力学学报

2017, 49(3)

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2017, 49(3)

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REVIEW ON NONLINEAR DYNAMICS IN SYSTEMS WITH COULPLING DELAYS

Zhang Shu, Xu Jian

With the deep understanding towards the objective laws of nature, requirements on refinement and complexity in engineering system design are increasing. Many coupled dynamic system designs need to take into account the dynamics induced by the time delay existing in the coupling process. Such coupling time delay may come from the process of coupling with the sensing system, the actuation system and the control system. Coupling delays also extensively exist in the fields such as transportation system, system biology, electronic communication, neural and information networks and etc. Firstly, based on the concept of coupling delay, this paper reviews the recent research progresses on dynamics induced by such delay from the following four aspects: (1) the delay-centered mechanism of complex dynamics in coupled systems; (2) experimental foundation and realization of stabilizing coupled systems by utilizing time delay; (3) dynamics of fast-slow coupled system with time delay; and (4) synchronization and desynchronization of delayed neural networks. Some advances in the general theory of systems with coupling delay are highlighted including the coupling-delay-induced bifurcation and singularity with high codimention and the novel quantitative method of analysis, normal form computation for neutral delay differential equations, identification of time delay and nonlinear parameters in nonlinear systems with coupling delay and the relevant experiment, relaxation oscillation in the fast-slow system with coupling delay, and transition of modes of synchronization induced by coupling delay in network systems. Secondly, as for the application, some new results are presented in details such as the coupling-delay-induced chatter in grinding process and its mechanism, bifurcation with high codimension and complex dynamics induced by coupling delay in neural networks with inertial terms, and design and experiments of vibration absorber and isolator using coupling delay. Finally, some problems which are worthy of attention in near future are highlighted from perspectives of the general theory of systems with coupling delay and the potential applications.

2017, 49(3): 565-587. doi: 10.6052/0459-1879-17-123

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A MACROSCOPIC PHENOMENOLOGICAL CONSTITUTIVE MODEL FOR THE UNIAXIAL TRANSFORMATION RATCHETING OF SUPER-ELASTIC NiTi SHAPE MEMORY ALLOY

Zhou Ting, Kan Qianhua, Kang Guozheng, Qiu Bo

Super-elastic NiTi shape memory alloy (SMA) has been extensively used in many fields such as civil engineering, aerospace and bio-medical fields due to its good mechanical properties, including unique super-elasticity and shape memory effect. In practical applications, the SMA-based devices are unavoidable subjected to cyclic loadings at different stress levels. However, it is necessary to establish a cyclic constitutive model to describe the transformation ratcheting behavior, i.e., the peak strain and valley strain accumulate cyclically during forward transformation and reverse transformation. Based on the existing experimental results of the transformation ratchetting of the super-elastic NiTi shape memory alloy obtained under the stress-controlled cyclic tension-unloading tests with different peak stresses, the one-dimensional macroscopic phenomenological constitutive model of super-elastic NiTi shape memory alloy proposed by Graesser, where super-elastic behavior is reflected by the nonlinear evolution equation of back stress, was extended to describe the uniaxial transformation ratchetting within the framework of generalized visco-plasticity. In the extended model, the differences of characteristic variables and their evolutions between the forward transformation and reverse transformation were considered, the evolution equations of the start stress of forward transformation, the start stress of reverse transformation, maximum transformation strain and residual strain were introduced by the internal variable of relative accumulated inelastic strain. In the meantime, the correlation coefficients in these evolution equations were determined by the ratio of the peak stress and the finish stress of forward transformation. The comparison of the experiments and simulations shows that the extended model can reasonably describe the dependence of uniaxial transformation ratchetting of super-elastic NiTi shape memory alloy on the peak stress, and the simulated results are in good agreement with the experimental ones.

