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2016年 第37卷 第2期    刊出日期：2016-02-01

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论文

Coupling model for unsteady MHD flow of generalized Maxwell fluid with radiation thermal transform

Yaqing LIU, Boling GUO

2016, 37(2):  137-150.  doi:10.1007/s10483-016-2021-8

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This paper introduces a new model for the Fourier law of heat conduction with the time-fractional order to the generalized Maxwell fluid. The flow is influenced by magnetic field, radiation heat, and heat source. A fractional calculus approach is used to establish the constitutive relationship coupling model of a viscoelastic fluid. We use the Laplace transform and solve ordinary differential equations with a matrix form to obtain the velocity and temperature in the Laplace domain. To obtain solutions from the Laplace space back to the original space, the numerical inversion of the Laplace transform is used. According to the results and graphs, a new theory can be constructed. Comparisons of the associated parameters and the corresponding flow and heat transfer characteristics are presented and analyzed in detail.

Quasi-optimal complexity of adaptive finite element method for linear elasticity problems in two dimensions

Chunmei LIU, Liuqiang ZHONG, Shi SHU, Yingxiong XIAO

2016, 37(2):  151-168.  doi:10.1007/s10483-016-2041-9

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This paper introduces an adaptive finite element method (AFEM) using the newest vertex bisection and marking exclusively according to the error estimator without special treatment of oscillation. By the combination of the global lower bound and the localized upper bound of the posteriori error estimator, perturbation of oscillation, and cardinality of the marked element set, it is proved that the AFEM is quasi-optimal for linear elasticity problems in two dimensions, and this conclusion is verified by the numerical examples.

Differential transform method for solving Richards' equation

Xi CHEN, Ying DAI

2016, 37(2):  169-180.  doi:10.1007/s10483-016-2023-8

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An approximate solution to Richards' equation is presented, mathematically describing a sort of unsaturated single phase fluid flow in porous media. The approach is a differential transform method (DTM) with intermediate variables. Two examples are given to demonstrate the accuracy of the presented solution.

Sufficient conditions of Rayleigh-Taylor stability and instability in equatorial ionosphere

Sicheng WANG, Sixun HUANG

2016, 37(2):  181-192.  doi:10.1007/s10483-016-2022-8

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Rayleigh-Taylor (R-T) instability is known as the fundamental mechanism of equatorial plasma bubbles (EPBs). However, the sufficient conditions of R-T instability and stability have not yet been derived. In the present paper, the sufficient conditions of R-T stability and instability are preliminarily derived. Linear equations for small perturbation are first obtained from the electron/ion continuity equations, momentum equations, and the current continuity equation in the equatorial ionosphere. The linear equations can be casted as an eigenvalue equation using a normal mode method. The eigenvalue equation is a variable coefficient linear equation that can be solved using a variational approach. With this approach, the sufficient conditions can be obtained as follows:if the minimum systematic eigenvalue is greater than one, the ionosphere is R-T unstable; while if the maximum systematic eigenvalue is less than one, the ionosphere is R-T stable. An approximate numerical method for obtaining the systematic eigenvalues is introduced, and the R-T stable/unstable areas are calculated. Numerical experiments are designed to validate the sufficient conditions. The results agree with the derived suf-ficient conditions.

Unsteady MHD flow over exponentially stretching sheet with slip conditions

T. HAYAT, A. SHAFIQ, A. ALSAEDI, S. A. SHAHZAD

2016, 37(2):  193-208.  doi:10.1007/s10483-016-2024-8

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The present paper examines the hydromagnetic three-dimensional flow in-duced by a stretched surface. An incompressible material saturates the porous medium. Velocity and thermal slip boundary conditions are considered. Suitable transformations are used to obtain the nonlinear ordinary differential equations. Series solutions of the resulting systems are constructed. The effects of various pertinent parameters on the axial velocity and temperature distributions are analyzed graphically. The skin friction and the Nusselt number are computed numerically and graphically.

A class of exact solutions for N-dimensional incompressible magnetohydrodynamic equations

Ping LIU

2016, 37(2):  209-214.  doi:10.1007/s10483-016-2025-8

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In this paper, a sufficient and necessary condition is presented for existence of a class of exact solutions to N-dimensional incompressible magnetohydrodynamic (MHD) equations. Such solutions can be explicitly expressed by appropriate formulae. Once the required matrices are chosen, solutions to the MHD equations are directly constructed.

