力学学报

2017, 49(4)

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DYNAMIC ANALYSIS ON GAS-WATER TWO-PHASE UNSTEADY SEEPAGE FLOW IN LOW-PERMEABLE COALBED GAS RESERVOIRS

Liu Wenchao, Liu Yuewu

At present, the research on the seepage flow models in low-permeable coalbeds is only limited to the single phase flow cases, which simultaneously considerate the existence of threshold pressure gradient in the seepage flow process, its produced moving boundary and the desorption function of adsorbed gas inside the moving boundary; however, the research on the gas and water two-phase seepage models with moving boundaries, which are more consistent with the actual situations, has not been reported yet. In comprehensive consideration of these influential factors including the desorption function of the adsorbed gas in coalbeds, gas-water two-phase seepage flow, the non-Darcy seepage flow characteristics in the low-permeable formations, the stress-sensitive effect of the formation, etc., modeling the gas-water two-phase seepage flow in low-permeable coalbeds is studied in this paper. According to the "phase separation" method involved in the well testing technology, both the comprehensive compressibility coefficient and the fluidity are modified for the two-phase seepage flow problem; and then based on the assumption of the linear spatial distribution of the gas saturation, a coupled model of gas-water two-phase seepage flow in low-permeable coalbeds is built. The mathematical model can not only depict the moving boundary that represents the change of the effectively disturbed coalbed area with time due to the existence of threshold pressure gradient in the seepage flow process in low-permeable coalbeds, but also can depict the desorption phenomena of the adsorbed gas in the effectively disturbed coalbed area, and the increase of the gas saturation in coalbeds caused by the desorption function of the adsorbed gas; furthermore, in order to improve the accuracy of the model, the quadratic pressure gradient term is retained in the governing equation of the model. A fully implicit finite difference method is adopted to numerically solve the model, and the correctness of the numerical method is also verified. Eventually, the log-log type curves regarding the transient wellbore pressure response and its derivative are obtained from the model, and then the sensitive-effects of some seepage flow parameters can be analyzed. The presented research results in the paper can provide theoretical foundations of seepage flow mechanics for the well testing technology for the gas-water two-phase seepage flow in the development of low-permeable coalbed gas reservoirs.

2017, 49(4): 828-835. doi: 10.6052/0459-1879-17-034

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UNIFIED SOLUTIONS OF LIMIT INTERNAL PRESSURE FOR THICK-WALLED CYLINDER WITH DIFFERENT BEHAVIOUR IN TENSION AND COMPRESSION

Zhao Junhai, Jiang Zhilin, Zhang Changguang, Cao Xueye

Thick-walled cylinder is widely used in practical engineerings. If the limit internal pressure is calculated accurately, it is great significance to prevent accidents and reduce risk. There are many engineering materials that the tensile strength and tensile modulus are different. These differences have a significant effect on the ultimate internal pressure. Previous studies have shown that only considering one aspect of the tension and compression strength and the modulus of tension and compression has a certain error with the actual situation. With consideration of the intermediate principal stress and the different elastic modulus and different strength in tension and compression, elastic and plastic stress distribution, the unified analytical solutions of the elastic limit internal pressure, the plastic limit internal pressure and the shakedown limit internal pressure of thick-walled cylinder under internal pressure are deduced based on twin shear unified strength theory. The correctness of the calculation results is proved through the verification and comparative analysis with other literatures. The influence of radius ratio, unified strength theory parameter, tension-compression ratio and coefficient of tensile-compression modulus of materials on the solutions is analyzed. It is shown that each unified solution increases with increasing the radius ratio and unified strength theory parameter but decreases with increasing the tensioncompression ratio. The elastic limit internal pressure decreases with increasing the coefficient of tension-compression modulus. When the wall thickness increases to a certain value, the shakedown limit internal pressure decreases with increasing the coefficient of tension-compression modulus. The different elastic modulus and strength in tension and compression have significant influence on the stability of the thick-walled cylinders. The consideration of the intermediate principal stress effect can make materials give full play to their potential. The variable law of the limit internal pressure with radius ratio provides reference for selecting reasonable wall thickness. The conclusion furnishes some theoretical basis for the engineering application of thick-walled cylinders.

