力学学报

2017, 49(1)

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2017, 49(1): 1-2.

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ESSENTIAL ISSUES AND THEIR RESEARCH PROGRESS IN TUNNEL AND UNDERGROUND ENGINEERING

Zhang Dingli

As three essential issues in tunnel and underground engineering contain stability of surrounding rocks, interact relation between support and surrounding rock as well as structural dynamic response of a support system are also the key problems in subject study.All around these issues, this paper emphatically analyzes the surrounding rock mechanical characteristics and load effect, and establishes mechanical model of internal and external surrounding rock.Based on the study of stability of structure layer in model above, analytic formula of ground reaction curve and computing method of surrounding rock load effect are given.According to the analysis of interact relation between support and surrounding rock, this interactional dynamic process is divided into four stages:free ground deforming, advance supporting, preliminary supporting, secondary supporting, thus description method of the dynamic process is raised.On idea of generalized load and special load, basic functions of support: "mobilizing" and "assisting" are proposed, then their implementations are clarified, which are"mobilizing" surrounding rock to bear the load reinforcement by applying surrounding rock reinforcement, advance reinforcement and bolt support, "assisting"surrounding rock to bear the load by using the supporting structure.Aiming at the complex tunnel support system, the concept of dynamic optimization of multi-objective and staged synergistic effect is put forward, which can realize the coordination of various supporting structures in terms of time and space to improve the reliability.In view of the safety characteristics of extremely unstable complex surrounding rock, the safety accident mechanism model of three patterns is established.A new concept of safety classification is put forward based on the characteristics of engineering response, and a gradation index system and classification method are established.On account of the underwater tunnel and water-enriched surrounding rock, three patterns of water inrush mechanism model are established, and the theory and method of safety control based on deformation control of surrounding rock are put forward.At last, the hotspot and core problems of the discipline development are analyzed and prospected.

2017, 49(1): 3-21. doi: 10.6052/0459-1879-16-348

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MECHANICAL MECHANISM AND DEVELOPMENT TREND OF WATER-INRUSH DISASTERS IN KARST TUNNELS

Li Shucai, Wang Kang, Li Liping, Zhou Zongqing, Shi Shaoshuai, Liu Shang

The water-inrush disasters in karst tunnels are commonly characterized by strong outburst, high water pressure, mass flow and multi-type, and its evolutionary process and dynamic instability is very complex and still unclear.The occurrence condition, criterion and safety thickness of different types of water inrushes are proposed, and the development trend of water inrush mechanism are analyzed in the present study.Firstly, the conception, type and three constituted elements of water inrush are introduced.Secondly, currently research achievements of mechanical mechanism and model, instability criterion and the minimum safety thickness of water inrush are summarized.Finally, the current situation and problems of water-inrush mechanism are analyzed from the point of the three constituted elements.The development trend and research are proposed, including (1) solid-liquid-gas replacement mechanism and energy-releasing pattern of the sources of water inrush disasters, (2) multiphase material migration and evolution law of flow regime in water-inrush passage, (3) dynamic catastrophe mechanism of water-proof structures, and (4) analysis method for simulating the forma tion of water-inrush passage.

2017, 49(1): 22-30. doi: 10.6052/0459-1879-16-345

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THEORETICAL ANALYSIS OF INTERACTION BETWEEN SURROUNDING ROCKS AND LINGING STRCTURE OF SHIELD TUNNEL BASED ON DRUCKER-PRAGER YIELD CRITERIA

He Chuan, Qi Chun, Feng Kun, Xiao Mingqingy

In calculating the load for segment lining structure of shield tunnel, the soil column or pressure arch theory are often used to describe surrounding rock loosening pressure.But when it comes to the deep-buried condition and the deformation pressure should be calculated, this method is considered as unreasonable and is difficult to apply.In view of this, based on the Drucker-Prager yield criterion, an analytical elasto plastic solution is derived for the interaction between surrounding rock and lining structure considering the influence of seepage effect, and the formula of the relationship between the support pressure and some key parameters such as the stress and displacement of surrounding rock elastic and plastic zone as well as the radius of the plastic zone is given.The analytical results can be applied in the determination of the load of the lining structure by establishing the static equilibrium state of the surrounding rock and the lining structure and finding the intersection point of the two curves.Further, rigidity reduction factor is induced to equivalent considering the influence of the overall rigidity decrease of assembled segment liner for the existence of joints to the interaction of surrounding rock and lining structure.In the load determination, the influence of the fluid-solid coupling effect during construction and seepage force on support characteristic curve of lining structure is also simplified considered.Finally, an engineering instance of underwater shield tunnel is introduced to compare the calculated load with the measured value and numerical simulated value.The results show that the caculated analytical load values of segment lining structure are greater by 28% and 12% comparing to measured values during the construction period and the stable period, and are greater by 5% comparing to numerical simulated value during the stable period, respectively.The research results of this paper can provide some reference for the design and construction of similar projects.

