应用数学和力学

2013 Vol. 34, No. 1

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Inter-Belt Finite Element for the Analysis of Incompressible Material Problems

WU Feng, SUN Yan, ZHONG Wan-xie

2013, 34(1): 1-9. doi: 10.3879/j.issn.1000-0887.2013.01.001

Abstract(2564) PDF(1413)

Abstract:
A concept of the flow function and the corresponding variational principle were developed to deal with the absolute incompressible material system, and the numerical analysis was also presented. When the flow function was introduced, the higher order differential system was involved, which led to a new type of element, the inter-belt finite element, based on the belt theory. The belt finite element can overcome well the problem derived by the variational principle with the higher order differential.

Surface Effects of AdsorptionInduced Resonance Analysis of Micro/Nanobeams via Nonlocal Elasticity

XU Xiao-jian1, DENG Zi-chen1

2013, 34(1): 10-17. doi: 10.3879/j.issn.1000-0887.2013.01.002

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Abstract:
The governing differential equation of micro/nanobeams with atom/molecule adsorption was derived in presence of surface effects using the nonlocal elasticity. The effects of nonlocal parameter, adsorption density and the surface parameter on resonant frequency of the micro/nanobeams were investigated. It is found that, in addition to the nonlocal parameter and surface parameter, the bending rigidity and the adsorptioninduced mass exhibit different behaviors with the increase of adsorption density depending on the adatom category and the substrate material.

N-S Bifurcation of an Oscillator With Dry Friction in 1∶4 Strong Resonance

GUO Yong, XIE Jian-hua

2013, 34(1): 18-26. doi: 10.3879/j.issn.1000-0887.2013.01.003

Abstract(2022) PDF(1319)

Abstract:
An oscillator with dry friction under external excitation was considered. The Poincaré map was established according to the series solution near equilibrium in the 1∶4 resonance case. By theory of normal forms, the map was reduced into its normal form. It is shown that there exist phenomena of N-S bifurcations. The theoretical results are verified by numerical simulations.

New Smooth Gap Function for Box Constrained Variational Inequalities

ZHANG Li-li, LI Xing-si

2013, 34(1): 27-37. doi: 10.3879/j.issn.1000-0887.2013.01.004

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A new smooth gap function for box constrained variational inequality problem was proposed based on an integral global optimality condition. The smooth gap function was simple and had some good differentiable properties. The box constrained variational inequality problem could be reformulated as a differentiable optimization problem by using the proposed smooth gap function. Conditions under which any stationary point of the optimization problem was the solution to box constrained variational inequality problem were discussed. A simple frictional contact problem was analyzed to illustrate the application of this smooth gap function. Finally, numerical experiments confirmed the good theoretical properties of the method.

Scattering of Elastic Waves by Multi-Size Defects in Rock Mass

TAN Zi-han, XU Song-lin, LIU Yong-gui, XI Dao-ying

2013, 34(1): 38-48. doi: 10.3879/j.issn.1000-0887.2013.01.005

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Abstract:
Scattering laws in rock mass which contained flat ellipse crack was researched. The Green function method was presented at mesoscopic scale; linear superposition idea was applied into this model to get wave velocity dispersion and attenuation coefficient at macroscopic scale. The characteristic frequency in frequency dispersion curve is negative correlation with crack size. It had been discovered that a Ladder jump pattern could be presented in frequency dispersion curve if rock mass contains discontinuous size crack, while its characteristic frequency region would be widened if the crack size continues to distribute, such as uniform distribution or Gauss distribution. With two acoustic testsc combined, the rationality and feasibility of this theoretic model is been discussed.

Electroelastic Interaction Between a Piezoelectric Screw Dislocation and a Circularly Layered Inclusion With Imperfect Interfaces

FANG Qi-hong, FENG Hui, LIU You-wen

2013, 34(1): 49-62. doi: 10.3879/j.issn.1000-0887.2013.01.006

Abstract(1980) PDF(1039)

Abstract:
The interaction between a piezoelectric screw dislocation and an interphase layer in piezoelectric solids was theoretically investigated. Here, the dislocation located at arbitrary points inside either the matrix or the inclusion, and the interfaces of the interphase layer were imperfect. By complex variable method, the explicit solutions of complex potentials were given and electroelastic fields could be derived from them. The image force acting on the dislocation could be obtained by the generalized PeachKoehler formula. The motion of the piezoelectric screw dislocation and its equilibrium positions were discussed for variable parameters. The important results show that, if the inner interface of interphase layer is imperfect and the magnitude of degree of interface imperfection reaches the certain value, two equilibrium positions of the piezoelectric screw dislocation in the matrix near the interface are found for certain material combination which has never been observed in previous studies (without considering the interface imperfection).