2017, 49(4): 836-847. doi: 10.6052/0459-1879-17-006

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WEIGHT FUNCTION METHODS AND ASSESSMENT FOR AN EDGE CRACK IN A SEMI-INFINITE PLATE

Tong Dihua, Wu Xueren, Hu Benrun, Chen Bo

Weight function method (WFM) is highly efficient and accurate for the determination of stress intensity factors (SIFs) and crack opening displacements (CODs) of cracked bodies under arbitrary load conditions. Comparing to the numerical methods such as the finite element method, WFMs have distinct advantage in terms of computational efficiency and reliability. This paper makes systematic analyses and comparisons of three WF approaches by Wu-Carlsson, Glinka-Shen and Fett-Munz, respectively, which are representative in the international fracture mechanics community. By employing the Wigglesworth analytical solutions to CODs of an edge crack in a semi-infinite plate under uniform tension, the WF and corresponding Green's function (SIF for a pair of point forces acting at an arbitrary location along the crack) are derived and used as the base for point-to-point comparison. The results are also compared with other existing WFs in the literature, including those by Bueckner, Hartranft-Sih and Wigglesworth using different analytical approaches. The study also includes the influence of selection of three reference load cases, including uniform, linear and reverse-linear stress distributions and their combinations, and geometric conditions related to CODs on the WF accuracy. Results show that the WF based on COD analytical expression for one reference load case are more accurate than that based on two SIFs due to two reference load cases. Furthermore, solution accuracy of the later approach is considerably affected by the selected reference load case(s). The geometric condition that the third derivative of COD vanishes at crack mouth has little effect on the accuracy of one-reference-load-case-based weight function. Finally, SIFs for four load cases calculated by using various WFMs are presented and compared.

2017, 49(4): 848-857. doi: 10.6052/0459-1879-17-024

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THE CONTACT ENERGY DISSIPATION OF THE LATERAL AND INTERACTIONAL BETWEEN THE ELASTIC-PLASTIC ASPERITIES

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

The traditional studies about a mechanical interface were mostly based on the assumption that a smooth rigid plane contacts with an equivalent rough surface, which ignored the lateral contact and interaction between asperities, so there has a serious error in those theoretical models. Aimed at an interface bearing normal static and dynamic force, the energy dissipation was studied from a micro level, which considered the lateral contact and interaction between asperities. The normal force can be divided into a normal component of force and a tangential component of force. The relation between the normal component and the deformation, and the relation between the tangential component and the displacement can be gotten during loading/unloading in the elastic stage, elastic-plastic stage, and plastic stage, respectively. According to the composition of forces, the relation between the normal force and total deformation can be derived. Because of the plastic deformation and friction between asperities, the curves of the loading and the unloading not coincide, and there is a hysteresis loop. One cycle of energy dissipation can be calculated by integrating the area of the hysteresis loop, which includes the strain energy dissipation and the friction energy dissipation. The simulation analysis shows that:the energy dissipation nonlinear increases with the increase of the deformation. The bigger contact angles the more energy dissipation, and it's the most obvious in the elastic stage. There are only the friction energy dissipation in the elastic stage, so under the low loads must use the assumption of double rough surfaces. In the plastic stage, there are only the strain energy dissipation, and the effects of the contact angle on the energy dissipation are very little, so under the heavy loads can use the assumption of the single rough surface to study the mechanical interface. Comparing with the KE and Etsion models, our proposed model is well agreed with the Bartier's experiments.

2017, 49(4): 858-869. doi: 10.6052/0459-1879-17-103

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MEASURING SUBSEQUENT YIELD SURFACE OF PURE COPPER BY CRYSTAL PLASTICITY SIMULATION

Zhang Keshi, Huang Shihong, Liu Guilong, Lu Damin

With the methods of single-specimen and multiple-specimen, the subsequent yield surfaces of the copper underwent tension, torsion and combined tension torsion pre-deformation respectively are studied by crystal plasticity simulation comparing with the real test employing thin-walled tubular specimens. Not the variances of measured subsequent yield surface but also the phenomena of subsequent yield surface appearing concave are discussed under considering different conditions, including different pre-deformation, the number of probing point, the test sequence of the probing points, and the specified offset strain, etc. On this basis, the rationality and validity of the two methods for subsequent yield testing are compared. The simulations probing yield surface are conducted using the FE model of thin-walled tubular specimen, in which the crystal lattice orientation for each element is arranged randomly, associated with a modified crystal plasticity constitutive model that is able to reflecting the Bauschinger effect for material under reversed loading, so that the deformation characteristic of polycrystal can be exhibited. The loading procedure of modeling test is designed as same as the real test. The investigated results show that:(1) the proposed simulation method can reproduce the real test procedure, the simulated subsequent yield phenomena are found fairly consistent with that observed in actual experimental measurements, which confirmed the rationality and validity of the method; (2) both the simulated and real tests show that the subsequent yield surface measured by using the thin-walled tube under combination of tension-torsion load may be concave, and the result tested by the single specimen method is more obvious in yield surface concave no matter for simulated or real test; (3) if the test material is fairly consistent in quality, the multiple-specimen method should be more reasonable than the single-specimen method for subsequent yield surface test.