2017, 49(3): 588-596. doi: 10.6052/0459-1879-17-116

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SURFACE WAVES IN A PIEZOELECTRIC HALF-SPACE WITH SURFACE EFFECT

Zhou Weijian, Chen Weiqiu

The fast developments in nanotechnology enable the wide applications of piezoelectric nano-structures in nano-electromechanical systems, forming new research directions such as nanopiezotronics. Compared with the traditional macroscopic piezoelectric materials, nano-scaled piezoelectric materials present different mechanical properties, possibly due to the existence of surface effect, one of the main reasons for explaining the difference. This paper concerns the propagation of surface waves in a generally anisotropic piezoelectric half-space with surface effect. Stroh formalism, Barnett-Lothe integral matrices, and surface impedance matrices are adopted to theoretically derive the dispersion equations of surface waves. For transversely isotropic piezoelectric materials with the isotropic basal plane parallel with the sagittal plane, Rayleigh waves and B-G waves are found to be decoupled from each other, and their dispersion equations are derived in an explicit and compact form. It is rigorously shown that the velocity of Rayleigh waves should be smaller than that of the bulk waves polarized in the depth direction, whilst the velocity of B-G waves should be smaller than that of the bulk waves polarized in the direction perpendicular to the sagittal plane. In the numerical simulations, PZT-5H is taken as an example to numerically illustrate the influences of surface residual stress and electrical boundary conditions on the dispersion properties of surface waves. It is found that surface residual stress has a significant effect only on the first-order Rayleigh wave, and the B-G wave under the electric open-circuit condition propagates faster than under the electric closed-circuit condition. The theoretical predictions and numerical results presented in the paper should be helpful in understanding size-dependent dynamic behaviors of piezoelectric structures with surface effect and may provide a solid basis for the design of nano-sized surface acoustic wave devices as well as for the nondestructive testing of nano-sized piezoelectric structures.

2017, 49(3): 597-604. doi: 10.6052/0459-1879-17-152

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SHEAR RESPONSE OF GRAIN BOUNDARIES WITH HYDROGEN DEFECTS

Zhao Dongwei, Yu Wenshan, Shen Shengping

The segregation energy distributions of hydrogen in four α-Fe symmetric tilt grain boundaries (GBs) are analyzed by using molecular statics (MS), and then the shear responses of four GBs embedded with different number of hydrogen atoms at the room temperature are investigated by using molecular dynamics (MD) methods. To facilitate our quantitative analysis, the hydrogen density ρ is defined as the ratio between the number of hydrogen atoms and the GB area. At different hydrogen densities, the variations of initial critical stress of GB plasticity and GB migration displacements are analyzed, and the micro-deformation mechanisms in each GB with the presence of hydrogen atoms are analyzed as well. It is found that the hydrogen segregation energies are generally lower in GB than those inside grain, which lead four GBs to absorb hydrogen atoms in the vicinity of GBs. With the increase of hydrogen density ρ the critical stress of incipient plasticity as well as the flow stress could be reduced. Moreover, the micro-deformation mechanisms of fours GBs with hydrogen atoms are different from those of GBs without hydrogen atoms. In particular, presence of hydrogen atoms remarkably affects GB migration velocity. Thus, GB with hydrogen atoms may undergo a pure sliding deformation instead of the shear-coupling deformation for GB without hydrogen atoms. Meanwhile, in contrast to GBs without hydrogen atoms, the micro-structures of GB with hydrogen atoms drastically evolve upon loading. In addition, the diffusion and agglomeration of hydrogen atoms may lead to the formation of nanovoid in GBs.

2017, 49(3): 605-615. doi: 10.6052/0459-1879-17-132

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EFFECT OF VIBRATION EXCITATION ON HYPERSONIC AERODYNAMIC AND AEROTHERMODYNAMIC

Zhang Zijian, Liu Yunfeng, Jiang Zonglin

With the increasing of flight Mach number, the high-temperature gas effect of air has becoming remarkable, which has significant impacts on the aerodynamics and aerothermodynamic characteristics of hypersonic vehicles. Because of the complex mechanism and numerous key parameters of high-temperature gas effect, it has not been fully studied at home and abroad. When the high-temperature gas effect occurs, multiple nonlinear physical processes are coupled together. However, ground tests and numerical simulations can not decouple these processes and can not explain the key physical mechanisms. To solve this problem, a new two-step asymptotic approximation method combining theoretic analysis and numerical simulation is proposed. In this method, the oblique shock relation with vibration excitation effect is obtained by Newton iterative method, then the results are used as the boundary conditions of the boundary layer and it is solved numerically. By using this method, the effect of vibration excitation on the aerodynamics and aerothermodynamic characteristics of a two dimensional wedge is studied. The results show that, the vibration excitation process has great effect on the shock angle, the temperature, density, Mach number, and Reynolds number behind the oblique shock, but little influence on the pressure and velocity. The inviscid flow behind the oblique shock is coupled together with the boundary layer flow. The changes of multiple physical quantities, including the increase of velocity and the decrease of the temperature behind the oblique shock, and the decrease of the boundary layer thickness due to the increase of the Reynolds number, have an effect on the friction and aerodynamic heating in the boundary layer. Comparing with perfect gas model, vibration excitation increases the wall friction and decreases the wall heat flux of the wedge. By influencing the shock layer and the boundary layer respectively, the effects of vibration excitation on heat flux are strong coupled, while they are weak coupled on friction.

