Applied Mathematics and Mechanics (English Edition)

Deformation of metallic single-walled carbon nanotubes in electric field based on elastic theory

洪文亮郭兴明

2010, 31(3): 271-278. doi:10.1007/s10483-010-0301-9

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The electromechanical properties of metallic single-walled carbon nanotubes (SWCNTs) in the electric field are demonstrated with a column shell model in this paper. A hemisphere model is introduced to determine the charge distribution and the local electric field in SWCNTs. By treating the SWCNT as an elastic column shell, the analytical solutions of the charged SWCNT’s axial strain and the radial strain are obtained. SWCNTs with a larger aspect ratio show greater deformation. The greatest radial deformation appears at the end of the tube. The significant axial strain can be induced in CNTs with a large length (around 100 nm) even though the applied electric field is not strong enough. When SWCNTs are fixed at both ends, the radius of SWCNTs becomes small along the axial position.

Nonlinear stability of double-deck reticulated circular shallow spherical shell

徐加初李勇王璠刘人怀

2010, 31(3): 279-290. doi:10.1007/s10483-010-0302-7

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

Analysis of transient temperature field in coke drums

宁志华刘人怀

2010, 31(3): 291-304. doi:10.1007/s10483-010-0303-7

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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 twodimensional heat conduction theory, an analytical solution of the transient temperature field in the coke drum is obtained, which is different from the known FEM results. The length of the coke drum is considered finite. The dynamic boundary conditions caused by fluid uninterrupted rising in oiling and watering stages are simulated with the iteration method. Numerical results show that the present theoretical model 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

钟卫洲宋顺成陈刚黄西成黄鹏

2010, 31(3): 305-316. doi:10.1007/s10483-010-0304-z

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Based on the constancy hypothesis of material volume, the circumferential and radial stresses of a cylinder specimen are analyzed when the cylinder is subject to a loading along the axial direction. The circumferential and radial stress distribution is a power function of radius parameter when the constitutive relation of specimen material is orthotropic. The stress distribution is a quadratic function of radius parameter for transversely isotropic material. Along the cylinder axial line, the circumferential and radial stresses are maximum and equal to each other. In the circumference boundary surface, the radial stress is zero and the circumferential stress value is minimal. The failure theory of maximum tensile circumferential strain is applied to calculate the critical axial loading. The circumference-boundary-layer failure criterion of orthotropic cylinders is described with the Hill-Tsai strength theory. The obtained strength theory is related to axial stress and mechanical properties of specimen material and to the specimen axialdeformation strain rate and the 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 under variable stream conditions

Ramasamy KANDASAMY Ismoen MUHAIMIN

2010, 31(3): 317-328. doi:10.1007/s10483-010-0305-6

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This paper examines a steady two-dimensional flow of incompressible fluid over a vertical stretching sheet. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equations. The system remains invariant due to some relations among the transformation parameters. 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 are derived. The equations along with the boundary conditions are 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 but the temperature increases with the decreasing viscosity. The impact of the thermophoresis particle deposition plays an important role in the concentration boundary layer. The obtained results are presented graphically and discussed.

Effects of magnetohydrodynamic flow past a vertical plate with variable surface temperature

Ibrahim A. ABBAS G.PALANI

2010, 31(3): 329-338. doi:10.1007/s10483-010-0306-9

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An analysis is performed to study the magnetohydrodynamic 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. The heat due to viscous dissipation and the induced magnetic field are assumed to be negligible. The dimensionless 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 velocities of air and water.