2017, 49(4): 870-879. doi: 10.6052/0459-1879-17-074

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ANALYSIS OF STRAIN LOCALIZATION BY ENERGY EQUIVALENCE:Ⅱ.FINITE ELEMENT SOLUTION

Wu Shouxin, Wei Jirui, Yang Shuwei

Founded on the nonlocal plasticity and the state space theories, a new approach is proposed to find the meshindependent solution of the strain localization problems by equating the rates of plastic energy dissipation in the local and nonlocal state spaces. Following the previous paper by the authors, general formulas are developed for the solution of the nonlocal internal variables in the two-and more than two-dimensional problems. A stress updating algorithm is proposed to integrate the rate form constitutive equations in the finite element context. To verify the proposed approach, a one-dimensional model problem and three two-dimensional plane strain problems are solved numerically by the finite element method. Numerical results show that the plastic strain distributions and the load-displacement curves stably converge with refinement of the finite element mesh. The size of the localization zone depends only on the internal length scale and is insensitive to the mesh size. For the one-dimensional problem, numerical solutions converge to the analytical ones. For the two-dimensional problems, although no analytical solutions are available, the numerical solutions converge toward the unique ones. The width and the inclination are almost not changed as the mesh size is reduced. Also, the distribution of the plastic strains and the deformation patterns are smooth in the entire domain. A slope stability problem and a plane strain test of a coal specimen are also solved numerically to demonstrate the robustness of the proposed approach. It is well shown that the proposed approach can overcome the drawbacks of the classical continuum theory and lead to physically meaningful, mesh-independent solution of strain softening problems. Because only C⁰ continuity is needed between element boundaries, the proposed approach is easy to be incorporated into the existing finite element code without substantial modification.

2017, 49(4): 880-893. doi: 10.6052/0459-1879-16-330

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IMPLEMENTATION OF MULTI-TRANSMITTING BOUNDARY CONDITION FOR WAVE MOTION SIMULATION BY SPECTRAL ELEMENT METHOD:TWO DIMENSION CASE

Xing Haojie, Li Hongjing

The spectral element scheme of multi-transmitting formula (MTF) which proposed by Xing and Li is developed and expanded to numerical simulation of SH-type wave motion in homogeneous linear medium. The spectral elements adjacent to the artificial boundaries are supposed to be rectilinear quadrilateral elements, in order that each node on the artificial boundary locates on a unique grid line pointing to the interior domain, hence the displacement of a particular artificial boundary node at a certain time can be inferred from displacements of nodes on the grid line at earlier times. Two numerical examples, the plane wave propagation with a certain angle (outer-source problem) and the free spread of a pulse wave originated from a point (inner-source problem), are employed for verification of this wave motion simulation procedure which combines the spectral element method with MTF boundary. The main parameters affecting reflection error of the MTF scheme, such as order of interpolation polynomial, artificial wave speed and transmitting order, are investigated in time domain via a series of initial-value problems. The results show that the order of interpolation polynomial influences the reflection error very little, while higher interpolation order may lead to better accuracy. For the choice of artificial wave speed, it is preferable to choose values equal or slightly greater than the physical wave speed, otherwise bigger reflection errors come about. Transmitting order exerts the most significant impact on reflection error, which would be reduced greatly with the increase of transmitting order of MTF, but the undesired drift instability may arise when transmitting order reaches three or two for inner-source and outer-source problems, respectively. Although the work combining MTF boundary with spectral element method is conducted on simulation of SH wave propagation in infinite homogeneous medium in this paper, it has laid the foundation of research on more complicated situations, such as issues of layered soil sites, propagation of P-SV wave or Rayleigh wave, etc.

2017, 49(4): 894-906. doi: 10.6052/0459-1879-16-393

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REVIEW OF BANDGAP CHARACTERISTICS AND ACOUSTO-OPTICAL COUPLING IN PHOXONIC CRYSTALS

Ma Tianxue, Su Xiaoxing, Dong Haowen, Wang Yuesheng, Zhang Chuanzeng

Phoxonic crystals are periodic structures which possess photonic and phononic bandgaps simultaneously. Phoxonic crystals can be applied as systematic platforms for manipulating electromagnetic and elastic waves simultaneously, and can be utilized in various fields such as optical, acoustic and acouto-optical devices, and cavity optomechanics. This paper firstly introduces the basic concepts of phoxonic crystals, including the constituting materials, their classifications according to spatial periodicity, the numerical calculation methods of band structures. We elaborate the characteristics of phoxonic dual bandgaps for different systems, and the topology optimization method applied in optimizing the bandgap width of phoxonic dual bandgaps. The field of cavity optomechanics, as well as the quasistatic method and optomechanical coupling coefficient method for evaluating the acousto-optical coupling strength are introduced. The acousto-optical coupling phenomena in various phoxonic crystal structures are summarized. Then this paper introduces the research works related to phoxonic crystal waveguides and sensors. Finally, we outline the prospects of phoxonic crystals based on state of the art, including the enhancements of acousto-optical interaction in phoxonic crystal cavities, the investigations of three-dimensional phoxonic crystals, the designs of different phoxonic metamaterials, the phoxonic crystal device designs and related applications, and so on.