2017, 49(1): 31-40. doi: 10.6052/0459-1879-16-344

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AN APPROACH FOR PREDICTING THE EFFECTIVE PROPERTIES OF MULTIPHASE COMPOSITE WITH HIGH ACCURACY

Zhu Hehua, Chen Qingy

The effective medium approach is one of the common micromechanical methods, which can be utilized to predict the material's effective properties and set up the quantitative relationship between the material's microstructures and macroscopic properties.It is helpful and meaningful for the new material design and reducing the (experimental) workload to use these micromechanical estimations of the material's properties.However, the calculation accuracy will decline when the effective medium method is adopted to estimate the effective properties of the composite with high volume fraction of inclusions.Therefore, in this paper the two-phase composite is taken as the example firstly and the strain of the reference medium is assumed to be the product of the average strain of the matrix and a modifying tensor.Then the expressions of the effective modulus are derived with the proposed reference medium.What's more, the solutions for modifying tensor are reached by using the achievement we obtained recently.Further, through optimizing the reference medium repeatedly, with the help of multi-level homogenization scheme, the proposed modified method is extended to predict the properties of the multiphase composite with many types of inclusions.To verify our proposed framework, the predictions are compared with the experimental data and the results of existing models.The comparisons show that the estimations of the presented method are more reasonable and acceptable.When the volume fraction of inclusions is higher, the calculation accuracy of the presented method in this paper is better than those of the existing effective medium methods.

2017, 49(1): 41-47. doi: 10.6052/0459-1879-16-347

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AERODYNAMIC LOAD AND STRUCTURE STRESS ANALYSIS ON HOOD OF HIGH-SPEED RAILWAY TUNNEL

Wang Yingxue, Gao Bo, Ren Wenqiang

When high speed train passes through tunnel, aerodynamic effect will be induced.Setting hood at tunnel entrance is one of the convenient and effective measures for controlling aerodynamic effect.While the hood usually lay at tunnel entrance, in a long run, the aerodynamic load on the structure also should not be overlooked.In this paper, using Ansys-workbench simulation platform, the fluid structure coupling character induced by aerodynamic load on single top opening hood was analyzed.The research results showed that the extra-pressure stress induced by aerodynamic load was notable.To the train of running speed 350 km/h, the induced extra pressure stress on hood structure can reach 80 kPa.On the tunnel hood, the region around the openings appeared a relative high extra pressure stress.Since the tunnel is used for double railway line, the variation law of extra pressure stress on the tunnel hood inertial side wall of close to and far from train is almost same, while the stress pressure on inertial side wall of close to train is a little larger than that on the other side.Like the compression wave transportation in tunnel, the extra pressure stress induced by aerodynamic load also shows reciprocating transmission characteristics.The reason of stress concentration around the hood openings was deduced and showed that hood structure condition is the intrinsic fact for resulting in the detrimental effect.These conclusions on aerodynamic load are advisable for tunnel hood design and safety checking.

2017, 49(1): 48-54. doi: 10.6052/0459-1879-16-343

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SEISMIC RESPONSE OF SUBWAY STATION WITH LARGE SPAN AND Y SHAPED COLUMN

Tao Lianjin, Liu Chunxiao, Bian Jiny, Wu Binglin, Li Jidongyy, Xu Youjun

Along with the development of subway construction, a new type of structure with long span and Y shaped column comes up.It is different from the existing subway station structure, the space is tall and spacious, which shows a comfortable environment.In order to study the seismic performance of subway station structure with this new type, taking Xinhua Street station of the Beijing Metro Line 6 as engineering background, FLAC^3D was used to build the soilunderground structure dynamic model of three-dimensional finite difference to simulate the response process under the Xinhua Street artificial seismic wave excitation.Emphasis is put on the analysis of the law of acceleration, displacement and strain of both Y shaped column and side wall of the station.The numerical results are also compared with the shaking table test.The results show that the numerical results are basically identical with the shaking table test, which reflects the similar structure response.The maximum acceleration of Y shaped column occurred at the position just a little down from the top of the column, not at the top.Strain changes suddenly at the bifurcation position of Y shaped column, where this position also has the largest response displacement relative to the bottom of column and with abrupt change, so this is the part to be reinforced in aseismic design.The acceleration and change of displacement of Y shaped column are both larger than side wall.The results above may provide reasonable reference and guidance to improve the seismic performance and seismic design for similar subway station structure.

