力学学报

A FULLY NONLINEAR BOUSSINESQ MODELFOR WAVE PROPAGATION BASED ON MUSTA SCHEME

Fang Kezhao, Wang Lei, Liu Zhongbo, Zou Zhili, Yin Jing

A hybrid finite-difference/finite-volume scheme is developed to solve the 2D fully nonlinear Boussinesq equations. Finite volume method, in conjunction with the MUSTA scheme, is used to evaluate the flux terms while finite difference method is used to approximate the rest terms in the conservative governing equations. The third order Runge-Kutta method with TVD property is adopted for time marching. The proposed model has the advantages of shock capturing, easy coding and strong stability preserving, and contains less adjustable parameters. Two typical numerical tests are conducted for model validation, and the calculated results are in good agreement with experimental data.

2014, 46(5): 647-654. doi: 10.6052/0459-1879-13-338

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MODEL EXPERIMENT ABOUT RESPONSE OF FLOATING ICE SHEET SUBJECTED TO MOVING AIR CUSHION VEHICLE

Zhang Zhihong, Gu Jiannong, Wang Chong, Hu Mingyong, Lu Zaihua, Lu Feifei

According to the differential equation of thin elastic vibrating plate and the similarity theory, the similar relationships of corresponding parameters were determined between model and prototype about floating ice sheet subjected to moving air cushion vehicle (ACV). The calculation formulas of phase speed and group speed about wave propagation of floating ice sheet with free vibration were derived, and the minimum phase speed and propagation speed of shallow wave were as the first and the second critical speed of ACV, respectively. A high accuracy non-contact laser system was developed to measure the surface displacement, and a series of experiments were carried out about response of film deformation causing by air cushion load (ACL) moving at different speeds in towing channel with variable depth. The existence of critical speeds of ACL which could bring maximum film deformation was confirmed. The first critical speed made maximum depression deformation of film after ACL, and the second critical speed made maximum raised deformation of film before ACL. The influence of moving air cushion speed, height, pressure and water depth on film deformation and critical speeds was further analyzed by experimental results; the resonant effect of energy accumulation and mechanism of amplification about film deformation caused by moving ACL were revealed, and the research provides the theoretical basis and technical support to develop a efficient ice-breaking way by ACV.

2014, 46(5): 655-664. doi: 10.6052/0459-1879-13-331

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EFFECT OF TWO-DIMENSIONAL MICROPILLAR ARRAYED TOPOGRAPHY ON SPREADING OF INSOLUBLE SURFACTANT-LADEN DROPLET

Li Chunxi, Chen Pengqiang, Ye Xuemin

For the spreading of liquid droplet containing insoluble surfactant over two-dimensional micropillar-arrayed surface, the lubrication theory was adopted to derive the evolution equations of liquid film thickness and interfacial surfactant concentration, and then the droplet spreading characteristics and the effects of related parameters were numerically simulated. Results show that when the surfactant-laden droplet was spreading over micropillar-arrayed surface, the depression appears at the groove while the ridge is shaped at the bump, and the ridge and the depression move towards both sides gradually, and the numbers of ridge and depression increase. Furthermore, when the surfactant film is flowing over the bump, the height of the ridge presents a hump shape. The numbers of ridges and depressions in the spreading region increase and the droplet spreading velocity accelerates with the improved preset film thickness and initial surfactant concentration. Increasing the groove depth or decreasing the steepness can enhance the capillary force effects, resulting in suffering the rupture possibility of the film. Improving the groove width enlarges the film deformation and promotes the film flow.

2014, 46(5): 665-672. doi: 10.6052/0459-1879-14-099

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NUMERICAL STUDY ON THE SEDIMENTED MOTION CHARACTERISTICS OF THREE ALIGNED CIRCULAR PARTICLES IN THE INCLINED CHANNELS