2017, 49(3): 616-626. doi: 10.6052/0459-1879-16-307

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ACCURACY VERIFICATION OF UNSTRUCTURED SECOND-ORDER FINITE VOLUME DISCRETIZATION SCHEMES BASED ON THE METHOD OF MANUFACTURED SOLUTIONS

Wang Nianhua, Zhang Laiping, Zhao Zhong, He Xin

With the great improvement in computer technology, computational fluid dynamics have progressed significantly. Even though it is fast and easy to obtain discretized results via numerical simulations, the validity and accuracy of the results need to be carefully validated and verified. As an important approach in verification and validation, the method of manufactured solutions (MMS) was widely applied in code verification, accuracy analysis and verification of boundary conditions. This paper first established the procedures for the MMS with scalar manufactured solutions and vector man-ufactured solutions. Verification of these two procedures was performed by comparing results of accuracy testing for a typical exact solution (2D inviscid isentropic vortex). The MMS procedures were then employed to the study of unstructured finite-volume discretization schemes, such as gradient reconstruction methods, convective fluxes discretization and diffusive fluxes discretization. It demonstrated that some schemes employing certain Green-Gauss based gradient degrade to 1st order on irregular meshes and discretization error increases significantly, while the least squares based gradient is insensitive to mesh irregularity. Besides, all tested convective fluxes discretization schemes were 2nd order accurate and they exhibited similar performance in terms of accuracy. But the method of computing the interface gradient was an essential factor affecting the accuracy of diffusive fluxes discretization.

2017, 49(3): 627-637. doi: 10.6052/0459-1879-16-260

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DEVELOPMENT OF NONLINEAR MECHANICS FOR LAMINATED COMPOSITE PLATES AND SHELLS

Liu Renhuai, Xue Jianghong

Laminated composite plates and shells are made from a variety of materials. They have quite different mechanical features compared with those made of single material, such as uncertain principal direction of the material, discontinuity of material between layers, highly geometrical and material nonlinearity, etc. Their failure modes include matrix cracking, debonding, delamination, crack deflection, multi delamination and delamination propagation, which are much more complex than those of single material. Based on different considerations, various methods have been proposed by scholars from different countries to study the failure of laminated composite plates and shells. This paper summarizes the fundamental theory of linear mechanics and reviews the development of nonlinear theories for laminated plates and shells. In particularly, theoretical systems and basic formulas are expatiated for the classical nonlinear theory of large deformation, the first order shear deformation theory, the high order shear deformation theory, the zig-zag theory, and the layer-wise theory. The relevance and differences among these theories are stated. Current research progress in the field of nonlinear mechanics for laminated composite plates and shells are overviewed and the latest achievements are introduced in research hotspots regarding the failure mechanism and optimization design of typical laminated composite plates and shells, the failure mechanism of laminated composite plates and shells in complex environments, material nonlinearity of composite plates and shells, failure mechanism of fiber reinforced delaminated composite plates and shells, and so on. Based on the review, prospects for future research in the area of nonlinear mechanics of laminated composite plates and shells are proposed.

2017, 49(3): 487-506. doi: 10.6052/0459-1879-16-253

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PROBLEMS AND CHALLENGES OF MECHANICS IN SHALE GAS EFFICIENT EXPLOITATION

Liu Zhanli, Zhuang Zhuo, Meng Qingguo, Zhan Shige, Huang Keh-Chih

Shale gas is unconventional natural gas stored in shale in free or absorbed forms and sometimes in free fluid phase. The exploitation of shale gas has become a promising field of green energy development in China. Although great success has been achieved in shale gas revolution in North America with the technique of hydraulic fracturing, there is only 5%~15% of the stored oil and gas could be exploited, which is still a puzzle for petroleum engineers. Compared with the North America, China's shale gas reservoirs are deep burial, the geologic construction conditions are complicated and natural quality is low, therefore, efficient exploitation is facing more difficulties and challenges. In recent years, aiming at the national major energy strategy and the frontier of technological development, China's academia and industry have carried out the preliminary study on some of the key scientific and technical issues. Around the new issues encountered in the shale gas extraction in Sichuan and Chongqing areas in recent three years, this paper introduces and summarizes the key mechanics problems and challenges that the high efficient shale gas extraction is facing, mainly includes the multifield coupling safe and high quality drilling mechanics, hydraulic fracturing and multi-scale fracture network formation mechanism and multi-scale seepage and desorption mechanism of shale gas, to solve the challenges in deep exploitation below 3500 meters in China, such as geologic sedimentation, different fracture development, increasing overburden pressure, the change of horizontal stress, etc. The deep shale gas exploitation is not only to adapt to the national energy demand, but also has scientific and engineering significance. To realize the efficient exploitation of shale oil and gas, it needs the interdisciplinary collaboration of mechanical engineering, petroleum engineering, geophysics, chemical engineering and environmental engineering to carry out basic theoretical research, physical simulation, numerical simulation and field experiment. It has been recognized that interdisciplinary research is the bridge and the key to breakthrough the technology bottleneck and realize the efficient exploitation of shale gas. It is necessary of the deep collaboration between mechanics, petroleum engineering, earth science and other disciplines to promote the development of shale gas and other unconventional oil and gas resources.