2017, 49(1): 55-64. doi: 10.6052/0459-1879-16-346

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NUMERICAL SIMULATION OF EROSION AND TRANSPORT OF FINE SEDIMENTS BY LARGE EDDY SIMULATION

Bai Jing, Fang Hongweiy, He Guojiany, Xie Chongbao, Gao Hong

In general Reynolds-averaged simulation (RANS) is used in the traditional numerical simulation of water flow and sediment transport.Large eddy simulation (LES) can reflect flow structures more accurately and give more details of water flow compared with RANS.The development of computing technology makes it possible to study the rules of water flow and sediment transport by an LES model.In this paper, we tried to introduce boundary conditions for suspended sediment transport for the LES model under the net-erosion condition.Water flow and sediment transport in a cyclic case and a one-way flow case were calculated via the LES model with a dynamic sub-grid stresses module and a suspended sediment calculation module in the paper.Direct numerical simulation (DNS) results were used to calibrate the LES model and the results from LES showed good agreements with the DNS results.The distribution characteristics of sediment concentration, turbulence intensity and turbulent fluxes of sediment were explored in the paper.Under the neterosion condition, the equilibrium sediment concentration profile was coincident with the line of the Rouse equation.It showed that the turbulence intensity and turbulent fluxes of sediment had peak values near the bottom and then decreased rapidly along the vertical direction.The turbulent viscosity and diffusion coefficients were calculated and their peak values were or near the mid-depth of water.The turbulent Schmidt number was not constant along the vertical direction, and it was larger near the free surface and the bottom while it was smaller near the mid-depth of water flow.

2017, 49(1): 65-74. doi: 10.6052/0459-1879-16-235

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EFFECT OF COMPRESSION SURFACE DEFORMATION ON AERODYNAMIC PERFORMANCES OF WAVERIDERS

Cui Kai, Xu Yingzhou, Xiao Yao, Li Guangli

A waverider is a type of hypersonic lifting body that has the entire bow shock underneath the body as well as attached to the leading edge when flying at its design Mach number.Present research for improving the aerodynamic performance of waveriders mainly focused on searching an optimal profile of the leading edge on the condition of given a specific generating flow field.In order to further extend the design space of waveriders, a novel design method that is based on a local shape deformation technique is presented in this paper.Moreover, an inviscid analysis-based optimization study was carried out to research the effect of compression surface deformation on aerodynamic performances of waveriders by integrating the increment-based parameterization method, the computational fluid dynamic analysis, and the differential evolution algorithm.Afterwards, six selected waverider configurations were polished to blunt leading edges, and then their aerodynamic performances were evaluated by solving the Navier-Stokes equations.The results show that both the L/D and the relative pressure center coefficient of the waveriders produce significant changes with the variation of compression surface shape.Among all waveriders, the maximal difference of the L/D is more than double.Even by considering the lift constraint, the increment of the L/D is more than 14 percent in comparison with the baseline configuration.In addition, the value of relative migration of the relative pressure center coefficients is remarkable.

2017, 49(1): 75-83. doi: 10.6052/0459-1879-16-041

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A COMPARATIVE STUDY OF TWO TURBULENCE MODELS FOR MAGNUS EFFECT IN SPINNING PROJECTILE

Shi Lei, Yang Yunjun, Zhou Weijiang

Magnus force and moment must be predicted precisely during calculating trajectories and designing rotating projectiles.Domestic studies have focused on adult spin projectile, and foreign studies have not compared turbulence model utility in spinning wind-body combination either.This paper simulated the flow field around a spinning wind-body combination by solving unsteady compressible three dimensional Navier-Stokes equations with dual time step method.At the same time the discrepancy between Splalrt-Allmaras (SA) and k-!shear stress transport (SST) turbulence models are studied.For both turbulence models, dynamic coefficients have a good agreement with the Arnold Engineering Development Center (AEDC) experimental data and Army Research Laboratory (ARL) computational data.Flow field parameters such as velocity gradient, pressure magnitude, show significant change in the latter half profile due to spin.Distortion of boundary layer in middle and rear part is conspicuous.Asymmetric distortion of circumferential surface pressure and shear stress is the fundamental reasons for the Magnus effect.Flow field parameters on the left side of body show larger variance between SA and SST turbulence models than the right side, indicating that speed pulse and pressure fluctuation are stronger on the left.The turbulent viscosity coefficient near the wall computed by SA is larger than SST.According to the slice of y=0 m, surface pressure shows SA is smaller than SST, reaching a maximum difference of 6%, and shear stress of SA is larger than SST, up to a maximum difference of 35%.The inhibition strength for flow separation indicates that SA is stronger than SST.