Multi-objective optimization design of radar absorbing sandwich structure

陈明继裴永茂方岱宁

2010, 31(3): 339-348. doi:10.1007/s10483-010-0307-z

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By introducing a dimensionless parameter to couple the two objectives, weight and radar absorbing performance, into a single objective function, a multi-objective optimization procedure for the radar absorbing sandwich structure (RASS) with a cellular core is proposed. The optimization models considered are one-side clamped sandwich panels with four kinds of cores subject to uniformly distributed loads. The average specular reflectivity calculated with the transfer matrix method and the periodic moment method is utilized to characterize the radar absorbing performance, while the mechanical constraints include the facesheet yielding, core shearing, and facesheet wrinkling. The optimization analysis indicates that the sandwich structure with a two-dimensional (2D) composite lattice core filled with ultra-lightweight sponge may be a better candidate of lightweight RASS than those with cellular foam or hexagonal honeycomb cores. The 2D Kagome lattice is found to outperform the square lattice with respect to radar absorbing.

Fold catastrophe model of strike-slip fault earthquake

潘岳李爱武

2010, 31(3): 349-362. doi:10.1007/s10483-010-0308-9

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Using a differential form of the potential energy function and taking the effect of work applied by external force in far field into account, the mechanism of strike-slip fault earthquake is analyzed. The research indicates that each characteristic displayed with a fold catastrophe model in the catastrophe theory corresponds to a specific primary characteristic of the strike-slip fault earthquake. The fold catastrophe can describe the positions of starting and end points of a fault failure and the distance of fault dislocation. These include the description of stability of the surrounding rock-fault system before and after the earthquake. Two different illustrations about elastic energy releasing amount of the surrounding rock with the fault failure are shown with the primary characteristics mutually demonstrated. The intensity of strike-slip fault earthquake is related to the surrounding rock press and the stiffness ratio of surrounding rock and fault. The larger the surrounding rock press, the smaller the stiffness ratio. The larger the included angle between the tangential stress axis and the causative fault surface, the stronger the earthquake.

Hodograph method of flow on two-dimensional manifold

李开泰史峰

2010, 31(3): 363-376. doi:10.1007/s10483-010-0309-x

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For some special flows, especially the potential flow in a plane, using the hodograph method has obvious advantages. Realistic flows have a stream surface, namely, a two-dimensional manifold, on which the velocity vector of the flow lies on its tangent space. By introducing a stream function and a potential function, we establish the hodograph method for potential flows on a surface using the tensor analysis. For the derived hodograph equation, we obtain a characteristic equation and its characteristic roots, from which we can classify the type of the second-order hodograph equation. Moreover, we give some examples for special surfaces.

Existence of solutions for fourth-order boundary value problem with parameter

杨阳张吉慧

2010, 31(3): 377-384. doi:10.1007/s10483-010-0310-x

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This paper is a sequel to a previous paper (Yang, Y. and Zhang, J. H. Existence of solutions for some fourth-order boundary value problems with parameters. Nonlinear Anal. 69(2), 1364–1375 (2008)) in which the nontrivial solutions to the fourthorder boundary value problems were studied. In the current work with the same conditions near infinity but different near zero, the positive, negative, and sign-changing solutions are obtained by the critical point theory, retracting property, and invariant sets.

Wavefront solutions in diffusive Nicholson’s blowflies equation with nonlocal delay

张存华颜向平

2010, 31(3): 385-392. doi:10.1007/s10483-010-0311-x

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This paper is concerned with the diffusive Nicholson’s blowflies equation with nonlocal delay incorporated as an integral convolution over the entire past time up to now and the whole one-dimensional spatial domain R. Assume that the delay kernel is a strong generic kernel. By the linear chain techniques and the geometric singular perturbation theory, the existence of travelling front solutions is shown for small delay.

Stabilized Crouzeix-Raviart element for the coupled Stokes and Darcy problem

冯民富祁瑞生朱瑞鞠炳焘

2010, 31(3): 393-404. doi:10.1007/s10483-010-0312-z

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This paper introduces a new stabilized finite element method for the coupled Stokes and Darcy problem based on the nonconforming Crouzeix-Raviart element. Optimal error estimates for the fluid velocity and pressure are derived. A numerical example is presented to verify the theoretical predictions.

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