2017, 49(4): 743-757. doi: 10.6052/0459-1879-17-130

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STUDY OF SURFACE INSTABILITY ABOUT HYPERELASTIC FILMS ON AUXETIC SUBSTRATES UNDER COMPRESSION

Huang Chunyang, Tang Shan, Peng Xianghe

When a bilayer structure consisting of a thin stiff film and a thick compliant substrate subjected to compressive deformation, its free surface would be wrinkled to minimize the energy of the system, and different wrinkle patterns may appear for different ratios of the modulus of the film to that of the substrate. In this article, we developed a novel approach to suppress the surface instability of such bilayer materials under severe compression by adjusting the Poisson's ratio of the substrates. This approach is also applicable to the bilayer consisting of a soft substrate and a film with elastic modulus similar to that of the substrate. We developed an analytical approach for surface instability of the bilayer based on NeoHookean model in the case of small deformation, and obtained the critical strain of the bilayer with a semi-analytical method. Then, we used finite element approach (FEA) to illustrate that the instability of the thin film can be delayed if the substrate has a negative Poisson's ratio. We showed that:(1) when the Poisson's ratio of the substrate is positive and close to 0.5 (nearly incompressible), the surface instability may occur to the bilayer system at a very small compressive strain; (2) if the Poisson's ratio of the substrate is negative and close to -1, the film can be compressed up to 46% without occurence surface instability. The approach developed and the results obtained in this article imply a great potential of auxetic materials used to enhance the compressibility of thin films, which can provide guidance for the design of laminate ductile electronic devices.

2017, 49(4): 758-762. doi: 10.6052/0459-1879-17-161

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MICROSTRUCTURE EVOLUTION MECHANISM BASED CRYSTAL-PLASTICITY CONSTITUTIVE MODEL FOR NICKEL-BASED SUPERALLOY AND ITS FINITE ELEMENT SIMULATION

Xiong Jun, Li Zhenhuan, Zhu Yaxin, Huang Minsheng

The nickel-based superalloy has been widely used in turbine engines of aerospace and marine industries for its excellent strength and high resistance to creep and oxidation at elevated temperature. These excellent mechanical behaviors root in its unique two-phases microstructure. Based on the homogenization method and representative volume cell (RVC) model, a crystal-plasticity (CP) constitutive model with information of two-phases microstructure and disloca-tion evolution was developed for nickel-based superalloys. By introducing various dislocation densities as major internal variables, the present constitutive model fully considered a series of dislocation mechanisms, including octahedral glide, cubic slip, climb, cross slip and bowing-out in the γ phase, and precipitate shearing and the Kear-Wilsdolf lock formation in the γ' phase. Based on this, a user material subroutine (UMAT) for this CP constitutive model was realized in the FEM software ABAQUS. By using this UMAT module, the creep, monotonic and cyclic mechanical behaviors of single-crystalline and poly-crystalline nickel-based superalloys were modeled under different temperatures and various loading orientations. The computationally obtained results were in good accordance with the experimental data, indicating that the present CP constitutive model with information of microstructures and dislocations evolution could uniformly describe various mechanical behaviors of nickel-based superalloys under different temperatures and loadings, including the monotonic plasticity, creep and cyclic plasticity.