2017, 49(1): 84-92. doi: 10.6052/0459-1879-16-151

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NUMERICAL ANALYSIS OF UNSTEADY MOTION IN SHOCK WAVE/TRANSITIONAL BOUNDARY LAYER INTERACTION

Tong Fulin, Li Xinliangy, Tang Zhigong

The unsteadiness in shock wave and boundary layer interactions is one of foundation problems in the aerodynamic design of high-speed vehicles.Most previous researches have focused on laminar and turbulent interaction.The intrinsic physical origin of separation shock low-frequency oscillation is still under debate.There exist two utterly opposite theoretical explanations, upstream influence and downstream influence.The analysis of unsteady motion in shock wave and transitional boundary layer interactions are helpful to aware of the effects of boundary layer state and separation bubble structures on low-frequency oscillation, which providing an insight to point out new direction for forcing mechanism.A numerical analysis of unsteady motion in shock wave and transitional boundary layer interaction for a 24 deg compression ramp at Mach 2.9 is performed by the mean of direct numerical simulation.The blowing and suction disturbances are added upstream at specified stream wise locations to induce the interaction of shock wave with early stage of transitional boundary layer in compression ramp.Firstly, the reliability of the used program is verified.Secondly, the intermittency and oscillation of shock motion are then analyzed in detail.Through analysis of power spectral density of wall pressure signals, effects of separation bubble structure on unsteady motion are studied.Finally, the physical mechanisms of low-frequency oscillation are initially discussed.Results indicate that the unsteady shock motion is highly intermittent, the characteristic of shock oscillation is low-frequency.The time scale is about 10 times the magnitude of fluctuating signals in the incoming boundary layer.Three dimensional structure of separation bubble has little effect on the low-frequency unsteadiness.Based on the low-pass filtered instantaneous flow fields, evidence is found of a correlation between the low-frequency oscillation of shock and the contraction/dilation of separation bubble in the downstream.

2017, 49(1): 93-104. doi: 10.6052/0459-1879-16-224

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ADAPTIVE CONSISTENT HIGH ORDER ELEMENT-FREE GALERKIN METHOD

Shao Yulong, Duan Qinglin, Gao Xin, Li Xikui, Zhang Hongwu

The recently developed consistent high order element-free Galerkin (EFG) method not only dramatically reduces the number of quadrature points in domain integration but also accurately passes the linear and quadratic patch tests, and remarkably improves the computational efficiency, accuracy and convergence of the standard EFG methods.On this basis, this work presents the h-adaptive analysis for consistent high order EFG method by taking advantage of the convenience of the EFG method in adding approximation nodes locally.The proposed method adaptively determines the region which needs nodal refinement according to the gradient of the strain energy density.The generation of the new approximation nodes is based on the multi-level local mesh refinement of the background integration mesh.The gradual transition between the regions with and without nodal refinement is also considered.The relative error of the strain energy in two successive computation is adopted as the stop-criterion of the adaptive process.The proposed adaptive meshfree method is applied to the analysis of stress concentration caused by geometry, external boundary loads and body forces.Numerical results show that the developed method is able to refine the region with high stress gradient adaptively and to generate reasonable distribution of approximation nodes automatically.In comparison with the existing adaptive schemes of the standard EFG method, the proposed method shows remarkable advantages on computational efficiency, accuracy and the smoothness of the resulting stress fields.In comparison with the consistent high order EFG method using uniform nodal distribution, the proposed adaptive method dramatically reduces the number of computational nodes.As a consequence, it significantly improves the computational efficiency and accuracy of the consistent high order EFG method for the analysis of problems with local high gradients such as stress concentration.