2017, 49(3): 507-516. doi: 10.6052/0459-1879-16-399

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AEROELASTIC MODEL OF REDUCED-ORDER FOR A SLENDER MISSILE

Yang Zhijun, Huang Rui, Liu Haojie, Zhao Yonghui, Hu Haian, Wang Le

In the design phase of slender missiles, it is essential to predict their aeroelastic/aeroservoelastic behaviors accurately. The accurate prediction, however, is faced with the tough problem of CFD for the aerodynamic loads on slender missiles. How to establish the aerodynamic models of reduced-order is the key technology to break through the bottleneck in the transonic aeroelastic analysis and control of the slender missiles. Although the aerodynamic reducedorder methods have made important progress in predicting the aerodynamic loads and aeroelastic response of the twodimensional airfoil, still there are few research reports about the aerodynamic reduced-order models of the more complex airplane models. In this study, the recursive Wiener model of reduced-order is constructed for the aerodynamic loads on a slender missile according to the training data of CFD, while the parameters of the model can be estimated via the predictorbased subspace identification algorithm and Levenberg-Marquardt algorithm. The recursive Wiener model of reducedorder can be integrated with the finite element model of the missile structure so that the aeroelastic/ aeroservoelastic model of reduced-order is established for the missile. The accuracy of the aeroelastic models of reduced-order is tested under different Mach number in the numerical simulations. The numerical simulations show that the aeroelastic models of reduced-order can accurately predict the unsteady aerodynamic loads and the aeroservoelastic frequency response of the slender missile model under different flight conditions.

2017, 49(3): 517-527. doi: 10.6052/0459-1879-16-358

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A COMPUTATIONAL MODEL FOR SEISMIC RESPONSE ANALYSIS OF UNDERGROUND STAUCTURES

Lin Gao

Under earthquake excitation, the deformation of underground structures is restricted by the surrounding soil media. The dynamic behavior of it displays quite differently from aboveground structures. Considerable progress has been made on the design and research of the underground structures since seventies-eighties of twentieth century. However, in the main, the widely used computational methods and guidelines in engineering design practice are based on rather simple assumptions, in reality, the actual soil conditions might be much more complex than ideally boundary conditions. Recent achievements of earthquake research on underground structures lie in the development of various computational methods for wave scattering problems of underground structures, such as the wave function expansion method, the boundary integral equation method etc. As the computation is somewhat complex, which impedes its application and dissemination in the engineering design practice. The author devotes himself to the improvement of the computational model for seismic analysis of underground structures, such that it achieves higher accuracy and efficiency, meanwhile it proves to be convenient for engineering design. To this end, a new model for seismic response analysis of underground structures is proposed. The model is versatile to deal with wave scattering and diffraction by canyons, subsurface cavities, subways and tunnels etc. In case of the presence of complex soil conditions like the layered half-space, a simple and effective technique is developed for the evaluation of Green's functions. Numerical examples are provided to validate the accuracy and efficiency of the proposed approach.

2017, 49(3): 528-542. doi: 10.6052/0459-1879-16-301

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REVIEW OF SOME RESEARCHES ON SUSPENSION OF SOLID PARTICLE IN NON-NEWTONIAN FLUID

Zhang Peijie, Lin Jianzhong

Suspension of solid particle in non-Newtonian fluid has a wide range of applications, and its special flow properties make it the core breakthrough point in some new technology fields. Meanwhile, the flow is more complex. Even in the case of low particle concentration, the characteristics of non-Newtonian fluid have an important influence on the microstructure of the whole system, which further affects the movement of solid particles. In this paper, the non-Newtonian fluid equation, particle motion equation and characteristic parameter of suspension of solid particle in non-Newtonian fluid are given, and the effect of these parameters is analyzed. The research findings, result analysis and open questions of some topics including the radial motion of single solid particle in a pipe, the interaction and aggregation of multi-particles, the chain structure formed by multi-particles, and motion of non-spherical particles are related. Finally, the topics mentioned above are summarized and prospected, and the concrete problems and contents that need to be studied deeply are given, which is aimed at providing references and basis for further research.

