应用数学和力学

2017 Vol. 38, No. 10

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The Founding Process of Institute of Mechanics, Chinese Academy of Sciences

KONG Peng-duan

2017, 38(10): 1081-1092. doi: 10.21656/1000-0887.380237

Abstract(1229) PDF(1155)

Abstract:
Institute of Mechanics (IM), Chinese Academy of Sciences (CAS), originated from Mechanics Laboratory of Institute of Mathematics (of which CHIEN Wei-zang was the director), was founded under the help of Peking University and Tsinghua University. The founding background and process of IM were retrospected and illustrated, the acts of Tsien Hsue-shen during IM’s construction and his thoughts on the development of IM, as well as the development goals and visions proposed by some prominent persons when they were discussing the construction of IM on the executive meeting of CAS, were reviewed. Finally, the founding personnel constitution of IMCAS was introduced.

Numerical Simulation of Flow Fields in Porous Media Based on the 3D CFD-DEM

REN Shi-lei, HAN Fei-peng, XIE Bin, HUANG Bo, HAO Peng-fei

2017, 38(10): 1093-1102. doi: 10.21656/1000-0887.370326

Abstract(1588) PDF(1287)

Abstract:
In numerical simulation the microscopic flow in porous media was combined with the macroscopic porous media model based on the Darcy law. The 3D CFD-DEM was applied to the microstructure of porous media to figure out the inertial resistance and the viscous resistance. Then, the resistances obtained with the CFD-DEM were introduced in the porous media model based on the Darcy law. The Voronoi polyhedron was used in mesh generation, so the porosity of each mesh cell was calculated precisely. In this way, larger-scale fluid fields in porous media can be computed efficiently. For engineering applications, the proposed method balances between accuracy and efficiency of multi-scale methods, effectively saving the experiment cost and improving the computation reliability.

Effects of Horizontal Flow on Perturbation Growth and Convection Periodicity

HU Biao, NING Li-zhong, NING Bi-bo, TIAN Wei-li, WU Hao, NING Jing-hao

2017, 38(10): 1103-1111. doi: 10.21656/1000-0887.370314

Abstract(957) PDF(1070)

Abstract:
Numerical simulation of the 2D fully hydrodynamic equations for the pure fluid in a rectangular channel with horizontal flow for Prandtl number Pr=0.0272 was conducted. Growth and spatiotemporal evolution of the 1D traveling wave patterns in the RayleighBenard convection of the pure fluid were investigated. It is found that the convective growth process can be divided into 3 stages: the development stage, the exponential growth stage and the periodic variation stage. Through analysis on the variation of the maximum vertical velocity field with time for different relative Rayleigh numbers Ra_r in the exponential growth stage, a formula of variation of linear growth rate γ_m was obtained with respect to Ra_r. Furthermore, the traveling wave convection periodicity and its dependence on the horizontal flow Reynolds number were revealed.

Numerical Analysis of Anisotropic Mass Diffusion, Adsorption and Chemical Reaction Processes in Brain Tissues

LI Hong-shun, SHI Zhu, ZENG Shao-qun

2017, 38(10): 1112-1119. doi: 10.21656/1000-0887.370322

Abstract(1002) PDF(552)

Abstract:
The mechanism and influence factors of mass transfer processes inside brain tissues were analyzed, and a modified mathematical model was built to comprehensively involve the adsorption, the chemical reaction and the anisotropic diffusion inside the brain tissues. Then the model equations were solved by means of the finite volume implicit scheme. The results indicate that, in the brain tissues, the mass diffuses more slowly as the tortuosity increases but spreads faster in a certain direction with a smaller tortuosity value. Owing to the heterogeneity of the brain tissues, a phenomenon of competition effect exists during the mass diffusion process inside the brain. The presences of adsorption and chemical reaction show an inhibitory action on the procedure of diffusion. The increase of the adsorption rate leads to a greater inhibition effect on the process. According to the Michaelis-Menten kinetics, the concentration value will significantly decrease with increment of the reaction rate constant, but increase with increment of the Michaelis-Menten constant. Furthermore, compared with the action of adsorption inside the brain, the Michaelis-Menten kinetics presents a more notable inhibitory effect on the concentration distribution towards the mass transfer process inside the brain tissues.