2017, 49(1): 105-116. doi: 10.6052/0459-1879-16-252

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A MODIFIED MODE II DYNAMIC FRACTURE TEST TECHNIQUE BASED ON SHTB

Zou Guangping, Chen He, Chang Zhongliang

Dynamic fracture toughness under impact shear loading is an essential aspect in fracture behavior and mechanical property of material.Experiments have been done by several researchers using different specimens and test methods in order to measure mode II fracture toughness.But due to crack opening during loading process, the results obtained in these tests are not mode II but mixed mode I+II.Since crack opening are not be considered, dynamic shear fracture toughness of material can not be accurately detected.In view of this problem, a modified compact tension shear (MCTS) specimen based on split Hopkinson tension bar (SHTB) apparatus is proposed in this paper.The specimen was constrained with special designed clamp to prevent crack opening, so mode II fracture are ensured.Numerical analysis was carried out using experimental-numerical method.The incident pulse detected in test are introduced in ANSYS-LSDYNA as input pulse.Stress intensity factor at crack tip of MCTS specimen was calculated by relative displacement of corresponding nodes on crack surface in two directions.Simulation of compact tension shear (CTS) specimen was also done with same incident pulse as control.In addition, experimental study was also carried out using digital image correlation method based on SHTB apparatus to validate numerical results.Experimental results shows that during loading process, MCTS specimen ensures K_I$\ll $K_II and crack opening are not observed.However, for same incident pulse, the maximum mode I stress intensity factor of CTS specimen is even higher than mode II.Which indicates that dynamic shear fracture toughness of material can be measured effectively using MCTS specimen.This work provides an effective and convenient test technique for evaluating dynamic properties of a certain material.

2017, 49(1): 117-125. doi: 10.6052/0459-1879-16-239

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A 2.5-D COUPLED FE-BE MODEL FOR THE DYNAMIC INTERACTION BETWEEN TUNNEL AND SATURATED SOIL

He Chao, Zhou Shunhua, Di Honggui, Xiao Junhua

This paper presents a 2.5-D coupled FE-BE model to simulate the three-dimensional dynamic interaction between saturated soils and tunnels with arbitrary sections.The tunnel is modeled using 2.5-D FEM and the ground is modeled using 2.5-D BEM for saturated porous media.The auxiliary problems are introduced to eliminate the Cauchy singularity of the 2.5-D boundary integral equation.The coupled FE-BE equations are obtained using the continuity conditions on the soil-tunnel interface.The presented model is appropriate for tunnels with arbitrary sections and high computational efficiency.The model is verified through the comparison with the existing models.Finally, a case study of dynamic responses of a quasi-rectangular tunnel in saturated soil due to moving loads is presented.The effects of soil permeability on displacements and pore pressure are investigated.The results show that:(1) The pore pressure decreases drastically with the increment of soil permeability, while displacements are not susceptible to soil permeability;(2) the pore pressure and displacements are mainly distributed in the vicinity of 2m around the loading point;(3) In the direction of gravity, the dissipation of the pore pressure beneath the tunnel is faster than that of displacements;the distributions along the depth to tunnel invert of pore pressure and axial displacement are evidently influenced by the soil permeability.

2017, 49(1): 126-136. doi: 10.6052/0459-1879-16-176

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THE INTERVAL ANALYSIS OF MULTILAYER-METAMATERIALS WITH PERFORATED APERTURES BASED ON CHEBYSHEV EXPANSION

Liu Jian, Lei Jirong, Xia Baizhan

Up to now, the response analysis and optimization of acoustic metamaterials are mostly based on deterministic parameters and deterministic models.However, in the real engineering world and structure design fields where there are many uncertainties, such as the uncertain of material properties and geometric parameters.If the effects of uncertain variables on analysis and optimization of acoustic metamaterials are not taken into account, the analysis and optimization results may not true.Aiming at this problem and situation, in this paper where the interval model is introduced into multilayer-metamaterials with perforated apertures, and interval Chebyshev expansion-Monte Carlo simulation method (ICE-MCSM) of multilayer-metamaterials with perforated apertures for transmission characteristic is proposed.In ICE-MCSM, truncated Chebyshev polynomials is applied to surrogate the transmittance of multilayer-metamaterials with perforated apertures;therefore, the surrogate model of transmittance is constructed.The samples of interval variables are produced by Monte Carlo method, then the values of these samples are substituted into the surrogate model of transmittance to predict the interval bounds of multilayer-metamaterials with perforated apertures under single-interval variable and multi-interval variables.The results of numerical analysis show that the upper interval bounds and lower interval bounds calculated by ICE-MCSM match the response yields by direct Monte Carlo simulation method (DMCSM).Compared to DMCSM, ICE-MCSM achieves a higher accuracy in interval bound analysis, so ICE-MCSM can effectively and efficiently analyze the interval bounds of multilayer-metamaterials with perforated apertures under uncertain interval variables.Thus, this proposed method in this paper can have promising prospects in real world engineering applications.