Modeling Based on the Random Resistance Network Carbon Felt Composite Layer

FANG Xi, GE Quan-geng

2013, 34(1): 63-71. doi: 10.3879/j.issn.1000-0887.2013.01.007

Abstract(1627) PDF(1068)

Abstract:
Based on the statistical rule of the influence factors of carbon fiber monofilament force-resistance effects, the conductive network quantitative model of carbon felt composite layer forceresistance sensing properties was revealed. The length after the lapping of carbon fiber monofilament was discussed, and got the statistics relationship between the average length, density, number of carbon fiber; on the assumption that the fiber random uniform distributed in the felt and the lap points normal distribution, the resistances of 4 different sizes carbon fiber composite layer was estimated, and through the box plot analysis showed that the measured value in the corresponding estimation range, which showed that this model could be good for estimating the resistances of carbon felt composite layer who’s fiber random distributed; finally, basic on the statistics model of carbon felt resistance network, the forceresistance effects of carbon felt composite layer was researched. Through the comparison of theory resistance change rate and the measured resistance change rate, find that composite layer force-resistance effects sensitivity coefficient the model gave is comparatively stable, and the simulated result shows that random resistance network model can imitate the resistance behavior when the carbon felt is loaded well.

Application of Composite Laminated Plates With Bonding Imperfection in Hamilton System

DAN Min

2013, 34(1): 72-84. doi: 10.3879/j.issn.1000-0887.2013.01.008

Abstract(1628) PDF(1100)

Abstract:
The weak interfacial bonding seriously affected the mechanical behavior of laminated plates. Different imperfect bonding models of laminated plates were discussed in Hamilton canonical equation. By combining the modified HR variational principle for elastic material with the quadratic interpolation functions, the linear formulation of laminated plates with 8node for Hamilton canonical equation in the Cartesian coordinate was derived. The relationship between stress and displacement on the interface between layers was considered to improve the normal bonding model, and the state equation with delamination situation was established. The stress and displacement were obtained by solving the overall model. Numerical examples showed that the methods presented were correct, and this paper studied the linear and nonlinear bonding models of the laminated plate respectively. The last results show that the application of improved models can simulate the process of fail better.

Fluid Dynamics Traffic Flow Models and Their Related Non-Linear Waves

ZHANG Peng, WANG Zhuo, S.C.Wong

2013, 34(1): 85-97. doi: 10.3879/j.issn.1000-0887.2013.01.009

Abstract(2526) PDF(2111)

Abstract:
Fluid dynamics methods were used in modeling traffic flow problems, which demonstrated many interesting nonlinear propagation phenomena. It was summarized that the propagation was related to traffic pressures and self-driven forces, which generated shock and rarefaction waves in the LWR model, stop-and-go waves in the higher-order model, overtaking waves (shock or rarefaction waves) in the multi-class LWR model, and a contact discontinuity in problems with discontinuous fluxes. The Riemann problem arising from extension of the LWR model to traffic networks was also introduced in detail. And a system based on the Navier-Stokes equations was proposed to model the 2-dimensional pedestrian flow problem with application of the Eikon equation for determination of a pedestrian’s desired motion direction.

Survival Analysis Approach for Estimating Urban Traffic Congestion Duration

ZHOU Ying-xue, YANG Xiao-bao, HUAN Mei, SI Bing-feng

2013, 34(1): 98-106. doi: 10.3879/j.issn.1000-0887.2013.01.010

Abstract(1931) PDF(1485)

Abstract:
Based on the empirical traffic flow data on the second Ring Road in Beijing, the distribution characteristic of traffic congestion duration was analyzed. The hazardbased traffic congestion duration model was established through survival analysis method. The duration time of traffic congestion was estimated and the temporalspatial distribution was studied using nonparametric method. The results show that 70% of the congestion durations of road segments on the second Ring Road are not longer than four minutes. 89% of the congestion durations are not longer than 12 minutes. The hazard rate is less than 10% when the duration is longer than 12 minutes. The occurrence frequency of congestion on weekday is longer than that on weekend. Both the occurrence frequency and the duration of traffic congestion at morning peak are longer than those at evening peak. The occurrence frequency of congestion on the inner ring is longer than that on the outer ring while the congestion duration on the outer ring is longer than the duration on the inner ring. In the four directions of the second Ring Road, the occurrence frequency of xongestion in the west is lorgest. The congestion duration in the north is longest.