An Improved rd-Order WENO Scheme Based on Mapping Functions and Its Application

XU Wei-zheng, KONG Xiang-shao, WU Wei-guo

2017, 38(10): 1120-1135. doi: 10.21656/1000-0887.370345

Abstract(1341) PDF(930)

Abstract:
Low-dissipation and high-resolution shock-capturing schemes are of great significance for numerical simulation of flow fields containing shock waves. The WENO-M3 and WENO-MZ3 schemes were proposed with mapping functions based on the classical 3rd-order WENO scheme (WENO-JS3) and the 3rd-order WENO-Z scheme (WENO-Z3). Several classical 1D Riemann problems and double Mach reflection cases were simulated with the above schemes. The simulation results indicate that the WENO-MZ3 scheme has better characteristics of low numerical dissipation and high resolution for the flow features among all the schemes. To expand the application scope of the WENO-MZ3 scheme, the propagation and evolution of blast waves generated by cylindrical high pressure gas in a closed square cabin were investigated. Moreover, 2 typical pressure gauging points on the walls were monitored during the simulation. It is indicated that the WENO-MZ3 scheme is suitable for simulating the evolution of blast waves containing high pressure ratios and high density ratios. The WENO-MZ3 scheme gives lower-dissipation results than the WENO-JS3 scheme for the pressure load on the walls.

Prediction of Interfacial Tension Between CO₂ and Brine With the Wavelet Neural Network Method

JIANG An, LIU Ping-li, LI Nian-yin, ZHANG Yun-fei, DU Xin-wei

2017, 38(10): 1136-1145. doi: 10.21656/1000-0887.370339

Abstract(989) PDF(745)

Abstract:
Interfacial tension (IFT) between CO₂ and formation water is one of the most important parameters for CO₂ capture and storage, for it controls the transport properties of both phases in the formation. In order to rapidly and accurately predict the IFT of the CO₂-brine system, 1 677 sets of measured IFT data from previous studies were acquired. A wavelet neural network (WNN) prediction model was proposed in view of 6 parameters including the pressure, the temperature, the CH₄ molality and the N₂ molality in CO₂ gas, the monovalent cation (Na⁺ and K⁺) concentration and the bivalent cation (Ca²⁺ and Mg²⁺) concentration. The simulation results show that a 3-layer (6-16-1) WNN model comes out of 839 data as the training datasets. The mean absolute error (M_MAE), the mean relative error (M_MARE), the root mean squared error(M_MSE) and the determination coefficient (R²) of the WNN model were 1.23 mN/m, 3.30%, 2.30 mN²/m² and 0.988, respectively. The performance of the WNN model was further compared with one newly proposed multivariate fitting model and the BP neural network model. The comparison results suggest that the WNN model is better than the other 2.

Thermomechanical Stability Analysis of Shallow Spherical Shells

ZHAO Wei-dong, GAO Shi-wu, MA Hong-wei

2017, 38(10): 1146-1154. doi: 10.21656/1000-0887.370320

Abstract(1197) PDF(931)

Abstract:
Based on the geometric nonlinear theory for shallow shells, with the virtual work principle and the variational method, the displacement-type geometric nonlinear governing equations for shallow spherical shells in uniform temperature field under uniform external pressure were derived. With the shooting method, the numerical results of axisymmetric bending deformation of the shallow spherical shell in the immovable simply supported boundary condition were obtained. The critical geometric parameters were defined. The effects of various shell geometric parameters on the equilibrium paths and the critical loads were investigated. It is found that the upper critical load increases but the lower critical load first increases in a small range and then decreases with the geometric parameter in the range beyond its critical value. The effects of different values of the uniform temperature on the shell critical geometric parameter, the critical load and the equilibrium configurations were investigated under a given geometric parameter. Rise of the uniform temperature brings obvious increase of the upper critical load and obvious decrease of the lower critical load and the critical geometric parameter.