2017, 49(4): 763-781. doi: 10.6052/0459-1879-17-183

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STUDY ON COUPLING EFFECTS OF UNDERWATER LAUNCHED VEHICLE

Du Tezhuan, Wang Yiwei, Huang Chenguang, Liao Lijuan

As to underwater launch, it is important to study the characteristic of hydrodynamic forces and structural response. It includes complex flow with phase change, structural behavior under time-vary constraints and coupling effects between fluid and structure. Loosely coupled method is utilized in the present work, in which the structural solver is linked to the flow solver. Governing equations of fluid dynamics and structural dynamics are solved respectively. The coupled algorithm is achieved by exchanging data through the interface of fluid domain and solid domain every time step. The flow model is based on RANS equations. In this model, mixture model is used to simulate multiphase flow, a cavitation model is introduced to describe the phase change, a modified turbulence model is utilized to simulate the turbulent effect of mixture, and the dynamic mesh technique is adopted to deal with the moving boundary. Rigid motion and structural vibration are calculated respectively. The structural model is established based on the equivalent beam model, and computed by the time domain integral method in Body Axes System. The fluid-structure coupling method is set up aimed at underwater launch process and has been validated by the experiment. This method could not only capture the evolution of the natural cavitation, but also obtain hydrodynamics forces, structure vibration and bending moment of the projectile. We utilize the proposed model to study the influence of structural stiffness and launch velocity on coupling effect of cavity collapse and structural vibration. The results show that structural load is mainly affected by collapse pressure including pressure amplitude, acting location and phase relationship between collapse pressure and structural vibration.

2017, 49(4): 782-792. doi: 10.6052/0459-1879-16-401

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IMPROVEMENT OF BRAZILIAN TEST:FROM FLATTENED BRAZILIAN DISC TO GROOVED BRAZILIAN DISC

Wang Qizhi, Li Lian, Wu Lizhou, Huang Runqiu

Brazilian test, a standard method for measuring the tensile strength of concrete, ceramics, rock, and other brittle or quasi-brittle materials, has been widely applied in materials science and civil engineering, research on its improvement attracted ever-growing attention in scientific and engineering communities. We ideate a new specimen configuration to improve the Brazilian test, i.e. grooved Brazilian disc (GBD), with a pair of narrow and shallow groove produced at opposite ends of the loading diameter, GBD relieves the shortcoming of non-central crack initiation possibly inherent to the original complete Brazilian disc (BD) under diametrically compression, having the same merit pertaining to our previously-proposed flattened Brazilian disc (FBD). GBD is also more general in specimen configuration, as it represents both BD and FBD. More advantages may be obtained if the geometric parameters of GBD are suitably chosen by referring to the analytical stress formulas, derived by superposition of two models we proposed for solving the compressive stress and tensile stress respectively. The derived two simple stress formulas can be used to predict qualitatively the stress evolution trend, both at and near the front of the apex of the groove, and also the influencing geometric parameters of GBD, which are also confirmed by quantitative numerical calculations with finite element method. The analytical formulas, numerics and comparative experimental result jointly indicate:a slight change in the geometry and surface boundary condition of a disc-type specimen under diametral compression turns around a substantially favorable change for the stability and fracture process of the specimen, making the GBD more favourable in the Brazilian test.

2017, 49(4): 793-801. doi: 10.6052/0459-1879-17-031

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THE EFFECT OF TRANSITON LOCATION ON AEROTHERMOELASTICITY OF A HYPERSONIC ALL-MOVABLE CENTROL SURFACE

Liu Cheng, Ye Zhengyin, Ye Kun

The transition prediction of hypersonic boundary layer has been a difficulty in fluid dynamics. The friction coefficient and heat-transfer coefficient could be changed because of transition. The location of transition has an effect on thermal environment around the aircraft surface, which accounts for marked changes of Aeroelastic characteristics further. Considering the uncertainly of transition prediction of hypersonic boundary layer, this paper has analyzed the effects of transition location to aerothermodynamics of hypersonic all-movable control surface. First of all, the thermal environment around the control surface is obtained by solving the N-S (Navier-Stocks) equation using the model of laminar and turbulent flow respectively. In the next place, a parameterized model considering the given location of transition for temperature distribution is proposed. Base on this model, the structural thermal mode considering thermal stress and material inherent characteristics is analyzed. Finally the aeroelasticity is analyzed by the method of local flow piston theory based on CFD. This paper chooses an all-movable control surface as study subject with M=6, H=15 km and the calculation results show that:(1) As the transition location moving from leading edge to trailing edge, the structural frequencies increase and flutter velocity has an increased trend. Research indicates that maximum variation of flutter velocity is 6% brought by transition location; (2) When transition is located near the rudderpost, the flutter characteristics of the structure change violently. Decomposition and analysis of stiffness characteristic show that the major factor is the stiffness of rudderpost whose influence accounts for more than 80% of the whole structure.