2017, 49(1): 137-148. doi: 10.6052/0459-1879-16-254

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STABLE GENERALIZED BIRKHOFF SYSTEMS CONSTRUCTED BY USING A GRADIENT SYSTEM WITH NON-SYMMETRICAL NEGATIVE-DEFINITE MATRIX

Chen Xiangwei, Zhang Yey, Mei Fengxiang

The Birkhoff system is a more extensive constrained mechanical system than Hamilton system, which can be applied to atomic and molecular physics, and hadron physics.It is an important and difficult project to study the stability of non-steady mechanical system, and it is very difficult to study the stability by using the direct method of constructing Lyapunov function, here how to construct the Lyapunov function is always an open question.This paper gives an indirect method which is called the gradient system method.A kind of gradient systems with non-symmetrical negative-definite matrix is proposed, and the solution of the gradient system can be stable or asymptotic stable.The study of the gradient system is particularly suitable by using the method of Lyapunov functions, in which the function V is usually taken as the Lyapunov function.Firstly the equations of motion of the generalized Birkhoff system are listed.The generalized Birkhoff system is a kind of extensive constrained mechanical system, holonomic and nonholonomic constraint systems can be incorporated into the system.When the additional terms of the system are equal to zero, it becomes the Birkhoff system.Then the conditions under which the solutions of the generalized Birkhoff system can be stable or asymptotically stable are given.Further the generalized Birkhoff systems whose solution is stable are constructed by using the gradient system with non-symmetrical negative-definite matrix.The method is also suitable for the study of other constrained mechanical systems.Lastly some examples are given to illustrate the application of the results.

2017, 49(1): 149-153. doi: 10.6052/0459-1879-16-280

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PLANAR PERIODIC ORBIT CONSTRUCTION AROUND THE TRIANGULAR LIBRATION POINTS BASED ON POLYNOMIAL CONSTRAINTS

Qian Yingjing, Zhai Guanqiao, Zhang Wei

Libration points are the five equilibrium solutions in the circular restricted three-body problem (CRTBP).The linearized motions around triangular libration points are typical center×center type.Studies about probes moving around orbits in the vicinity of the libration points have theoretical significance.From the vibrational point of view, the polynomial series are used to derive approximately the relations in different directions during periodic motions, which provides a new point of view to exploring the dynamics and analyzing the overall characteristics of the whole system with general rules.The nonlinear relations in polynomial form between the directions of the planar motions can be treated as constraints to obtain the solutions by numerical integration.Numerical simulations verify the efficiency of the proposed method.The methodology of deriving topological relations has the potential to be extended to circular/elliptical R3BP in three dimensional cases.

2017, 49(1): 154-164. doi: 10.6052/0459-1879-16-215

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COMPLEX BURSTING OSCILLATION STRUCTURES IN A TWO-DIMENSIONAL NON-AUTONOMOUS DISCRETE SYSTEM

Chen Zhenyang, Han Xiujing, Bi Qinsheng

Bursting oscillations are the archetypes of complex dynamical behaviors in systems with multiple time scales, and the problem related to dynamical mechanisms and classifications of bursting oscillations is one of the important problems in bursting research.However, up to now, most of the structures of bursting revealed by researchers are relatively simple.In this paper, we take the non-autonomous discrete Duffing system as an example to explore novel bursting patterns with complex bifurcation structures, which are divided into two groups, i.e., symmetric bursting induced by Fold bifurcations and asymmetric bursting induced by delayed Flip bifurcations.Typically, the fast subsystem exhibits an Sshaped fixed point curve with two Fold points, and the stable upper and lower branches evolve into chaos by a cascade of Flip bifurcations.When the non-autonomous term (i.e., the slow variable) passes through Fold points, transitions to various attractors (e.g., periodic orbits and chaos) on the stable branches may take place, which accounts for the appearance of Fold-bifurcation-induced symmetric bursting patterns.If the non-autonomous term is not able to pass through Fold points, but to go through Flip points, delayed Flip bifurcations can be observed.Based on this, delayed-Flip-bifurcation-induced asymmetric bursting patterns are obtained.In particular, the bursting patterns reported here exhibit complex structures containing inverse Flip bifurcations, which has been found to be related to the fact that the nonautonomous term slowly passes through Flip points of the fast subsystem in an inverse way.Our results enrich dynamical mechanisms and classifications of bursting in discrete systems.

