应用数学和力学

Research Progress of the Soil Constitutive Relation Considering Principal Stress Axes Rotation

DONG Tong, ZHENG Ying-ren, LIU Yuan-xue, Abi Erdi

2013, 34(4): 327-335. doi: 10.3879/j.issn.1000-0887.2013.04.001

Abstract(1720) PDF(1427)

Abstract:
The experiments and constitutive models considering principal stress axes rotation were analyzed, and the proposals for further study were offered. Based on different loading conditions, the basic deformation characteristics of soils considering principal stress axes rotation were described systematically and more suggestions were thrown out in terms of pure principal stress axes rotation and coupling principal stress axes rotation. The representative soil constitutive models (bounding surface model, multimechanism model, kinematic hardening rotation and generalized plasticity model) were commented systematically. It was concluding that the generalized plasticity model was more suitable for describing deformation characteristics of soils considering principal stress axes rotation. It shows that the major research directions of the soil constitutive relation considering principal stress axes rotation for further study are detecting the essential properties under principal stress axes rotation, building the reasoning strict, simply formed and applicable convenient model, and then guiding the engineering practice based on the achievements.

Theoretical Simulation of Electrostatic Levitation of Lunar Dust

MAO Zi-rui, DI Bing, ZHANG Juan-juan

2013, 34(4): 336-344. doi: 10.3879/j.issn.1000-0887.2013.04.002

Abstract(1346) PDF(1118)

Abstract:
The electrostatic levitation of lunar dust particles in the lunar terminator region was simulated the main factors influencing levitation were analyzed. The reseach included two steps: PIC (particle-in-cell) simulations were carried out by using real ion to electron mass ratio to obtain plasma sheath, lunar surface charging, on the basis of which test particle simulations were adopted to simulate the levitation of dust particles from lunar surface. Results show that the solar elevation angle and dust grain radius are main controlling parameters for the levitation of lunar dust particles. The electrostatic levitation of lunar dust occurs during sunrise and sunset when the sun angle is small. The smaller the dust grain is, the higher it elevates due to electrostatic levitation on the same condition.

Analytic Functions in Stress Analysis of the Surrounding Rock for Caverns With the Complex Variable Theory

ZHU Jiang-hong

2013, 34(4): 345-354. doi: 10.3879/j.issn.1000-0887.2013.04.003

Abstract(2331) PDF(2493)

Abstract:
Two analytic functions must be derived from the stress equation for the boundary condition, when the surrounding rock stress is analyzed in the tunnel with arbitrary excavation cross section with the complex variable theory. Based on the Harnack theorem, the stress equation for the boundary condition was transformed into an integral equation in the surrounding rock. The mapping function expressed with the finite Laurent series was introduced into the integral equation, and then the boundary with arbitrary excavation cross section was change into the boundary with the unit circle line for solving two analytic functions. The analyticity was studied for each integrand in the integral equation in discussed domain. Using above result, each integral term of the equation was solved with the Residue theorem and the general formulas of two analytic functions were obtained to calculate the surrounding rock stress in tunnel with arbitrary excavation cross section. Moreover, study examples of the analytic functions were provide for the circular tunnel and the elliptic tunnel and two general formulas for analytic function. The results were accord with the literatures. General formulas of two analytic function obtained with the Residue theorem are adapt to calculate the surrounding rock stress in the caverns with arbitrary excavation cross section. Compared to other methods, it is much simpler to obtain the analytical solutions and the calculating results are more precise for the actual caverns.

Research on Scattering of SH-Waves on Multiple Hills and Canyons

HAN Feng, WANG Guang-zheng, CHEN Han

2013, 34(4): 355-363. doi: 10.3879/j.issn.1000-0887.2013.04.004

Abstract(1740) PDF(1049)

Abstract:
Taking two triangular hills joined by a semicylindrical canyon as an example, scattering of SHwaves by complicated terrain were studied. The model was divided into three domains. The wave functions satisfying the boundary condition at each domain were constructed by complex function and moving coordinate methods. The algebraic equations were constructed according to the conjunction of displacement and stress. After solving the equations, the unknown coefficients were acquired. At last, the surface displacement were provided and the influence of different factors such as wave numbers and incident angles were discussed.

Dynamic Stress Concentrations in Stretching Plates by Using the Refined Dynamic Theory

HU Chao, ZHOU Chuan-ping, TONG Guang-qing, LIU Dian-kui

2013, 34(4): 364-372. doi: 10.3879/j.issn.1000-0887.2013.04.005

Abstract(1680) PDF(1289)

Abstract:
In the past, the solution of elasticity plane problems is often used to investigate stress concentrations for the engineering design instead of solution of stretching plates. For example, Kirsch’s solution and the solution of elastodynamics plane problems. Based on the refined dynamic equation of stretching plates, elastic wave scattering and dynamic stress concentrations in plates with a circular cutout were studied. Numerical results demonstrated that dynamic stress concentration factors in stretching plates were different from the one which were obtained by elasticity plane problems and dynamic stress concentration factors trended to unit 1 at the high frequency of incident waves. The dynamic stress concentration factor of stretching plates with cutouts is up to a maximum of 3.30, and the one is 2.77 by using plane problem of elastic dynamics. The comparison of the numerical results was made and discussed. It is showed that as the cutout radius ratio to the thickness is smaller a/h=0.10,using the refined equation the dynamic moment factor may approach to the maximum value, which is more 19% than the result from the solution of plane problems of elastic dynamics. The results are more accurate because the refined equation of plates stretching is derivative without using any engineering hypotheses. The numerical results and the method can be used to analyze the dynamics and strength of platelike structures.