2017, 49(3): 543-549. doi: 10.6052/0459-1879-17-038

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SOME RECENT PROGRESSES IN NONLINEAR PASSIVE ISOLATIONS OF VIBRATIONS

Lu Zeqi, Chen Liqun

Vibrations in aircraft and marine structures, due to various extreme environmental loads, have been attributing factors in accidents and failures. Over the last decade, as the demands for vibration and shock isolation performance increasing, the general approaches following the conventional categorization of passive, active, semi-active and hybrid has been extensive presented. Nonlinear passive vibration isolation is the state of the art of vibration control techniques for combining robustness of the passive device and high performance of the active devices. This paper surveys theoretical and practical advances in nonlinear passive isolation of vibration in recent ten years. Stiffness and damping both nonlinearities is considered in modeling of vibration isolation system; Deterministic and stochastic analysis are both conducted on the investigation of the dynamic behavior. Initially, a review of a general approach to quantify the effectiveness of nonlinear vibrations isolation is presented. This is then followed by a review of high-static-low-dynamic stiffness vibration isolation, damping nonlinearity vibration isolation, two-stage nonlinear vibration isolation and nonlinear vibration isolation materi-als. The other vibration isolation methods considered in this review include chaotic anti-control technology, influence of internal resonance and usage of nonlinear energy sink. The article is closed by conclusions, which highlight resolved and unresolved problems and recommendations for future research treads.

2017, 49(3): 550-564. doi: 10.6052/0459-1879-17-064

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SUPERCRITICAL CO₂ WATER DISPLACEMENTS AND CO₂ CAPILLARY TRAPPING: MICROMODEL EXPERIMENT AND NUMERICAL SIMULATION

Hu Ran, Chen Yifeng, Wan Jiamin, Zhou Chuangbing

The CO₂ capillary trapping is an important scientific issue in geological carbon sequestration, but few researches focus on the trapping mechanism at pore scale under supercritical CO₂ condition. In this study, based on the high-pressure fluids-microscopy-micromodel experimental system, we performed drainage experiment, i.e. supercritical CO₂ displacing water, and imbibition experiment, i.e. water displacing CO₂, under the conditions of 45℃ and 8.5 MPa. The DSLR camera was used to capture pictures of CO₂-water two-phase immiscible flow and the microscopy was used to capture the capillary trapping behavior for the supercritical CO₂ at the pore scale. The computational fluid dynamic method was adopted to simulate the two-phase fluid flow processes. The numerical results are generally in agree-ment with the experimental observations, and further provide three-dimensional geometries on the interface during the drainage-imbibition processes and the trapped supercritical CO₂ droplet/cluster. Finally, the capillary trapping curve, i.e. the relationship between the initial CO₂ saturation and the residual saturation, was obtained from the numerical results, and we made an assessment of the three capillary trapping models, i.e. Land's, Jurauld's and Spiteri's trapping models. A comparison of the models performance indicates that Jurauld's model behaves slightly better than Land's model, whereas Spiteri's model behaves poorly. However, given that Land's model only contains one parameter of clear physical meaning, it is recommended for practical use.

2017, 49(3): 638-648. doi: 10.6052/0459-1879-16-237

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EMBEDDED STRONG DISCONTINUITY MODEL BASED MULTISCALE FINITE ELEMENT METHOD FOR STRAIN LOCALIZATION ANALYSIS

Lu Mengkai, Zhang Hongwu, Zheng Yonggang

Strain localization is a common factor that may lead to the failure of solid structure and its numerical analysis becomes an important aspect for the structural safety evaluation. Due to the heterogeneity and multiscale nature, however, traditional numerical methods need to resolve the structure at the fine scale to obtain reasonable results, which increases drastically the computational scale and cost. To solve this problem, an embedded strong discontinuity model based multiscale finite element method is proposed here. In this method, both coarse and fine scale elements are used to represent the structure. The embedded strong discontinuity model is first introduced into the fine element to describe the discontinuity and the corresponding additional displacement jump degree of freedom on the elemental level can be eliminated with the condensation technique, which keeps the dimensions of the stiffness matrix unchanged. Then, an enhanced multi-node coarse element technique is proposed, which can adaptively insert coarse nodes according to the intersection between the discontinuity line and coarse element boundary and thus guarantees the proper transformation of information between the fine and coarse elements. The problem can then be effectively solved on the coarse scale level. Moreover, a solution decomposition technique, in which the fine scale solution is decomposed into the downscaling and local perturbation solutions, is adopted to eliminate the unbalance forces within the unit cell in the elasto-plastic analysis. Finally, two representative examples are presented to demonstrate the accuracy and effectiveness of the proposed method through the comparisons with the results of the embedded finite element method.