Hu Ping, Zhang Xingwei, Niu Xiaodong, Meng Hui

The immersed boundary-lattice Boltzmann method (IB-LBM) is used to numerically investigate the sedimented motion characteristics of three rigid circular particles in the inclined channels. The gravity is considered, and the inclined angles of the channels are sequentially changed from 0° to 90°. The effect of inclined angles on the sedimented motion characteristics is firstly investigated. Present results show that the lagging particle will surpass the leading particle when inclined angles of channel are larger than 59°. Then, the effect of Re number on the sedimented characteristics is also studied. This study finds that the aggregation time of three particles decreases as Re number increases. In addition, this study also finds that the non-uniformity of the diameters of three circular particles can alter the sedimented characteristics. When the diameters of three longitudinally aligned particles gradually become smaller, the aggregation time can be shorten. The aggregation of the particles can also be accelerated as long as the diameter of particles in the middle is larger than the diameters of other two adjacent particles. Present results can provide useful information for related problems in environmental engineering and geology.

2014, 46(5): 673-684. doi: 10.6052/0459-1879-14-059

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MAGNETO-HYDRODYNAMICS MODELING OF CONFIGURATIONS IN MAGNETICALLY DRIVEN ISENTROPIC COMPRESSION EXPERIMENTS

Zhao Jibo, Sun Chengwei, Luo Binqiang, Cai Jintao, Wang Guiji, Tan Fuli, Zhao Jianheng

Based on the one-dimensional elastic-plastic reactive hydrodynamic code SSS, the one-dimensional magneto-hydynamics code SSS/MHD is developed successfully, which couples magneto-hydynamics calculation with centralized parameter circuit equations of simulative pulsed power source directly, and numerically simulates mechanical and electromagnetic kinetic processes and some kinds of parameter sections of samples according to original datum independent of real time experience circuit. The code SSS/MHD can simulate different thickness parallel configurations (sidestep target) with multi-medium and multi-cavities in magnetically driven isentropic compression experiments. The calculation of sidestep targets on aluminum, tantalum and plastic binder explosive in ICE experiments is described in this paper, and the velocity histories of samples free surface or optics window interface accord with experiment results tested by laser interference. It is important for magneto-hydrodynamics calculation to analyze the test results and improve the design. The purpose of this paper is to provide a simulation means with a certain extent prophecy and more perfect function for correcting and designing magnetically driven system and improving experiment configuration.

2014, 46(5): 685-693. doi: 10.6052/0459-1879-14-019

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A RECONSTRUCTION METHOD FOR FINITE VOLUME FLOW FIELD SOLVING BASED ON INCREMENTAL RADIAL BASIS FUNCTIONS

Liu Yilang, Zhang Weiwei, Jiang Yuewen, Ye Zhengyin

A reconstruction method of flow field solving, based on incremental RBF (Radial Basis Functions) interpolation, has been developed in the paper. Since the fluctuation of flow parameters in the stencil cells used to reconstruct is small compared with the mean value in flow field reconstruction, direct RBF reconstruction will bring large numerical oscillations. The incremental RBF reconstruction developed in this paper effectively improves convergence and stability of the interpolation scheme. In first example, a simple one-dimensional model is used to illustrate the effective of this method when the fluctuation of the objective function is much smaller than the mean value. Furthermore, applicability and effectiveness of incremental RBF reconstruction method is proved by using four typical flow fields, namely, two-dimensional subsonic, transonic inviscid steady flow fields around NACA0012, the viscid unsteady flow around a stationary cylinder and a Mach 3 wind tunnel case with a step problem. Research shows that incremental RBF reconstruction method can smoothly capture steep shock and effectively improve the convergence and stability of flow solver with small numerical dissipation and high computational efficiency.

2014, 46(5): 694-702. doi: 10.6052/0459-1879-14-028

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STUDY ON THE VIBRATION OF MICROCANTILEVERS IMMERSED IN FLUIDS UNDER PHOTOTHERMAL EXCITATION

Dong Tianbao, Song Yaqin

Microcantilever-based structures can be widely applied in Micro-Electro-Mechanical System and Nano-Electro-Mechanical System (MEMS and NEMS). In the practical application, the dynamical response of the cantilever strongly depends on the properties of coating film and surrounding medium. Based on the photothermal vibration model of bilayer microcantilever immersed in fluids, the dynamical responses of coating microcantilever were analyzed. The expressions for temperature, photothermal driving force and dynamical deflection fields were obtained analytically and showed graphically. Theoretical analysis showed that fluids, especially the liquids, have a significant influence on the vibration frequency spectra of microcantilever. Also it could be concluded that when the cantilever vibrated in air, the resonant frequency has a small shift (0.7%) to lower frequencies and resonant peak has almost no change compared to the response in vacuum. However, when the cantilever vibrated in liquids, the resonant frequencies have a distinct shifts (58～80%) to lower frequencies and resonant peaks are distorted, and quality factor decreased on the order of magnitude. This study can be of value to users and designers of microcantilever-based structures in micro-nano detections and AFMs.