2017, 49(1): 165-174. doi: 10.6052/0459-1879-16-267

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HHT METHOD WITH CONSTRAINTS VIOLATION CORRECTION IN THE INDEX 2 EQUATIONS OF MOTION FOR MULTIBODY SYSTEMS

Ma Xiuteng, Zhai Yanbo, Xie Shouyong

Equations of motion for multibody system with holonomic constraints in Cartesian absolute coordinates modeling method are index 3 differential-algebraic equations (DAEs).It is high index problem for numerical integration of index 3 DAEs.The index can be reduced to 2 by taking the derivative of position constraint equations, and velocity constraint equations can be obtained.During the integration of index 3 equations of motion, the velocity constraint equations are violated, and there are some problems in the integration of high index DAEs.Firstly, HHT (Hilber-Hughes-Taylor) direct integration method is used to the numerical integration of index 2 equations of motion.The velocity constraint equations involved in the integration, and they are satisfied in the view of computer precision.However, the position constraint equations are violated.Secondly, in order to eliminate the violation, the correction method based on MoorePenrose generalized inverse theory is adopted.HHT method with constraints violation correction for index 2 equations of motion is the combination of HHT and correction method.There are no position and velocity constraints violation during the integration in the view of computer precision.No new unknown variables are introduced, and the quantity of equations in nonlinear equations from discretization is the same as index 2 equations of motion.The new integration method is validated by numerical experiments.In addition, some characteristics of HHT method, such as controlled numerical damping and second-order accuracy, are persisted by the new integration method.Finally, the quantity of nonlinear equations from discretization and computational efficiency are compared with some other methods.The advantages of the new method are illustrated.

2017, 49(1): 175-181. doi: 10.6052/0459-1879-16-275

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MODEL ANALYSIS OF ENDOTHELIUM-DEPENDENT VASOMOTION OF SMALL ARTERY

Tang Yuanliang, He Ying

Metabolic substance exchange between blood and tissue occurs mainly in microcirculation, which can locally regulate blood pressure and blood flow by changing their diameters.Vascular endothelium plays an important role in the vasomotor regulation of small artery.In this paper, a model was adopted to study the endothelial regulation mechanism.Based on the continuum assumption, two layers of diffusion & kinetic processes of key agents in endothelial regulation were modeled, and the nonlinear viscoelastic properties of the wall material were considered in the computation of radial motion of small artery.The stationary distributions of nitric oxide (NO), calcium ion (Ca²⁺) and the contracting actinmyosin complexes (AMC) concentrations in the wall were firstly obtained;then the process of arterial passive dilation and the autoregulation process to the disturbance of blood flow were simulated.Numerical results showed that there was no oscillation of arterial diameter occurred during the passive dilation process.However, when there was a change in blood flow, the whole system transferred from the initial state to a new equilibrium state with slow damped oscillations.The oscillating period was about 60 s.It is supposed that the endothelial oscillation of artery diameter and NO concentration occurring during the dynamic regulating process is caused by the feedback control of shear stress.This oscillation characteristic can provide useful information for the diagnosis of endothelial dysfunction.

2017, 49(1): 182-190. doi: 10.6052/0459-1879-16-171

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ANALYSIS OF CHEST INJURY IN FRONTAL IMPACT VIA FINITE ELEMENT MODELLING BASED ON BIOMECHANICAL EXPERIMENT

Xiao Sen, Yang Jikuang, Xiao Zhi, Jeff R. Crandally

The usage of the seatbelt as a part of the vehicle protection system has immensely promoted occupant safety.However, recent accident investigation shows that it is necessary to increase the chest injury protective efficiency in frontal impact condition.This study aims to investigate the influence of seatbelt system design variables on occupant chest injury related physical parameters at varying impact conditions, especially concerning with the chest deflection and distribution of rib stress/strain.The study is conducted by using human body FE model in combination with post mortem human subjects tests.An FE model of the belted occupant is therefore established by using a baseline human body FE model (GHBMC), which is validated according to detailed experimental data regarding kinematics, seatbelt force and chest deflection.A parameter study is implemented in terms of seatbelt position, seatbelt angle and impact speed to determine the influence of seatbelt utilization on occupant thoracic injury in frontal impact.The results show that the influence of seatbelt position on chest deflection and distribution of rib stress/strain is greater than that of the seatbelt angle.Meanwhile, the trends of chest deflections are the same with the trends of the rib stress/strain responses while the changes of seatbelt design variables.This study provides a virtual test method on investigation of the chest injury biomechanics related to the seatbelt design variables.Furthermore, the results from this study of chest injury mechanism will also provide a reference for optimizing of the occupant restraint system.

