应用数学和力学

2010 Vol. 31, No. 3

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Deformation of Metallic Single-Walled Carbon Nanotubes in the Electric Field Based on Elastic Theory

HONG Wen-liang, GUO Xing-ming

2010, 31(3): 253-260. doi: 10.3879/j.issn.1000-0887.2010.03.001

Abstract(1721) PDF(949)

Abstract:
The electromechanical properties of metallic single-walled carbon nanotubes (SWCNTs) in the electric field are demonstrated via a column shell model. A model of hemisphere was in troduced to determine the charge distribution and localelectric field on SWCNTs. It is shown that, regarding the SWCNT's an elastic column shell, the analytical solutions of charged SWCNT's axial strain and radial strain are obtained. Single-walled carbon nanotubes with higher aspectratio can show greater deformation and the greatestradial deformation appears at the end of the tube, and significant axial strain can be induced in CNTs with long length (around 100 nm) even though the applied electric field is not strong enough; when the SWCNTs are fixed at both ends the radius of SWCNTs become smaller along axial position. These results redound to our understanding of metallic SWCNTs electrom echanical properties in the electric field and SWCNTs applications on nanoelectronic device and nanoelectrom echanical systems.

Nonlinear Stability of a Double-Deck Reticulated Circular Shallow Spherical Shell

XU Jia-chu, LI Yong, WANG Fan, LIU Ren-huai

2010, 31(3): 261-272. doi: 10.3879/j.issn.1000-0887.2010.03.002

Abstract(1793) PDF(1002)

Abstract:
Based on the variational equation of the nonlinear bending theory of double-deck reticulated shallow shells, equations of large deflection and boundary conditions for a doubledeck reticulated circular shallow spherical shell under a uniformly distributed pressure were derived by using coordinate transformation means and stationary complementary energy principle. The characteristic relationship and critical buckling pressure for the shell with two types of boundary conditions were obtained by taking the modified iteration method. The effects of geometrical parameters on the buckling behavior were also discussed.

Analysis of Transient Temperature Field in Coke Drums

NING Zhi-hua, LIU Ren-huai

2010, 31(3): 273-284. doi: 10.3879/j.issn.1000-0887.2010.03.003

Abstract(1928) PDF(1002)

Abstract:
One of the primary reasons leading to bulging and cracking in a coke drum is the severe temperature gradient due to cyclic temperature variation. Based on the two-dmiensional heat conduction theory, the analytical solution of the transient temperature field in the coke drum was derived, which was different from the known FEM results. The length of the coke drum was considered finite, and the dynamic boundary conditions caused by fluid uninterrupted rising in oiling and watering stages were smiulated by the iteration method. The numerical results show that the present theoreticalmodel can accurately describe basic features of the transient temperature field in the coke drum. Effects of the geometry of the coke drum and the rising velocity of quench water on the axial temperature gradient are also discussed.

Stress Field of Orthotropic Cylinder Subjected to Axial Compression

ZHONG Wei-zhou, SONG Shun-cheng, CHEN Gang, HUANG Xi-cheng, HUANG Peng

2010, 31(3): 285-294. doi: 10.3879/j.issn.1000-0887.2010.03.004

Abstract(1876) PDF(992)

Abstract:
Based on the material volume cons tancy hypothesis, circum ference and radial stresses of cylinder specmien were analyzed when the cylinder is loaded along the axial direction. Circum ference and radial stress distribution is radius parameter power function when specimen material constitutive relation is orthotropic. The stress distribution is radius parameter quadratic function for transverse isotropy material. A long the cylinder axial line, circum ference and radial stresses were maxmium and equal to each other. In the circum ference boundary surface, radial stress is zero and circum ference stress value is the minmium. The maxtensile circumference strain failure theory is applied to calculate critical axial loading. Circum ference boundary layer failure criterion of orthotropic material cylinder is described by HillTsai strength theory. The obtained strength theory is not only related to axial stress and specmien materialm echanical properties, but a lso to specmienaxial de formation strain rate and change rate of strain rate.

Lie Group Analysis for the Effect of Temperature-Dependent Fluid Viscosity and Thermophoresis Particle Deposition on Free Convective Heat and Mass Transfer in the Presence of Variable Stream Conditions

Ramasamy Kandasamy, Muhaimin

2010, 31(3): 295-305. doi: 10.3879/j.issn.1000-0887.2010.03.005

Abstract(1353) PDF(832)

Abstract:
A steady two-dmiensional flow of incompressible fluid over a vertical stretching sheet was studied. The fluid viscosity was assumed to vary as a linear function of temperature. A scaling group of transformations was applied to the governing equations. The system remained invariant due to some relations among the parameters of the transformations. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation and two second-order ordinary differential equations corresponding to energy and diffusion equations were derived. The equations along with the boundary conditions were solved numerically. It is found that the decrease in the temperature-dependent fluid viscosity makes the velocity decrease with the increasing distance of the stretching sheet. At a particular point of the sheet, the fluid velocity decreases with the decreasing viscosity while the temperature increases in this case. The impact of thermophoresis particle deposition plays an miportant role on the concen tration boundary layer. The results thus obtained are presented graphically and discussed.