2014, 46(5): 703-709. doi: 10.6052/0459-1879-14-095

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INVESTIGATION ON FATIGUE HYSTERESIS LOOPS MODELS OF FIBRE-REINFORCED CERAMIC-MATRIX COMPOSITES

Li Longbiao

When the fibre-reinforced ceramic-matrix composites (CMCs) are first loading to the fatigue peak stress, the matrix cracking and fibre/matrix interface debonding occur. Under the fatigue loading, the stress-strain hysteresis loops appear due to the fibre sliding relative to matrix in the fiber/matrix interface debonded region. The micromechanical hysteresis loops models for the fibre-reinforced CMCs have been developed in present analysis. The fibre/matrix interface debonded length upon first loading, the unloading interface counter-slip length and the reloading interface new slip length were determined by the fracture mechanics approach. The hysteresis loops of four different interface slip cases have been analysed. By assuming that the mechanical hysteresis behavior of cross-ply and woven CMCs was mainly controlled by the fiber/matrix interface slip in the 0o ply or the longitudinal yarns, the hysteresis loops of unidirectional, cross-ply and woven CMCs corresponding to different peak stresses and different cycles have been predicted, respectively. The predicted results agreed with the experimental data.

2014, 46(5): 710-729. doi: 10.6052/0459-1879-13-332

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EVALUATION ON STRESS INTENSITY FACTOR OF CRACK UNDER DYNAMIC LOAD USING NUMERICAL MANIFOLD METHOD

Yang Yongtao, Xu Dongdong, Zheng Hong

Compared to the traditional finite element method (FEM), one significant advantage for numerical manifold method (NMM) is not necessary to force the mesh to match the cracks, facilitating the simulation of failure in rock mass. Based on NMM containing enriched functions of crack tip, the Newmark implicit algorithm was used for time integration. Besides, emphasis was placed on the solution method of dynamic stress intensity factor (DSIF) of crack under dynamic loading condition. Numerical examples with NMM for typical elastic dynamic crack problems are presented. The results show that the NMM can not only accurately evaluate DSIF under dynamic loading condition, but also have very good convergence property to the theoretical solution.

2014, 46(5): 730-738. doi: 10.6052/0459-1879-14-024

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A NEW METHOD FOR DEALING WITH PSEUDO MODES IN TOPOLOGY OPTIMIZATION OF CONTINUA FOR FREE VIBRATION

Gao Xingjun, Ma Haitao

Pseudo modes may appear in topology optimization of continua when the SIMP (Solid Isotropic Material with Penalization) material model is used for eigenvalue problems. A new method based on the combined use of the frequency shift technique and pseudo mode identification is proposed to eliminate the detrimental effect of such pseudo modes. The topology optimization of continuum structures for maximum fundamental frequency subjected to volume constraint is considered in the study. The nodal densities are taken as design variables to describe the material distribution in the design domain. Based on an investigation of the characteristics of pseudo vibration modes, the eigenvalue shift technique is suggested for avoiding low-order pseudo modes with small eigenvalues from the eigenmode extraction, and further a pseudo mode identification criterion is constructed to exclude other high-order pseudo modes. A highly efficient and reliable algorithm for the topology optimization is then made possible. Numerical examples are presented illustrating the effectiveness of the proposed method.