2017, 49(3): 649-658. doi: 10.6052/0459-1879-16-397

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MESHLESS LOCAL STRONG-WEAK (MLSW) METHOD FOR IRREGULAR DOMAIN PROBLEMS

Yang Jianjun, Zheng Jianlong

The meshless local Petrov-Galerkin (MLPG) method is a representative meshless method, and is widely applied in computational mechanics. But, this method is necessary to execute the boundary integral operation, and it is always difficult to solve irregular domain problems. In order to remove this kind of limitation of the MLPG method, a meshless local strong-weak (MLSW) method is presented. The proposed method uses the MLPG method for domain discretization, adopts the meshless intervention-point (MIP) method for imposing the natural boundary conditions, and employs a collocation method for imposing the essential boundary conditions. Thus, the boundary integral is completely eliminated, and it favours to solve all kinds of irregular domain problem. Theoretically, the MLSW method deduced by coupling algorithm, not only has inherited the advantage of the MLPG method, which is always stable and accurate for numerical solution, but also has attained the superiority of the collocation-type method, which is naturally simple and flexible to cope with the domain of complex structure. Thereby, the method realizes advantageous complementarities of the weak-form method and the strong-form method. In addition, the MLSW method uses a moving least squares core (MLSc) approximation for constructing meshless shape function, which is an improvement for the traditional moving least squares (MLS) approximation. By replacing common basis function with core basis function, MLSc approximation is more stable and accurate, and also realizes a simple calculation for derivatives approximation. Early results with numerical tests have showed that the proposed new method is easy for numerical implementation, is accurate and stable for numerical solution, and is promising for engineering application.

2017, 49(3): 659-666. doi: 10.6052/0459-1879-16-383

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ANALYSIS OF STRAIN LOCALIZATION BY ENERGY EQUIVALENCE: Ⅰ. ONE-DIMENSIONAL ANALYTICAL SOLUTION

Wu Shouxin, Wei Jirui, Yang Shuwei

Based on the first law of thermodynamics and the nonlocal plasticity theories, a new approach is proposed to solve the strain localization problems induced by strain softening. For each material point, two state spaces, local and nonlocal state spaces, are defined such that the local internal variable can be mapped, from the local state space by integral transformation with the nonlocal weighting function, into the nonlocal internal variable in the nonlocal state space. During strain softening, the plastic deformation follows the normal flow rule in the local state space and the softening law is introduced in the nonlocal state space. It is assumed that the strain softening is a global material behavior and the plastic energy dissipation within the entire material body is always positive. However, the balance of momentum is still satisfied locally. By equating the rates of the plastic energy dissipation in the two state spaces during strain softening, the localization zone and the plastic strain distribution become well-defined. Analytical solution for the one-dimensional strain localization is developed, and it is well shown that the plastic strain distribution and load-displacement curves are well-defined by the material properties, such as the softening modulus and internal length scale, as well as the geometry of the material body. For the Gaussian-type weighting functions the width of the localization zone is approximately six times the internal length scale. Numerical example demonstrates that the size of the localization zone decreases as the internal length scale is reduced, and the distribution of the plastic strain in the localization zone becomes more concentrated when the internal length scale becomes smaller. As the internal length scale approaches to zero, the solution reduces to the one predicted by the conventional local plasticity theory.

2017, 49(3): 667-676. doi: 10.6052/0459-1879-16-328

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A TRANSVERSELY ISOTROPIC VISCO-HYPERELASTIC CONSTITUTIVE MODEL FOR SHORT FIBER REINFORCED EPDM

Tan Bingdong, Xu Jinsheng, Sun Chaoxiang, Jia Yunfei, Fan Xinggui

Short fiber reinforced EPDM inhibitor film is a new type composite material, which has been applied in solid rocket motor winding and coating. Based on viscoelastic theory and fiber reinforced continuum mechanics theory, a transversely isotropic visco-hyperelastic constitutive model is proposed to describe strain rate dependent mechanical behaviors under vibration, impact and other loading conditions. The strain energy function is decomposed into hyperelastic strain energy and viscous strain energy, in which hyperelastic strain energy includes two parts: representing the strain energy from isotropic rubber matrix and anisotropic fiber tensile deformation. A macro-phenomenological model is proposed to characterize the viscous response from rubber matrix and fibers. Then, select the function form of each strain energy. After a series of mathematical transformation, substitution and superposition, the final form of stress and strain is determined. Moreover, the specific steps to obtain model parameters are defined. Finally, the predicted and experimental results are compared and analyzed, which indicates high accuracy of the proposed model. Studies show that it can effectively predict their nonlinear and strain rate dependent mechanical behaviors in the fiber direction from 0° to 45° at low strain rate. It is concluded that the proposed model is easy to realize finite element development, which has reference value for the structural integrity analysis of solid rocket motor.