2017, 49(4): 802-810. doi: 10.6052/0459-1879-17-016

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INFLUENCE OF SMALL AMOUNT OF WETTING IMPURITY ON THE SLIP OF LIQUID FLOW OVER NON-WETTING SURFACE

Bao Luyao, Luo Kai, Wen Jun, Hu Haibao

The nanofluidic systems has great promise applications in many areas because of high efficiency and economic performance. During to the very large rate of surface and volume, the interface slip effect will significantly influence the flow properties in nanofluidic systems. The non-equilibrium molecular dynamics simulation was used to investigate the slip properties as liquid flows past non-wetting solid wall which contains small amount of wetting impurity. The underlying mechanism was also discussed based on the molecular kinetic theory. The simulation results indicate that the wetting impurity (uniformly or concentrated distributed) show insignificant influence on density profile of liquid but significantly alters the solid-like structure and slip property of liquid. As the percent of wetting impurity increasing, the solid-like phenomenon of liquid near walls becomes more significant and the contact density increases linearly. At the same time, the average velocity of liquid decreasing and the slip length decreases fast in a linearly way. The uniformly distributed wetting impurity reduces the magnitude of slip more significantly than concentrated distributed at the same percent of wetting impurity. For example, as the percent of wetting impurity is 28%, the slip length decreases 50% (concentrated distributed) and 56% (uniformly distributed) relative to the homogeneous non-wetting wall. The analysis based on the molecular kinetic theory indicates that the existence of wetting impurity enlarges the energy barrier as liquid atoms hopping from one sites to another in the first liquid layer. Thus, the probability of liquid atoms hoping along the flow direction was decreased, i.e. smaller the slip length. In the case of uniformly distributed wetting impurity, the smaller slip arbitrated to the decreasing incommensurability between fluid and wall.

2017, 49(4): 811-817. doi: 10.6052/0459-1879-16-368

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IDENTIFICATION AND CHARACTERISTICS OF HYDRODYNAMIC COEFFICIENTS FOR A FLEXIBLE CYLINDER UNDERGOING VORTEX-INDUCED VIBRATION

Xu Wanhai, Ma Yexuan, Luo Hao, Luan Yingsen

Vortex-induced vibrations (VIV) may cause serious fatigue damage on flexible cylinder structures, such as marine risers, mooring lines of floating platform and free spanning pipelines. Nowadays, in ocean engineering application, the hydrodynamic coefficients, used to predict the VIV of flexible cylinders, are mainly acquired from the forced oscillations of rigid cylinders in cross-flow, which may account for the unexpected errors. Taking the coupling between cross-flow (CF) and in-line (IL) vibrations into account, a fluid force model is proposed in this paper. Lift, impulse drag and added mass coefficients are obtained by the finite element method and least square method. A series of experimental tests of a flexible cylinder with a mass ratio of 1.82 and an aspect ratio of 195.5 are conducted in a towing tank to investigate the hydrodynamic coefficients on the flexible cylinder undergoing VIV. Comparing to the hydrodynamic characteristics of rigid cylinders, those of a flexible cylinder are further studied. Under the first-order mode, the hydrodynamic coefficients of a flexible cylinder share the same variation with those of rigid cylinders. A remarkable growth on lift and impulse drag coefficients is observed under the second-order mode. The added mass coefficients are strongly related to the displacement as the frequency is low. The large displacement region is the energy dissipation region with low frequency. While, the large displacement region may turn into the energy input region with high frequency.

2017, 49(4): 818-827. doi: 10.6052/0459-1879-16-263

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PRIMARY RESONANCES OF AN INTERNALLY DAMPED ROTATING COMPOSITE SHAFT WITH NONLINEARITIES IN CURVATURE AND INERTIA

Ren Yongsheng, Yao Donghui

The rotating shaft made of anisotropic composites is a class of typical rotor dynamic system which has a wide application in the structural design of advanced helicopter power transmission and automotive drive system. The nonlinear rotordynamic behavior study of these system has significance in theory and practice. However, at present, the research about nonlinear dynamic of rotordynamic system has restrainedly been the rotating isotropic shaft, and the effect of internal material damping is seldom considered. In this paper, the primary resonances of an internally damped rotating composite shaft are investigated. Nonlinearity comes from curvature and inertia induced by large deformation of in-extensionality composite shaft. Internal material damping comes from the dissipative properties of viscoelastic composite. The dynamical model incorporates rotary inertia and gyroscopic effect. The extended Hamilton principle is employed to derive the nonlinear equations of bending-bending vibration of rotating composite shaft. The Galerkin method is used to discretize these nonlinear equations, and the multiscale method is adopted to perturbtion analysis the ordinary differential equation, then the analytical expression of primary resonances are derived. The internal damping, external damping, ply angle, length-diameter ratio, stacking sequence, and eccentic distance are numerically analyzed, the effects of above parameters on stable forced vibration-response behaviors of rotating nonlinear composite shaft are discussed. The results show that the internal damping coefficient of angle-ply laminated shaft increases as the increase of ply angle. The primary resonance curves appeared at forward linear natural frequency are found to be of the hardening type. The developed model is capable of describing primary resonance behaviors of rotating composite shaft. This is an important generation of nonlinear dynamic model of in-extensional rotating isotropic shaft.