Analysis of periodic and aperiodic convective stability of double diffusive nanofluid convection in rotating porous layer

S. AGARWAL, P. RANA

2016, 37(2):  215-226.  doi:10.1007/s10483-016-2026-8

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The onset of periodic and aperiodic convection in a binary nanofluid satu-rated rotating porous layer is studied considering constant flux boundary conditions. The porous medium obeys Darcy's law, while the nanofluid envisages the effects of the Brow-nian motion and thermophoresis. The Rayleigh numbers for stationary and oscillatory convection are obtained in terms of various non-dimensional parameters. The effect of the involved physical parameters on the aperiodic convection is studied graphically. The results are validated in comparison with the published literature in limiting cases of the present study.

Theoretical model for elliptical tube laterally impacted by two parallel rigid plates

Haibo WANG, Ruirui LIU, Jialing YANG, Hua LIU, Yuxin SUN

2016, 37(2):  227-236.  doi:10.1007/s10483-016-2027-8

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An analytical model is developed to study the crushing behavior and energy absorption capability of a single elliptical tube impacted by two parallel rigid plates, with and without consideration of the strain hardening effect. The four-hinge collapse mechanism is used, and the governing equation is derived from Lagrange equations of the second kind. The numerical simulation of the dynamic response of the elliptical tube under impact using the finite element explicit code LS-DYNA is performed. The reaction force-displacement curve and displacement-time curve of the plate obtained from the two methods are in good agreement.

Saint-Venant torsion analysis of bars with rectangular cross-section and effective coating layers

H. TEIMOORI, R. T. FAAL, R. DAS

2016, 37(2):  237-252.  doi:10.1007/s10483-016-2028-8

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This paper investigates the torsion analysis of coated bars with a rectangular cross-section. Two opposite faces of a bar are coated by two isotropic layers with different materials of the original substrate that are perfectly bonded to the bar. With the Saint-Venant torsion theory, the governing equation of the problem in terms of the warping function is established and solved using the finite Fourier cosine transform. The state of stress on the cross-section, warping of the cross-section, and torsional rigidity of the bar are evaluated. Effects of thickness of the coating layers and material properties on these quantities are investigated. A set of graphs are provided that can be used to determine the coating thicknesses and material properties so as to keep the maximum von Mises stress on the cross-section below an allowable value for effective use of the coating layer.

Second-order two-scale computational method for ageing linear viscoelastic problem in composite materials with periodic structure

Yang ZHANG, Junzhi CUI, Yufeng NIE

2016, 37(2):  253-264.  doi:10.1007/s10483-016-2029-8

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The correspondence principle is an important mathematical technique to compute the non-ageing linear viscoelastic problem as it allows to take advantage of the computational methods originally developed for the elastic case. However, the correspon-dence principle becomes invalid when the materials exhibit ageing. To deal with this problem, a second-order two-scale (SOTS) computational method in the time domain is presented to predict the ageing linear viscoelastic performance of composite materials with a periodic structure. First, in the time domain, the SOTS formulation for calcu-lating the effective relaxation modulus and displacement approximate solutions of the ageing viscoelastic problem is formally derived. Error estimates of the displacement ap-proximate solutions for SOTS method are then given. Numerical results obtained by the SOTS method are shown and compared with those by the finite element method in a very fine mesh. Both the analytical and numerical results show that the SOTS computational method is feasible and efficient to predict the ageing linear viscoelastic performance of composite materials with a periodic structure.

Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes

R. KOLAHCHI, A. M. MONIRI BIDGOLI

2016, 37(2):  265-274.  doi:10.1007/s10483-016-2030-8

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In this study, a model for dynamic instability of embedded single-walled carbon nanotubes (SWCNTs) is presented. SWCNTs are modeled by the sinusoidal shear deformation beam theory (SSDBT). The modified couple stress theory (MCST) is considered in order to capture the size effects. The surrounding elastic medium is described by a visco-Pasternak foundation model, which accounts for normal, transverse shear, and damping loads. The motion equations are derived based on Hamilton's principle. The differential quadrature method (DQM) in conjunction with the Bolotin method is used in order to calculate the dynamic instability region (DIR) of SWCNTs. The effects of different parameters, such as nonlocal parameter, visco-Pasternak foundation, mode numbers, and geometrical parameters, are shown on the dynamic instability of SWCNTs. The results depict that increasing the nonlocal parameter shifts the DIR to right. The results presented in this paper would be helpful in design and manufacturing of nano-electromechanical system (NEMS) and micro-electro-mechanical system (MEMS).