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2019年 第40卷 第10期    刊出日期：2019-10-01

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论文

Large deformation analysis of a cantilever beam made of axially functionally graded material by homotopy analysis method

Xin LIN, Yixin HUANG, Yang ZHAO, Tianshu WANG

2019, 40(10):  1375-1386.  doi:10.1007/s10483-019-2515-9

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Large deformation of a cantilever axially functionally graded (AFG) beam subject to a tip load is analytically studied using the homotopy analysis method (HAM). It is assumed that its Young's modulus varies along the longitudinal direction according to a power law. Taking the solution of the corresponding homogeneous beam as the initial guess and obtaining a convergence region by adjusting an auxiliary parameter, the analytical expressions for large deformation of the AFG beam are provided. Results obtained by the HAM are compared with those obtained by the finite element method and those in the previous works to verify its validity. Good agreement is observed. A detailed parametric study is carried out. The results show that the axial material variation can greatly change the deformed configuration, which provides an approach to control and manage the deformation of beams. By tailoring the axial material distribution, a desired deformed configuration can be obtained for a specific load. The analytical solution presented herein can be a helpful tool for this procedure.



Crystallization of self-propelled particles on a spherical substrate

Yan FANG, Chen WANG, Hongyuan JIANG

2019, 40(10):  1387-1398.  doi:10.1007/s10483-019-2525-8

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In this paper, we investigate the self-propelled particles confined on a spherical substrate and explore the structural and dynamic properties of self-propelled particles by controlling the packing fraction and activity. We find that these self-propelled particles freeze into the crystal with the increase in the packing fraction. We observe the pattern evolution of inevitable topological defects due to the geometric constraints of the spherical substrate. During the process of freezing, there is a transition from twelve isolated grain boundaries to the uniform distribution of defects with the increase in the self-propelled velocity. Finally, we establish a phase diagram of the freezing process. These results may deepen our understanding of active particles in complex and crowded environments.

Torsional wave frequency in heterogeneous earth crust lying over dry sandy semi-infinite substratum

S. K. VISHWAKARMA, R. KAUR, T. R. PANIGRAHI

2019, 40(10):  1399-1412.  doi:10.1007/s10483-019-2529-7

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The present study is carried out to investigate the transference of torsional surface waves in a heterogeneous anisotropic crust lying over a dry sandy half-space. The rigidities and densities as well as the initial stress are assumed varying as a function of depth in both the media. These variations are the product of the polynomial function of depth in degree n (n ∈ R) and the exponential function of depth. Following the theory of elastic waves, the mathematical model is established. Separation of variables is used to obtain the displacement in the layer and the half-space. Intrinsic boundary conditions are imposed to derive the dispersion equation. The inhomogeneity parameters associated with the rigidity, the density, and the initial stress of the medium are found to have substantial influence on the phase velocity of the torsional surface wave. The graphical presentations are drawn to exhibit the findings. The results thus obtained are significant for the investigation and characterization of torsional surface wave in the heterogeneous anisotropic layer.

Random heterogeneous microstructure construction of composites via fractal geometry

Siwen WANG, Zhansheng GUO

2019, 40(10):  1413-1428.  doi:10.1007/s10483-019-2522-5

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The microstructures of a composite determine its macroscopic properties. In this study, microstructures with particles of arbitrary shapes and sizes are constructed by using several developed fractal geometry algorithms implemented in MATLAB. A two-dimensional (2D) quadrilateral fractal geometry algorithm is developed based on the modified Sierpinski carpet algorithm. Square-, rectangle-, circle-, and ellipse-based microstructure constructions are special cases of the 2D quadrilateral fractal geometry algorithm. Moreover, a three-dimensional (3D) random hexahedron geometry algorithm is developed according to the Menger sponge algorithm. Cube-and sphere-based microstructure constructions are special cases of the 3D hexahedron fractal geometry algorithm. The polydispersities of fractal shapes and random fractal sub-units demonstrate significant enhancements compared to those obtained by the original algorithms. In addition, the 2D and 3D algorithms mentioned in this article can be combined according to the actual microstructures. The verification results also demonstrate the practicability of these algorithms. The developed algorithms open up new avenues for the constructions of microstructures, which can be embedded into commercial finite element method softwares.

Abstraction and operator characterization of fractal ladder viscoelastic hyper-cell for ligaments and tendons

Jianqiao GUO, Yajun YIN, Gexue REN

2019, 40(10):  1429-1448.  doi:10.1007/s10483-019-2524-8

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This study investigates the viscoelastic behavior of soft bio-fibres in association with their fractal structures. A spring-dashpot fractal network with the self-similar topology, named the Π-type fractal ladder hyper-cell (FLHC), is abstracted from the micro/nano-structure of ligaments and tendons (LTs). Its constitutive operator is derived by the Heaviside operational calculus, which is of intrinsic fractional order. In terms of this operator, the long-term viscoelastic relaxation of bio-fibres arising from the fractal ladder topology is expounded. In addition, the fractional-order viscoelastic constitutive equation is obtained based on the FLHC of LTs, and its results are consistent with those of available human knee and spinal LT relaxation experiments. Results on the constitutive equation of FLHCs are formulated into two propositions. The multidisciplinary invariance and implications from the fractal ladder pattern of bio-fibres are also discussed.