Analytical Solution of Butler-Volmer Equation in Battery System Modeling

SONG Hui, LI Fen, XU Xian-zhi

2013, 34(4): 373-382. doi: 10.3879/j.issn.1000-0887.2013.04.006

Abstract(2788) PDF(1580)

Abstract:
Butler-Volmer equation is the constitutive equation to describe the dynamic process of electrode reaction in electrochemical systems. Due to its strong nonlinearity in the mathematical form, the computing efficiency by numerical methods was frequently limited. Aiming at solving this equation (coupled with two Ohm equations) more efficiently, an improved homotopy analysis method(HAM) was presented, in which a generalized nonlinear operator satisfying simple conditions was developed to replace the nonlinear operator in the original homotopy. The construction of generalized nonlinear operator guaranteed the linear property of higher-order deformation equations. The validity of this method was verified through some examples. Furthermore, this method was successfully applied in solving Butler-Volmer equation. The analytical solutions of overpotential and current density agree very well with the numerical solutions and the high efficiency is shown in the computing process.

Multistability of Delayed Neural Networks With Discontinuous Activations

CHEN Xiao-feng, SONG Qian-kun

2013, 34(4): 383-398. doi: 10.3879/j.issn.1000-0887.2013.04.007

Abstract(1740) PDF(1135)

Abstract:
The problem on the multistability was investigated for delayed neural networks with discontinuous activations. For the neural networks under studied,the traditional assumptions on the continuity and the monotonicity of the activation functions were not required. Several sufficient conditions for checking the coexistence and local exponential stability of equilibria for the considered neural networks were given. Finally, two numerical examples were given to show the effectiveness and less conservatism of the proposed criteria.

An Epidemic Model With Saturated Media/Psychological Impact

LIU Yu-ying, XIAO Yan-ni

2013, 34(4): 399-407. doi: 10.3879/j.issn.1000-0887.2013.04.008

Abstract(1984) PDF(1752)

Abstract:
Media has important influence on incidence rate of infectious disease. An epidemic model with segmented incidence rate was formulated and analyzed to describe the saturated media/psychology impact. Firstly all possible regular/virtual equilibria of the system was found out, and the local stability of the equilibria was analyzed in terms of the basic reproduction number. The global asymptotic stability of the positive equilibriums could then be obtained by excluding the existence of limit cycle for the system. The effect of saturated media/psychology impact on dynamics was discussed.

Combination Forecasting Algorithm Based on Non-Equal Interval Weighted Grey Model and Neural Network

HAN Jin, YANG Yue, CHEN Feng, LI Xiong-bin

2013, 34(4): 408-419. doi: 10.3879/j.issn.1000-0887.2013.04.009

Abstract(1600) PDF(1628)

Abstract:
The nonequal interval forecasting algorithm plays an important role in trend analysis and forecasting of sequences with different intervals. Based on the traditional grey forecasting theory, a combination forecasting algorithm based on nonequal interval weighted grey model and neural network was proposed. By constructing the nonequal interval weighted grey forecasting model, the average of original data sequence was regarded as the initial value of cumulative sequence, the integral area of continuous accumulation function was used as the background value, and the cumulative sequence was processed by weighting in order to truly reflect the impact of time sequences development to forecasting results. On this basis, BP neural network was introduced to correct the residuals sequence of grey forecasting which further improved the forecasting accuracy. The numerical example indicates that the forecasting accuracy level of the algorithm is 1 and higher than similar algorithms.

On Coordination Ratio of a Mixed Routing Game

YU Xiao-jun

2013, 34(4): 420-426. doi: 10.3879/j.issn.1000-0887.2013.04.010

Abstract(1328) PDF(1262)

Abstract:
The upper bound of the coordination ratio for a mixed routing game associated with oblivious users and altruistic users with fixed demand was investigated by algorithmic game theory. Firstly, the variational inequality model was established to describe this mixed routing game. Then, the upper bound of coordination ratio was derived by analytic derivation. The results took the results in existence literatures as its special case.

Extinction for a Class of Fast Diffusion System With Nonlocal Sources

WANG Juan, CHEN Yu-juan, ZHANG Hai-xing, LU Chen

2013, 34(4): 427-435. doi: 10.3879/j.issn.1000-0887.2013.04.011

Abstract(1369) PDF(1134)

Abstract:
The sufficient conditions for the extinction of solutions of a class of fast diffusion system with nonlocal sources were investigated, where the upper and lower solution method and integral estimates were used. It is shown that when the initial values and the parameters satisfy some conditions, the solution of the system extincts in finite time.

2013 Vol. 34, No. 4