2017, 49(1): 191-201. doi: 10.6052/0459-1879-16-088

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THE PHASE SHIFT OF SH₀ GUIDED WAVE PROPAGATING IN BONDING STRUCTURE

Ding Juncai, Wu Bin, He Cunfu

It is a difficult and challenging subject for non-destructive testing and evaluation of adhesive structure by ultrasonic guided waves.For this issue, the phase shift of SH₀ guided wave transmitting in perfect connected trilaminar plate-like adhesive structure was researched.Firstly, the phase-difference analytical model between the incident and transmission/reflection SH₀ guided wave, which based on the control equation of wave propagation, was established.Then, the phase-difference curves of reflection/transmission SH₀ guided wave in aluminum/epoxy resin/aluminum adhesive structure were calculated by numerical simulation.Finally, the effects of changes of incident angle and frequency-thickness product on the phase-difference of reflection/transmission SH₀ guided wave were analyzed.The results show that the changes of phase-difference of reflection/transmission SH₀ guided wave transmitting in adhesive structure mainly depend on the parameter as incident angle or frequency of acoustic wave, for the concrete bonding structure.The reflection and incident SH₀ guided waves are in the same phase when the ultrasound is incident under a particular frequency-thickness product.Despite the angle of incidence, the phase-difference curve of reflection SH₀ guided wave shows periodic res-onance with the increasement of frequency-thickness product.For the transmission SH₀ guided wave, the change of the phase-difference curve has no law to follow when the ultrasound is normal incident.But the phase-difference curve changes from irregularity to regularity as the angle of incidence increase.The results obtained could provide the theory support for studying the propagation characteristics of SH₀ guided wave in plate-like bonding structure and information retrieving of echoed SH₀ guided wave and positioning during the experiment.

2017, 49(1): 202-211. doi: 10.6052/0459-1879-16-245

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HIGHER-ORDER NUMERICAL MANIFOLD METHOD BASED ON ANALYSIS-SUITABLE T-SPLINE

Liu Dengxue, Zhang Youliang, Liu Gaomin

Numerical manifold method (NMM) is a very flexible numerical method which contains and combines finite element method (FEM) and discontinuous deformation analysis (DDA).High-order numerical manifold method can be constructed by increasing the order of the weight function.This method often needs to configure the appropriate edge nodes along the element boundary, the emergence of these nodes increase the complexity of pre-processing, especially for large and complex spatial problems.On the other hand, the level of approximation of NMM can be improved by splitting the elements into smaller ones (known as h-refinement).With regard to the h-refinement, a cover refinement strategy is necessary to overcome the singularity of the stress when simulating crack propagation in NMM.One traditional solution is to refine the entire mesh which can lead to a significant decrease in the computational efficiency.In this paper analysis-suitable T-spline is introduced into NMM and regular rectangular meshes are used as the mathematical cover system.Specifically, analysis-suitable T-spline is linearly independent, forms a partition of unity, and can be locally refined which make it meet the demands of both design and analysis.The basis function of analysis-suitable T-spline is adopted as the weight function in NMM to construct high-order NMM and make the local refinement for feasible adaptive procedure.Two numerical examples are given to demonstrate the accuracy and efficiency of the proposed method and the results show that the higher order AS T-spline based NMM shows higher accuracies when solving both continuous and discontinuous problems.Furthermore, the local mesh refinement using analysis-suitable T-spline reduces the number of degrees of freedom while maintaining calculation accuracy at the same time.

2017, 49(1): 212-222. doi: 10.6052/0459-1879-16-217

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REVIEW OF THE SEVENTH NATIONAL SYMPOSIUM ON SOLID MECHANICS FOR YOUNG SCHOLARS

Lü Haibao, Liang Jun, Guo Xuy, Zhan Shige, Zhang Panfeng

Here, we briefly reports on the scientific reports and discussion presented at Seventh National Symposium on Solid Mechanics for Young Scholars hosted by Harbin Institute of Technology, as well as we proposes a few constructive suggestions on the development of solid mechanics subject in the new era.

2017, 49(1): 223-230. doi: 10.6052/0459-1879-16-370

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2017, 49(1): 231-237.

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2017 Vol. 49, No. 1

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