Threshold and decay properties of transient isolated turbulent band in plane Couette flow

Jianzhou LU, Jianjun TAO, Weitao ZHOU, Xiangming XIONG

2019, 40(10):  1449-1456.  doi:10.1007/s10483-019-2531-6

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By direct numerical simulations of the plane Couette flow (PCF) in a large computational domain, it is shown that an isolated turbulent band decays monotonically at low Reynolds numbers but experiences transient growth before the eventual relaminarization at moderate Reynolds numbers. The lower bound Reynolds number of the transient-growth regime is determined as 286. The width, length, and tilt angle of the isolated band structure are defined based on the disturbance kinetic energy in the mid-plane, and the geometric characteristics of the band can be described with a tilted rectangle. It is illustrated that before its eventual fragmentation, the isolated turbulent band decays in a style of longitudinal contraction, where the center, width, and tilt angle of the band keep almost constant but the band length contracts with a statistically constant velocity.

Electroviscous effect on electromagnetohydrodynamic flows of Maxwell fluids in parallel plate microchannels

Yongbo LIU, Yongjun JIAN

2019, 40(10):  1457-1470.  doi:10.1007/s10483-019-2526-9

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Considering the influence of the streaming potential and electroviscous effects, the analytical solutions for electromagnetohydrodynamic (EMHD) flows in parallel plate microchannels are obtained. The electrolyte solutions in the microchannels are taken as generalized Maxwell fluids, and slip boundary conditions are adopted. To accurately analyze the EMHD flow characteristics, the variation trends of the electroviscous effects with the corresponding parameters must be understood. The results show that the electroviscous effects increase with the increase in the relaxation time De, the slip coefficient α, and the wall zeta potential ψ₀. However, the increase in the inverse of the electrical double-layer (EDL) thickness K, the electrical oscillating Reynolds number Re, and the ionic Péclet number Pe can decrease the electroviscous effects. We also demonstrate that the electroviscous effect on the EMHD flows of generalized Maxwell fluids is larger than that of Newtonian fluids. This work will be useful in designing EMHD flows in parallel plate microchannels.

Unsteady three-dimensional MHD flow of the micropolar fluid over an oscillatory disk with Cattaneo-Christov double diffusion

A. RAUF, S. A. SHEHZAD, Z. ABBAS, T. HAYAT

2019, 40(10):  1471-1486.  doi:10.1007/s10483-019-2530-6

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Cattaneo-Christov heat and mass flux models are considered rather than Fourier and Fick laws due to the presence of thermal and concentration transport hyperbolic phenomena. The generalized form of the Navier-Stokes model is considered in hydromagnetic flow. Three-dimensional (3D) unsteady fluid motion is generated by the periodic oscillations of a rotating disk. Similarity transformations are used to obtain the normalized fluid flow model. The successive over relaxation (SOR) method with finite difference schemes are accomplished for the numerical solution of the obtained partial differential non-linear system. The flow features of the velocity, microrotation, temperature, and concentration fields are discussed in pictorial forms for various physical flow parameters. The couple stresses and heat and mass transfer rates for different physical quantities are explained via tabular forms. For better insight of the physical fluid model, 3D fluid phenomena and two-dimensional (2D) contours are also plotted. The results show that the micropolar fluids contain microstructure having non-symmetric stress tensor and are useful in lubrication theory. Moreover, the thermal and concentration waves in CattaneoChristov models have a significance role in the laser heating and enhancement in thermal conductivity.

A hybrid subcell-remapping algorithm for staggered multi-material arbitrary Lagrangian-Eulerian methods

Haihua YANG, Ping ZHANG

2019, 40(10):  1487-1508.  doi:10.1007/s10483-019-2523-5

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A new flux-based hybrid subcell-remapping algorithm for staggered multimaterial arbitrary Lagrangian-Eulerian (MMALE) methods is presented. This new method is an effective generalization of the original subcell-remapping method to the multi-material regime (LOUBÈRE, R. and SHASHKOV, M. A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods. Journal of Computational Physics, 209, 105-138 (2005)). A complete remapping procedure of all fluid quantities is described detailedly in this paper. In the pure material regions, remapping of mass and internal energy is performed by using the original subcell-remapping method. In the regions near the material interfaces, remapping of mass and internal energy is performed with the intersection-based fluxes where intersections are performed between the swept regions and pure material polygons in the Lagrangian mesh, and an approximate approach is then introduced for constructing the subcell mass fluxes. In remapping of the subcell momentum, the mass fluxes are used to construct the momentum fluxes by multiplying a reconstructed velocity in the swept region. The nodal velocity is then conservatively recovered. Some numerical examples simulated in the full MMALE regime and several purely cyclic remapping examples are presented to prove the properties of the remapping method.

Influence of Hall current and Joule heating on entropy generation during electrokinetically induced thermoradiative transport of nanofluids in a porous microchannel

B. MALLICK, J. C. MISRA, A. R. CHOWDHURY

2019, 40(10):  1509-1530.  doi:10.1007/s10483-019-2528-7

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A comprehensive theoretical study of entropy generation during electrokinetically driven transport of a nanofluid is of prime concern in the paper. The flow is considered to take place on a wavy channel under the action of an external transverse magnetic field and an external pressure gradient. Navier slips at the walls of the channel and thermal radiation have been taken into account in the study. The theoretical study has been carried out by developing a mathematical model by taking into account the effects of Joule heating, viscous dissipation, and the transverse magnetic field on heat transfer during the electrokinetic transport of the fluid. The derived analytical expressions have been computed numerically by considering the nanofluid as a mixture of blood and ferromagnetic nanoparticles. Variations in velocity, streaming potential, temperature distribution, Nusselt number, and Bejan number associated with the electrokinetic flow in capillaries have been investigated by the parametric variation method. The results have been presented graphically. The present investigation reveals that streaming potential decreases due to the Hall effect, while for the cooling capacity of the microsystem, we find an opposite behavior due to the Hall effect. The study further reveals that the fluidic temperature is reduced due to increase in the Hall current, and thereby thermal irreversibility of the system is reduced significantly. The results presented here can be considered as the approximate estimates of blood flow dynamics in capillaries during chemotherapy in cancer treatment.