2017, 49(3): 677-684. doi: 10.6052/0459-1879-16-380

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THE CLOSED-FORM SOLUTION OF STEADY STATE RESPONSE OF HYSTERETIC SYSTEM UNDER STOCHASTIC EXCITATION

Liu Jun, Chen Lincong, Sun Jian-Qiao

The hysteretic system is one of the typical strongly nonlinear systems. Hysteretic force depends not only on the instantaneous deformation but also on the past history of deformation. In the last few decades, random vibration of hysteretic system has been studied extensively, but no closed-form solution of random response of hysteretic systems is available so far. In this paper, the newly developed nonlinear random vibration scheme called iterative method of weighted residuals is explored to obtain the closed-form solution of steady-state probability density function (PDF) of the Bouc-Wen hysteretic system under Gaussian white noise excitation. First, a Gaussian PDF is obtained with equivalent linearization technique, which is used as a weighting function. Then, the method of weighted residuals is utilized to determine the non-Gaussian PDF of exponential polynomial type. Finally, an iterative procedure is introduced to improve the accuracy of the solutions obtained from the method of weighted residuals. As an illustrative example, the steadystate stochastic response of the steel fiber reinforced ceramsite concrete column under random excitation is studied, in which the hysteretic parameters associated with Bouc-Wen hysteretic model is identified from the pseudo-static test by using the method of least square. Compared to the Monte Carlo results, the accuracy of results obtained from equivalent linearization method is poor. The results obtained from weight residue method can show the nonlinearity of Bouc-Wen systems, but its accuracy is still unsatisfactory. The iterative method of weight residuals can lead to results with higher accuracy. In the case of stronger random excitation, the progressive iterative method of weighted residuals has high efficiency. The obtained solutions agree well with the Monte Carlo simulation data. The proposed closed-form solution of PDF of Bouc-Wen hysteretic system not only is significant to the civil engineering, but also can be a benchmark to examine the accuracy of solutions obtained by other methods.

2017, 49(3): 685-692. doi: 10.6052/0459-1879-17-003

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QUASI-SYMMETRY AND NOETHER'S THEOREM FOR FRACTIONAL BIRKHOFFIAN SYSTEMS IN TERMS OF CAPUTO DERIVATIVES

Zhang Yi

The dynamical behavior and physical process of a complex system can be described and studied more accurately by using a fractional model, at the same time the Birkhoffian mechanics is a generalization of Hamiltonian mechanics, and therefore, the study of dynamics of fractional Birkhoffian systems is of great significance. Fractional Noether's theorem reveals the intrinsic relation between the Noether symmetric transformation and the fractional conserved quantity, but when the transformation is replaced by the Noether quasi-symmetric transformation, the corresponding extension of Noether's theorem is very difficult. In this paper, the Noether quasi-symmetry and the conserved quantity for fractional Birkhoffian systems in terms of Caputo derivatives are presented and studied by using a technique of timereparametrization. Firstly, the technique is applied to the study of the Noether quasi-symmetry and the conserved quantity for classical Birkhoffian systems and Noether's theorem in its general form is established. Secondly, the definitions and criteria of Noether quasi-symmetric transformations for fractional Birkhoffian systems are given which are based on the invariance of fractional Pfaff action under one-parameter infinitesimal group of transformations without transforming the time and with transforming the time, respectively. Based on the definition of fractional conserved quantity proposed by Frederico and Torres, Noether's theorem for fractional Birkhoffian systems is established by using the method of timereparametrization. The theorem reveals the inner relationship between Noether quasi-symmetry and fractional conserved quantity and contains Noether's theorem for the symmetry of fractional Birkhoffian system and Noether's theorem for classical Birkhoffian system as its specials. Finally, we take the Hojman-Urrutia problem as an example to illustrate the application of the results.

2017, 49(3): 693-702. doi: 10.6052/0459-1879-16-350

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PSEUDO ARC-LENGTH NUMERICAL ALGORITHM FOR COMPUTATIONAL DYNAMICS

Ning Jianguo, Yuan Xinpeng, Ma Tianbao, Li Jian

Differential equations are often used to describe the dynamic problems. Classical approaches are always hard to solve it in engineering practice due to its characteristics of strong discontinuity, rigidity and shock singularity, among which singularity problem is one of the most difficult and hot issues among scholars. Pseudo arc-length numerical algorithm is proposed for singularity problems in computational dynamics, whose basic idea is to introduce a pseudo arc-length parameter in the original governing equations so that a constraint equation is added. Under the action of a pseudo arc-length parameter, the original discrete elements are distorted to achieve the goal of eliminating or weakening singularity. Firstly, this paper gave an introduction about the pseudo arc-length method for solving the singularity problem in steady diffusion-convection equations. Then the local pseudo arc-length algorithm is proposed for hyperbolic conservation laws. This algorithm has two steps. The first step is to determine the location of the strong discontinuity and the second one aims to eliminate or reduce the singularity by reconstructing the local mesh. Secondly, a global pseudo arc-length algorithm is put forward for high dimensional problems, which can reconstruct the mesh in whole area. Since the reconstructed mesh can adaptively catch the singularity points, the singularity is greatly reduced. Thirdly, the threedimensional global pseudo arc-length algorithm and its computational difficulties in numerical algorithm convergence caused by large grid distortion in three-dimensional space are presented. Then the combination of block reconstruction and integral calculation strategy is adopted in the algorithm design process to achieve the pseudo arc-length numerical algorithm in three-dimensional space. Finally, numerical examples were employed to verify the validity of the pseudo arc-length algorithm.