2017, 49(4): 907-919. doi: 10.6052/0459-1879-17-002

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A MODIFIED MODEL FOR THE VIBRATIONS OF A TWO-DEGREE-OF-FREEDOM HYDROFOIL-ROD SYSTEM CONSIDERING 3D EFFECT

Wang Renfeng, You Yunxiang, Chen Ke, Duan Jinlong

The classical Theodorsen equation for the motions of two-degree-of-freedom foils is modified with associated mass parameter ε and circulation parameter δ by considering the 3D effect of low aspect ratios, and the comparison between the calculation and classical experimental values demonstrates the modified equation is effective. According to the shape of V-g curve which varies with the mass ratio μ, two types (Type Ⅰ and Type Ⅱ) of flutter are defined. The influences of the bracing stiffness k_h, the torsional stiffness k_α, the locations of the center of gravity x_α and the angle of attack AOA on the characteristics of the flutter of a hydrofoil-rod system have been analyzed, and the comparison with experimental values shows that the numerical results are reasonable. The calculation shows the significant impacts of k_h, k_α, x_α and AOA on the flutter speed V_F. When the values of the parameters are in certain ranges respectively, flutter Type Ⅱ may occur. Specifically, a larger kh or a smaller AOA leads into a larger V_F. While, V_F first increases and then decreases with the increase of k α or x_α. Moreover, V_F only exists in a relatively narrow range of x_α, which reflects that the vibration pattern of the hydrofoil-rod system is high sensitive to x_α. Therefore, the probability of the occurrence of flutter can be reduced by avoiding the narrow range of x_α during design phase. On the other hand, according to the slow reaction of V_F to k_h and k_α, once flutter occurs, flutter can be eliminated by locking the rigid shaft with hydraulic devices.

2017, 49(4): 920-928. doi: 10.6052/0459-1879-17-042

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FREE VIBRATION ANALYSIS OF CURVILINEARLY STIFFENED KIRCHHOFF-MINDLIN PLATES

Liu Jingze, Jiang Dong, Han Xiaolin, Fei Qingguo

Compared with traditional stiffened plates, curvilinearly stiffened plates can deliver the mechanical properties of materials more adequately. In mechanical analysis of stiffened thick plates, Reissner-Mindlin theory is usually adopted. However, difficulties are encountered in connection with shear locking when the plate thickness approaches zero. In order to avoid the above problem, the discrete Kirchhoff-Mindlin theory was investigated by employing the assumption of shear strain field. An efficient finite element approach for free vibration analysis of curvlinearly stiffened KirchhoffMindlin plates is presented in this paper. The discrete Kirchhoff-Mindlin triangular (DKMT) element and the Timoshenko curved beam element are employed for modeling the plate and the stiffeners, respectively. The finite element equation is established through the displacement interpolation function of plate and the displacement compatibility conditions at the plate-stiffener interfaces. In order to verify the efficiency and accuracy of the present method, linearly stiffened thin plate and curvilinearly stiffened thin and thick plates are used as numerical examples. The reasonable finite element mesh density is selected by convergence and accuracy analysis. The first 20 natural frequencies of the linearly stiffened plate are in good agreement with the literature. In the examples of the curvilinearly stiffened plate, the number of plate elements satisfying the convergence condition is 2469, while the number in Nastran model is 6243. The maximum error of the natural frequency between the present method and Nastran is 3.4%. Results show that present approach can guarantee the accuracy of calculation with less number of elements. The present method can be applied to the free vibration analysis of both stiffened thin and thick plates.

2017, 49(4): 929-939. doi: 10.6052/0459-1879-17-041

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STUDY ON STRAIN RATE EFFECT AND STRENGTH CRITERION OF CONCRETE UNDER STATIC-DYNAMIC COUPLED LOADING

Lu Dechun, Li Meng, Wang Guosheng, Du Xiuli

In practical engineering, the concrete structures are usually subjected to an initial static load before dynamic loading. Most previous studies on the strain rate effect of concrete do not consider the influence of initial static load on the dynamic strength, which leads to the computed results of dynamic strength larger than the actual value. Therefore the structural designed by these methods is unsafe. Based on the mechanism analysis of concrete rate effect under staticdynamic coupled loading, a clear definition of initial static load was given by authors. Then, the relationship of concrete material parameters with the initial static load and the strain rate was derived. And, a general method for static-dynamic coupled strength criterion was proposed. The combination influence of initial static load and strain rate on concrete strength is reflected by the strength parameter. The static-dynamic strength of concrete is consist of the initial static load, the dynamic cohesive strength and the frictional strength. Then a static-dynamic coupled multiaxial strength criterion of concrete was established by combining the obtained concrete material parameters with nonlinear dynamic multiaxial strength criterion. The strength surface of the present strength criterion expands outward with the increase of strain rate under the same initial static load, while contracts inward with the increase of initial static load under the same strain rate. In another word, the strength of concrete increases with the increase of strain rate at the same initial static load, and decreases with the increase of initial static load at the same strain rate. Moreover, when the initial static load and the strain rate are invariable, the strength surface of this criterion is determined, and the loading path has no influence on the strain rate effect of concrete, but the hydrostatic pressure effect is influenced by the loading path. Thus, the strength of concrete at different loading path is different due to the various hydrostatic pressure effect. Finally, the established criterion was verified based on the static and dynamic combined strength test results of concrete.