Characteristics and Generation of Interface J integrals in Layered Elastic Materials

CHEN Chang-rong

2017, 38(10): 1155-1165. doi: 10.21656/1000-0887.370270

Abstract(960) PDF(612)

Abstract:
When a crack in a layered elastic material is perpendicular to the interface, the Jintegral along path Г surrounding the crack tip can be separated into 2 parts: J_Г=J_tip+J_int, where J_tip means the J integral generated by the crack tip, and J_int the J integral generated by the interface enclosed by Г. The J integral generated by the crack tip is path-independent, and its physical meaning is the energy release rate of crack growth; the J integral generated by the interface is pathdependent, and has no relation to the energy release rate of crack growth. Due to the existence of the interface J integral, J_Г loses the path-independent property and has no real physical meaning. To better understand the physical meaning and limitations of the J integrals in inhomogeneous materials, the generation and characteristics of the interface J-integrals in layered elastic materials were analyzed. The results show that, for a layered elastic material composed of different homogeneous materials, the interface J-integrals are generated by the jumps of the strain energy density at the interfaces, and the jumps of the residual stresses and Young’s moduli at the interfaces would result in the jump of the elastic strain energy density. Moreover, offset effects exist between interface J integrals.

Comparison Between Exact Solutions and Approximate Solutions of Deep Tunnels

ZHOU Feng-xi, CAO Xiao-lin

2017, 38(10): 1166-1179. doi: 10.21656/1000-0887.370196

Abstract(865) PDF(785)

Abstract:
Deep buried tunnels with different cross-section shapes were analyzed through comparison between the analytical solutions and the approximate solutions obtained by the equivalent radii for the surrounding rock stresses. Firstly, according to the basic theory of complex variable functions, the stress components were obtained and the analytical expressions for the surrounding rock stresses of deep tunnels with various section shapes including the circle, the ellipse, the rectangle and the straight-wall arch, were given. Secondly, with the converted forms of the equivalent radii, the section boundary was transformed into a standard circle and the surrounding rock stress components were calculated by means of the Lamé solution. Finally, in view of the variable parameters of the tunnel cross-section shapes, comparisons between the exact solutions and the approximate solutions were conducted based on numerical examples, and the accuracy of the converted equivalent radii was discussed. The accuracy of the analytic solutions of the complex variable functions was proved, and the accuracy of the equivalent radii was verified for different cross-section shapes. The results show that the similarity between the solutions of the converted forms and the exact solutions of the equivalent radii is closely related to the cross-section shapes of the tunnels and the geometrical parameters.

Lagrangian Stability of Complex-Valued Neural Networks With Distributed Time-Varying Delays

ZHANG Lei, SONG Qian-kun

2017, 38(10): 1180-1186. doi: 10.21656/1000-0887.370378

Abstract(1358) PDF(440)

Abstract:
The Lagrangian stability of complex-valued neural networks with distributed time-varying delays was investigated. By means of the Lyapunov-Krasovskii functional and the matrix inequality techniques, a delay-dependent sufficient condition was obtained to ensure the global exponential stability in a Lagrangian sense for the considered neural networks. The condition is expressed in the form of complex-valued linear matrix inequality, which can be checked numerically with the effective YALMIP toolbox in MATLAB.

Recession Functions and Unboundedness of Functions

LI Mei-shu, GAO Ying

2017, 38(10): 1187-1194. doi: 10.21656/1000-0887.370307

Abstract(1181) PDF(837)

Abstract:
The unboundedness of functions was investigated with the recession cones and recession functions. Firstly, the mean value theorem and recession cones were used to characterize the subdifferentials of convex functions on condition of nondifferentiability. Based on the above results, the necessary and sufficient conditions for recession functions under the subdifferentiable assumption were given. Secondly, the convexity was generalized to E-convex functions, and the unbounded feature of E-convex functions was studied by means of recession functions under the special sublinear assumption. Finally, an example was given to indicate that these results can not be extended to quasiconvex functions.