2017, 49(3): 703-715. doi: 10.6052/0459-1879-16-385

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CONDITION AND INFLUENCE FACTOR OF ROCK BURST IN HIGH GASSY COAL SEAM

Yin Wanlei, Pan Yishan, Li Zhonghua

Aiming at the problem of rock burst in high gassy coal seam, the occurrence conditions of rock burst are obtained by analytical analysis, the influence rule of main factors on the radius and the critical stress of the critical plastic zone are analyzed. In connection with Wulong mining practice, the effects of the coal modulus ratio, gas pore pressure, support stress, and internal friction angle on rock burst of in high gassy coal seam are analyzed in comparison. The results show that, non excavated solid coal plays a limiting role in the deformation of the roadway because of the spatial effect with excavation face nearby roadway heading face about high gassy coal seam. It reduces the danger of rock burst, the support stress of the roadway is increased in a certain distance from the rear along with the excavating face ahead. At the same time, along with the gas desorption seepage, the pore pressure of the tunnel wall is decreased, and the risk of rock and the critical stress of the high gassy coal seam tunnel decrease rapidly with the increase of the modulus ratio λ=E and the pore pressure, and they increase with the increase of the support stress, the radius of the critical plastic zone increases with the increase of the internal friction angle, the relationship between the critical stress and the internal friction angle is not monotone, there exists a minimum value, when the internal friction angle is less than the minimum value, the critical stress decreases with the increase of the internal friction angle; when the internal friction angle is larger, the results are opposite.

2017, 49(3): 716-725. doi: 10.6052/0459-1879-16-302

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A KIND OF STRENGTH AND YIELD CRITERION FOR GEOMATERIALS AND ITS TRANSFORMATION STRESS METHOD

Wan Zheng, Qiu Rendong, Guo Jinxue

It is assumed that the failure of geomaterials is determined by stress ratio between shear stress and normal stress on the characteristic surface based on its friction behavior. The concept of effective stress ratio is proposed and it is expressed by the ratio between shear stress and normal stress on characteristic surface. The stress ratio on characteristic surface can be expressed as the tangent value of straight line deducted by the intercept circumscribing the mohr's circle in σ-τ coordinates in two-dimensional condition. It is assumed that there is a three-dimensional physical space plane in XYZ space considering every two adjacent physical coordinate plane under three-dimensional space. The shear stress ratio on characteristic surface in three-dimensional space is the determinant factor influencing the failure behavior of material and the proposed criterion can be signed as a criterion. SMP (spatially mobilized plane) criterion and generalized Mises criterion are two special cases of the a criterion. When the value of intercept in two-coordinates is zero, the proposed criterion is degenerated to SMP criterion. When the value of tangent is zero, the proposed criterion is degenerated to generalized Mises criterion. When the intercept and angle of circumscribing line are not zero, the proposed criterion in deviatoric plane is between the above those. The curved triangular form is exhibited between the curves of SMP criterion and generalized Mises criterion in deviatoric plane. A coupling of compression and shear behavior yield criterion is adopted and a power function is adopted as failure criterion. A shape function is proposed based on the proposed criterion in deviatoric plane. The criterion expressed by p and q is substituted by the proposed criterion expressed by three dimensional stresses and the transformation stress equations are deduced based on proposed criterion. In general a constitutive model expressed by p and q can be converted as a three-dimensional model simply. Through yield and strength behaviors and a variety of stress paths test contrast, the rationality of the proposed criterion and transformation method are verified.

2017, 49(3): 726-740. doi: 10.6052/0459-1879-16-297

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THE INTRODUCTION OF APPLICATION PROJECTS ON MECHANICS IN 2017

Zhan Shige, Zhang Panfeng, Wang Jianshan, Cao Dongxing

The paper introduced the applications for NSFC programs on mechanics in 2017. The statistics of application projects for General Programs, Young Scientists Fund, Fund for Less Developed Regions, Key Programs, Excellent Young Scientists Fund, National Science Fund for Distinguished Young Scholars, and Joint Research Fund for Overseas Chinese Scholars and Scholars in Hong Kong and Macao are presented and compared with applications in 2016.

2017, 49(3): 741-742. doi: 10.6052/0459-1879-17-140

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2017 Vol. 49, No. 3

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