICLE FILTER METHOD FOR PREDICTING STRUCTURAL PERFORMANCE DEGRADATION

Guan Xuexue, Chen Jianqiao, Zheng Yaochen, Zhang Xiaosheng

Structural performances will degrade with time due to the influence of loading, environmental and material factors. To assess the status of a structure in service, the structural deterioration process is usually described through physical models with uncertain model parameters. Prior distributions of model parameters are often determined by using the data collected from similar structures. To improve the accuracy of the model, Bayesian inference incorporated with available data is often used to update the distribution of the parameters. In this work, an effective Bayesian method PF-DREAM is proposed. In this approach, firstly, the mixing combination rule of the Dempster-shafer theory (DST) is utilized to get the prior distribution. Thereafter, for evaluating the complicated multidimensional integral in the Bayesian inference formula and obtaining the posterior distribution, a differential evolution adaptive Metropolis (DREAM) approach integrated with the particle filter (PF) is developed. As compared with the original PF method, the proposed PF-DREAM method can enhance the sample particles’ diversity and improve the quality of the model. To illustrate the efficiency and accuracy of the proposed method, a lithium-ion battery problem and a fatigue crack propagation problem are presented. Results demonstrated that the proposed method can provide more accurate results in parameters updating as well as response prediction. As more data is incorporated, the model’s variance becomes smaller, and the predicted mean trajectory is more reliable in terms of the actual deteriorate curves. It is pointed out that PF-DREAM method can be applied to high-dimensional problems and implicit function problems with the same algorithm presented in this paper, only accompanying more iteration numbers and greater computational load for obtaining convergent results.

2018, 50(3): 677-687. doi: 10.6052/0459-1879-18-014

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MECHANISM ANALYSIS OF PRESSURE OSCILLATION IN PARTICLE METHOD

Zhu Yue, Jiang Shengyao, Yang Xingtuan, Duan Riqiang

The moving particle semi-implicit method was developed to simulate incompressible fluid using a meshless method. There was a big problem that the space distribution and the time variation of pressure oscillate drastically in the MPS method. In order to investigate the pressure oscillation in the MPS method, the simplified one-dimensional model was developed. The mechanism of pressure oscillation in the MPS method was illustrated by the movement and the relative position between the center particle and its neighbor particles. The collision model was employed in the simulation and the relative position between particles was controlled by choosing different collision parameters. The classical dam break problem was simulated. With the increase of collision parameter, the fluctuation of the deviation of particle number density decreased. According, the amplitude of pressure oscillation was suppressed. Two different kernel functions were also employed to investigate the pressure oscillations. The results showed that the gauss kernel function improved the stabilization of pressure calculation. It was the reason that the same movement of particles lead to less deviation of particle number density when the gauss kernel function was used. And the randomness of particles motion led to random fluctuation in the deviation of particle number density. As a result, the pressure fluctuation in MPS method occurred and it was difficult to be eliminated.

2018, 50(3): 688-698. doi: 10.6052/0459-1879-17-294

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AN IMPROVED ALGORITHM OF DYNAMIC GRAY-THRESHOLDING FOR SEGMENTING DENSE AEOLIAN SAND PARTICLES IMAGES

Mei Fanmin, Luo Sui, Chen Jinguang

Aeolian saltation plays a very key role in shaping varieties of landforms in arid area and in affecting global climate system and marine ecosystem. It is generalized as four sub-processes: aerodynamic entrainment, the grain trajectory, the grain-bed collision and wind modification. Among these sub-processes, individual particle trajectory formation is a key chain affecting grain-bed collision and interaction between sand particles and wind conditions. Nevertheless, up to date, the mechanism of sand particle trajectory formation has not yet disclosed perfectly due to lack of a sophisticated algorithm for extracting effectively sand particles from high-concentration images. The traditional algorithms with single thresholding often cannot segment sand particles effectively from backgrounds due to brightness difference among saltating particles, stable and stochastic noises in high-concentration images. The algorithm with dynamic thresholding proposed by Ohmi and Li, however, needs to preset arbitrarily empirical parameters as maximum, minimum and contrast threshold, probably introducing uncertainty of segmentation. Thus, an improved segmentation- algorithm with dynamic thresholding is proposed here, which covers denosing by substracting a background image, graying by green channel, differentiation, targets’ detection by gray-level variance and segmenting by maximum between-class variance of gray-thresholding. The highlights of new algorithm lie in two aspects: the denosing by substacting a background image and the targets’ detection. In virtue of the denosing method, such stable noise signs as stripes and maculae deriving from photography processes are removed effectively from the sand particles’ image. As the most an important precedure of the improved algorithm, the targets’ detection is able to distinguish effectively those dark sand particles from background in differential units by selection of appropriate variance of gray (3.5), but also to reduce fasle information that backgrounds could be recognized wrongly as particles. It seems that image segmented with the targets’ detection shows clearly more sand particles in contrast to image without the targets’ detection which is blurred with lots of stochastic noises. Based on horizontal and vertical coordinates of all sand particle in the study image recorded manually, such parameters as the number of sand particles identified correctly (N_ie), recall rate (R_c) (refers to ratio of the extracted automatically number of sand particles to the number of real particles (N_r)) and the precision (P_r refers to ratio of N_ie to N_r) were used to evaluate the algorithm. It shows that N_ie, R_c and P_r is 461, 71%和86% respectively, compared to 85, 13% and 82% by the traditional algorithm. The new algorithm is better than the traditional one. Nevertheless, it should be perfected in future through many new ways.

2018, 50(3): 699-707. doi: 10.6052/0459-1879-18-040

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THE INTRODUCTION OF APPLICATION PROJECTS ON MECHANICS IN 2018

Zhan Shige, Bai Kunchao, Cao Dongxing, Wang Gang

The paper introduced the applications for NSFC programs on mechanics in 2018. The statistics of application projects for General Programs, Young Scientists Fund, Fund for Less Developed Regions, Key Programs, Excellent Young Scientists Fund, and National Science Fund for Distinguished Young Scholars are presented and compared with applications in 2017.

2018, 50(3): 708-709. doi: 10.6052/0459-1879-18-143

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