2017, 49(4): 940-952. doi: 10.6052/0459-1879-17-013

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DAMAGE DETECTION OF MESO-SCALE CONCRETE STRUCTURES BASED ON TIME REVERSAL METHOD

Zhao Guoqi, Qiu Yaping, Luo Ying, Feng Kan

A specific time reversal imaging method is proposed in this article to detect defects in concrete structures. In order to detect the damage that the scale is the same as the aggregate, a meso-scale concrete model is introduced in this article. As the concrete is a composite material composed by cement, aggregate, water and concrete admixtures, the Monte Carlo random model and the aggregate grading curve of real concrete samples are introduced for designing this finite element model. Then, the damaged model was analyzed by employing a self-adapted time reversed model to achieve the ultrasonic wave field simulation. This imaging method contains two steps:the first is the forward detection. A series of reflected echo signals with damage information are obtained in this section. These received signals can be reversed in Matlab to serve as the incident signals in the next Time Reversal process; the second step is to image the damage location via interfering the wave-fronts actuated by different transducers to illustrate the peaks of waveform amplitudes. By determining the interfering wave peak time, obtaining the original wave field of that moment, we can forming the wavelet transform energy field, and then complete the damage imaging of the concrete model with defect. In the time reversal process, we introduced the equivalent elastic parameters as the same geometric dimension of the original mesosacle concrete model to locate the damage effectively. Compared with the original wave field, the energy field modified by wavelet transform can lower the effect of the environmental noise. Finally, we discussed the equivalent elastic parameters and the damage sizes to verify the robustness of this method which is applicable in monitoring and evaluating the damage in concrete structures.

2017, 49(4): 953-960. doi: 10.6052/0459-1879-17-007

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NUMERICAL ANALYSIS OF ASPERITY CONTACT MODEL BASED ON MOLECULAR DYNAMICS-GREEN'S FUNCTION METHOD

Huang Shiping, Wu Jie, Hu Junliang, Zheng Hengbin, Wang Weifeng

Rough contact is a prerequisite for surface friction. The rough contact behaviour such as the contact area, the pressure distribution and spatial distributions has been one of the core issues in contact mechanics and tribology. In this paper, the molecular dynamics-Green's function method (GFMD) is used to simulate the contact mechanism of the rough surface, where the asperity model is used for the rough surface, i.e., the surface is composed of numerous spherical asperities. Starting with the atomic or molecular force filed to consider the rough contact behaviour, the molecular dynamics-Green's function method is able to capture the mechanisms such as super-lubrication and multi-scale effect behaviour, which are not found in traditional continuum mechanics. The molecular dynamics-Green's function method demonstrates its high efficiency in large scale molecular dynamics simulations and is able to simulate the system composed of billions of atoms. The results of single asperity contact based on Hertz contact theory are very close to those simulated by the molecular dynamics-Green's function method, and the difference is less than 5%. It is found by numerical simulation that the contact area is linearly related to the contact force if the asperity heights follow the Gaussian distribution, and the contact force obtained by the asperity model is the upper limit given the same contact area. Although Asperity model is fast, it overestimates the stiffness of the elastomer due to the neglection of the interaction between the asperities. In real contact process, asperities have considerable effects on each other, especially on the deformation of the adjacent area, which makes the contact spots more discrete. The information of the real contact area and its spatial distributions, is of importance for the following simulation on surface friction.

2017, 49(4): 961-967. doi: 10.6052/0459-1879-17-084

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A BRIEF INTRODUCTION OF COMPLETED KEY PROGRAM PROJECTS ON MECHANICS IN 2016

Zhan Shige, Zhang Panfeng, Bai Kunchao, Wang Jianshan

The paper briefly introduced the completion and evaluation of 12 NSFC key program projects on mechanics in 2016. The projects list and the evaluation assessments provided by expert committee have been given in detail.

2017, 49(4): 968-972. doi: 10.6052/0459-1879-17-250

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