2014, 46(5): 739-746. doi: 10.6052/0459-1879-13-406

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SOLUTION AND ANALYSIS OF CIRCULAR TUNNEL FOR THE STRAIN-SOFTENING ROCK MASSES CONSIDERING THE AXIAL IN SITU STRESS AND SEEPAGE FORCE

Zou Jinfeng, Li Shuaishuai, Zhang Yong, Yuan Zhen

This paper presents an analysis for the distributions of stresses and displacements considering the effect of seepage force and the axial in-situ stress for strain-softening rock masses by using Mohr-Coulomb yield criterion. The plastic region is divided into a finite number of concentric rings. Using the stress and strain of the elastic portion of elastic-plastic interface as the initial value and the known differential increments of radial stress, the stress-strain increment can be obtained. Then, the stress and strain on each ring can be reduced. The displacement and plastic radius of surrounding rock can be gained. The derivations of the stress, strain and displacement solutions in strain-softening rock masses considering the influence of the axial in-situ stress and seepage force can be obtained by the use of reconstructed step-by-step solution. The theoretical results can be simplified into Wang's theory as well. The results calculated and analyzed by the approach of Matlab programming showed that the present theory developed in this paper is correct. This study found that the plastic radius and displacement of tunnel wall decrease while seepage force increases with the axial in-situ stress. And when the axial in-situ stress is the minor principal stress, the influence of seepage force is much more apparent. It can be found that the displacement of tunnel wall, the plastic radius and the distribution of stresses and strains are influenced by the consideration of seepage force.

2014, 46(5): 747-755. doi: 10.6052/0459-1879-14-029

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THRUST-AMPLITUDE CONTINUATION DESIGN APPROACH FOR SOLVING SPACECRAFT OPTIMAL CONTROLLED FLY-AROUND TRAJECTORY

Zhu Xiaolong, Liu Yingchun, Gao Yang

A continuation approach in which the thrust amplitude is the continuation parameter is proposed to solve the fuel-optimal spacecraft fly-around trajectories. On the basis of the two-impulse solution, the minimum thrust amplitude that ensures the feasibility of the fly-around trajectory is obtained by replacing impulsive thrust with finite thrust and decreasing the thrust amplitude gradually. Once obtaining the minimum-thrust solution, the thrust amplitude is increased step by step and the optimal thrusting switching sequence is determined by the primer vector in each step. Consequently, the fuel-optimal trajectories with both finite thrust and impulsive thrust are obtained by continuation from the minimum-thrust fly-around trajectory solution. By continuation on all feasible thrust amplitudes, the fuel-optimal solutions with both finite thrust and impulsive thrust are solved, and the costate variables in the optimal control problem are no longer acquired randomly. Numerical examples of slow and fast fly-around trajectories show the effectiveness of the proposed continuation approach.

2014, 46(5): 756-769. doi: 10.6052/0459-1879-14-030

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THE PARAMETRIC VARATIONAL PRINCIPLE AND NON-LINEAR FINITE ELEMENT METHOD FOR ANALYSIS OF ASTROMESH ANTENNA STRUCTURES

Tan Shujun, Hou Jian, Wu Zhigang, Du Jianming

A new stable algorithm is presented for AstroMesh antenna structure with large deformation based on the parametric variational principle (PVP) and nonlinear finite element method. Firstly, a parametric variable with its related complementary equation is introduced to model the bilinear constitutive relations of cable elements, and so a unified description of bilinear constitutive model is obtained, which avoids the prediction that the cable is tensioned or relaxed for traditional algorithms. Then, the Lagrangian strain is applied to tackle the large deformation problem of the AstroMesh structure. The nonlinear equilibrium equations and complementary equations are established based on the nonlinear geometric finite element method and parametric variatianal principle. The Newton-Raphson scheme combined with Lemke algorithm is employed to solve the equations. Numerical examples are given to demonstrate the convergence and accuracy of the PVP method in this paper are better than those of the traditional method. The proposed method is particularly suitable for high-precision analysis and prediction for large deformation of AstroMesh antenna structure.