Effects of Magneto Hydro Dynamic Flow Past a Vertical Plate With Variable Surface Temperature

Ibrahim A. Abbas, G. Palani

2010, 31(3): 306-314. doi: 10.3879/j.issn.1000-0887.2010.03.006

Abstract(1690) PDF(650)

Abstract:
An analysis was performed to study them agneto hydrodynamic flow of an electrically conducting, viscous incompressible fluid past a semi-infinite vertical plate with variable surface temperature, under the action of transversely applied magnetic field was carried out. The heat due to viscous dissipation and the induced magnetic field were assumed to be negligible. The dimension less governing equations are unsteady, two-dimensional, coupled and non-linear governing equations. It is found that the magnetic field parameter has a retarding effect on the velocity of air and water.

Multi-Objective Optimization Design of Radar Absorbing Sandwich Structure

CHEN Ming-ji, PEI Yong-mao, FANG Dai-ning

2010, 31(3): 315-323. doi: 10.3879/j.issn.1000-0887.2010.03.007

Abstract(1836) PDF(984)

Abstract:
By introducing a dimen sionless parameter to couple the two objectives, weight and radar absorbing performance, in a single objective function, a multi-objective optmiization procedure for radar absorbing sandwich structure (RASS) with cellular core has been proposed. The optmiization models considered were one-side clamped sandwich panels with four kinds of cores which were subject to uniformly distributed loads. The average specular reflectivity calculated by transfer matrix method and periodic moment method was utilized to characterize the radar absorbing performance, while the mechanical constraints included facesheet yielding, core shearing and facesheet wrinkling. The optimization analysis indicated that sandwich structure with two-dmiensional (2D) composite lattice core filled with ultra-lightweight spongy may be a better candidate of lightweight RASS than those with cellular foam or hexagonal honeycomb cores. The 2D Kagome lattice was found to outperform the square lattice with respect to radar absorbing.

Fold Catastrophe Model of Strike-Slip Fault Earthquake

PAN Yue, LI Ai-wu

2010, 31(3): 324-336. doi: 10.3879/j.issn.1000-0887.2010.03.008

Abstract(1827) PDF(833)

Abstract:
By using differential form of potential energy function, and taking the effect of work applied by external force in far field in to account, the mechanism of strike-slip fault earthquake was analyzed. The researching indicates that, in catas trophe theory the characters displayed by fold catastrophe model correspond to the primary characteristics of strike-slip fault earthquake one by one. Fold catastrophe can describe the position of starting point and end point of fault failure, distance of fault dislocation etc, including the description about the stability of surrounding rock-fault system before and after the earthquake. Two different illustrations about~elastic energy releasing amount of the surround ing rock with fault failure were shown, their primary characteristics can demonstrate each other. The in tensity of strike-slip fault earthquake was related to the surrounding rock press, and to the stiffness ratio of surrounding rock and faultetc. The bigger the surrounding rock press was, the smaller stiffness ratio was. The bigger the included angle between the tangential stress axis to causative fault surface was, the bigger the earthquake intensity was.

Hodograph Method of Flow on Two-Dimensional Manifold

LI Kai-tai, SHI Feng

2010, 31(3): 337-350. doi: 10.3879/j.issn.1000-0887.2010.03.009

Abstract(1875) PDF(817)

Abstract:
For some special flow, especially the potential flow in the plane, there are obvious advantages using the tool of hodograph method. For the realistic flow, there exists stream surface, namely, two-dmi ensionalmanifold, on which the velocity vector of the flow liesits tangent space. By in troducing the stream function and potential function, the hodograph method for potential flow on a surface was established with the help of tensor analysis, which provided a kind of analysis method. For the derived hodograph equation, the characteristic equation and its characteristic roots were also derived, from which the type of the hodograph equation of the second order can be classified. Moreover, some examples for special surfaces were given.

Existence Results for Some Fourth Order Boundary Value Problems With a Parameter

YANG Yang, ZHANG Ji-hui

2010, 31(3): 351-359. doi: 10.3879/j.issn.1000-0887.2010.03.010

Abstract(1456) PDF(715)

Abstract:
A sequel to Yang, Zhang [Nonlinear Anal, 2008, 69:1364-1375.] in which nontrivial solutions for the fourth order boundary value problems are studied. Now under the same conditions near in finity, but different from the conditions near zero, positive, negative, and sign-changing solutions are obtained by combining critical point theory, retracting property and invariant sets.

Wavefront Solutions in the Diffusive Nicholson’s Blowflies Equation With Nonlocal Delay

ZHANG Cun-hua, YAN Xiang-ping

2010, 31(3): 360-368. doi: 10.3879/j.issn.1000-0887.2010.03.011

Abstract(1926) PDF(695)

Abstract:
The diffusive Nicholson.s blow flies equation with a nonlocal delay in corporated as an integral convolution over all the past tmie up to now and the whole one-dmiensional spatial doma in was studied. When the delay kernel is assumed to be the strong generic kernel, by using the linear chain te chniques and the geometric singularperturbation theory, the existence of trave lling front solutions is shown for small delay.

Stabilized Crouzeix-Raviart Element for the Coupled Stokes and Darcy Problem

FEGN Min-fu, QI Rui-sheng, ZHU Rui, JU Bing-tao

2010, 31(3): 369-378. doi: 10.3879/j.issn.1000-0887.2010.03.012

Abstract(2056) PDF(1003)

Abstract:
A new stabilized finite element method for the coupled Stokes and Darcy problem was introduced based on the noncom forming Crouzeix-Raviart element. Optimal error estimates for the fluid velocity and pressure were derived. Finally, a numerical example verifying the theoretical predictions was presented.