2014, 46(5): 770-775. doi: 10.6052/0459-1879-14-126

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A HIGH ORDER KERNEL INDEPENDENT FAST MULTIPOLE BOUNDARY ELEMENT METHOD FOR ELASTODYNAMICS

Rong Junjie, Xiao Jinyou, Wen Lihua

In this paper, a highly accurate kernel-independent fast multipole boundary element method (BEM) is developed for solving large-scale elastodynamic problems in the frequency domain. The curved quadratic elements are employed to achieve high accuracy in BEM analysis. By using the Nystr?m discretization, the boundary integral equation is transformed into a summation, and thus the fast BEM algorithms can be applied conveniently. A newly developed kernel-independent fast multipole method (KIFMM) is used for BEM acceleration. This method is of nearly optimal computational complexity; more importantly, the numerical implementation of the method does not rely on the expression of the fundamental solutions and the accuracy is controllable and can be higher with only slight increase of the computational cost. By taking advantage of the cheap matrix assembly of Nyström discretization, the memory cost of the KIFMM accelerated BEM can be further reduced by several times. The performance of the present method in terms of accuracy and computational cost are demonstrated by numerical examples with up to 2.3 million degrees of freedom and by comparisons with existing methods.

2014, 46(5): 776-785. doi: 10.6052/0459-1879-13-426

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BAND STRUCTURE AND TRANSMISSION CHARACTERISTICS CALCULATION OF PHONONIC CRYSTALS BASED ON MULTI-LEVEL SUBSTRUCTURE TECHNIQUE

Yin Jin, Zhang Sheng, Chen Biaosong, Zhang Hongwu

A fast scheme based on multi-level substructure technique is proposed to analyze band structure and transmission characteristics of phononic crystals. The main idea is that the finite element model of phononic crystal is divided into several substructures by a special multi-level decomposition. For the calculation of band structure, tree travelling technique and static condensation method are used to convert the internal stiffness matrix into the Bloch boundary of unit cell. Because the internal stiffness matrix does not change along with reduced wave vector, the scheme can reduce computation budget and improve efficiency greatly, while it does not introduce approximation into traditional finite element model. For the calculation of transmission characteristics, the proposed scheme can be also used to reduce computation, because unit cell of phononic crystal is periodic which has the same coefficient matrix. Moreover, the back substitution of internal displacements of unit cell can be selected flexibly. Some examples of three-dimensional locally resonant system and two-dimensional Bragg scattering phononic crystal are analyzed. Numerical results indicate that the proposed scheme is efficient and accurate, and suitable for complex phononic crystal problems.

2014, 46(5): 786-793. doi: 10.6052/0459-1879-13-431

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AN SEPARATION OF THE ALEATORY AND EPISTEMIC UNCERTAINTIES WITH CORRELATED NORMAL VARIABLES AND ANALYSIS OF THE INFLUENCE OF PARAMETERS

Wu Danqing, Lü Zhenzhou, Cheng Lei

For the structural system with correlated variables with aleatory and epistemic uncertainties, the influence of distribution parameters with epistemic uncertainty to the output is studied. Firstly, orthogonal transformation is used to separate the aleatory and epistemic uncertainties. The epistemic uncertainty is separated from the aleatory uncertainty of input variables through the auxiliary variable. After that, the main effect of distribution parameters to the model output is discussed. Secondly, the equality between the first order variance of parameters to the expectation of the output and the first order variance contribution of parameters to the output after separating uncertainties is validated. At last, some examples are utilized to demonstrate the rationality and efficiency of method used to separate the aleatory and epistemic uncertainties.

2014, 46(5): 794-801. doi: 10.6052/0459-1879-14-014

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DROPLET INTERACTIONS IN THERMOCAPILLARY MIGRATION

Zhang Shuoting, Hu Liang, Duan Li, Kang Qi

Experiments were performed, with the method of density match in a terrestrial environment, to study the migration and interaction of drops with different diameters in matrix liquid under temperature gradient field. Thermocapillary migrations for both single and double droplets are observed via shadow method. For double droplets migration experiments, it can be observed that small droplet always moves faster than large droplet for different types of oils. The results indicate that there exist horizontal movements for both small and large droplets, and the large droplet has larger extent than small droplet.

2014, 46(5): 802-806. doi: 10.6052/0459-1879-13-244

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THE SUPPORTED PROJECTS ON MECHANICS OF NSFC IN 2014

Zhan Shige, Zhang Panfeng, Wang Lifeng, Xu Xianghong

The paper brief introduced the supported NSFC projects for General Programs, Young Scientists Fund, Fund for Less Developed Regions on mechanics in 2014. The projects list is also given.

2014, 46(5): 807-808.

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