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Applied Mathematics and Mechanics(English Edition) 2019年第6期40卷 767-782页

作者： M. FARAJI-OSKOUIE A. NOROUZZADEH R. ANSARI H. ROUHI Department of Mechanical Engineering University of GuilanRasht 3756Iran Department of Engineering Science Faculty of Technology and EngineeringUniversity of GuilanRudsar-Vajargah 44891-63157Iran

A novel size-dependent model is developed herein to study the bending behavior of beam-type micro/nano-structures considering combined effects of nonlocality and micro-rotational degrees of freedom. To accomplish this aim, the micropolar theory is combined with the nonlocal elasticity. To consider the nonlocality, both integral (original) and differential formulations of Eringen’s nonlocal theory are considered. The beams are considered to be Timoshenko-type, and the governing equations are derived in the variational form through Hamilton’s principle. The relations are written in an appropriate matrix-vector representation that can be readily utilized in numerical approaches. A finite element (FE) approach is also proposed for the solution procedure. Parametric studies are conducted to show the simultaneous nonlocal and micropolar effects on the bending response of small-scale beams under different boundary conditions.

关键词： integral model of nonlocal elasticity differential model of nonlocal elasticity micropolar theory finite element (FE) analysis Timoshenko nano-beam

Quadrilateral 2D linked-interpolation finite elements for micropolar continuum

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Acta Mechanica Sinica 2019年第5期35卷 1001-1020页

作者： Sara Grbcic Gordan Jelenic Dragan Ribarc? Faculty of Civil Engineering University of RijekaRijekaCroatia Universitéde Technologie de Compiègne Sorbonne UniversitésCompiègneFrance

Quadrilateral finite elements for linear micropolar continuum theory are developed using linked *** order to satisfy convergence criteria,the newly presented finite elements are modified using the Petrov-Galerkin method in which different interpolation is used for the test and trial *** elements are tested through four numerical examples consisting of a set of patch tests,a cantilever beam in pure bending and a stress concentration problem and compared with the analytical solution and quadrilateral micropolar finite elements with standard Lagrangian *** the higher-order patch test,the performance of the first-order element is significantly ***,since the problems analysed are already describable with quadratic polynomials,the enhancement due to linked interpolation for higher-order elements could not be *** the presented elements also faithfully reproduce the micropolar effects in the stress concentration analysis,but the enhancement here is negligible with respect to standard Lagrangian elements,since the higher-order polynomials in this example are not needed.

关键词： micropolar theory Finite element method Linked interpolation Quadrilateral elements

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

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Applied Mathematics and Mechanics(English Edition) 2019年第10期40卷 1471-1486页

作者： A.RAUF S.A.SHEHZAD Z.ABBAS T.HAYAT Department of Mathematics COMSATS University Islamabad Sahiwal 57000 Pakistan Department of Mathematics The Islamia University of Bahawalpur Bahawalpur 63100 Pakistan Department of Mathematics Quiad-i-Azam University Islamabad 44000 Pakistan

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 Cattaneo-Christov models have a significance role in the laser heating and enhancement in thermal conductivity.

关键词： three-dimensional (3D) flow micropolar fluid magnetohydrodynamics (MHD) Cattaneo-Christov theory oscillatory disk

Remark on Mild Solution to the 3D Incompressible micropolar System in Fourier–Herz Framework

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Acta Mathematica Sinica,English Series 2019年第10期35卷 1595-1616页

作者： Yao NIE Xiao Xin ZHENG School of Mathematics and Systems Science Beihang University

This paper is devoted to investigating the existence and uniqueness of mild solution to the 3D incompressible micropolar fluid system in the Fourier–Herz framework. By taking advantage of microlocal analysis and the mutual effect in the same frequency range of convection term, we give a special initial data(u0,ω0) whose norm of FB1,q^-1(q>2) is arbitrarily small, however, the couple(u0,ω0) produces a solution which is arbitrarily large in FB1,q^-1 after an arbitrarily short time. This implies the system is ill-posed in the sense of "norm inflation" as q>2.

关键词： Ill-posedness micropolar system Fourier-Herz space norm inflation

Slip flow of Maxwell viscoelasticity-based micropolar nanoparticles with porous medium: a numerical study

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Applied Mathematics and Mechanics(English Edition) 2019年第9期40卷 1255-1268页

作者： H. WAQAS M. IMRAN S. U. KHAN S. A. SHEHZAD M. A. MERAJ Department of Mathematics Government College University Faisalabad Faisalabad 38000 Pakistan Department of Mathematics COMSATS University Islamabad Sahiwal 57000 Pakistan

This article presents the mass and heat transport aspects in viscoelastic nanofluid flows under the presence of velocity slip conditions. To explore the nonNewtonian behavior, a Maxwell viscoelasticity-based micropolar is considered. Moreover, a porous medium saturates the stretching sheet. A set of similarity variables is introduced to derive the dimensionless ordinary differential equations of velocity, concentration, and temperature profiles. The numerical solution is computed by using the MATLAB bvp4c package. The salient flow features of velocity, concentration, and temperature profiles are described and discussed through various graphs. It is observed that with an increase in the slip parameter, the micro-rotation velocity also increases. The temperature of nanoparticles gets maximum values by varying the viscoelastic parameter and the porosity parameter while an opposite trend is noted for the micro-rotation parameter. The local Nusselt number and the local Sherwood number increase by increasing the viscoelastic parameter, the porosity parameter, and the slip velocity parameter. The graphical computation is performed for a specified range of parameters, such as 0 ≤ M ≤ 2.5, 0 ≤σm ≤ 2.5, 0 ≤ K1 ≤ 1.5, 0.5 ≤ Pr ≤ 3.0, 0 ≤σ≤ 1.5, 0.5 ≤ Sc ≤ 2.0, 0.2 ≤ Nb ≤ 0.8, and 0.2 ≤ Nt ≤ 0.8.

关键词： viscoelasticity-based micropolar nanofluid porous medium slip effect numerical method

Response of loose bonding on reflection and transmission of elastic waves at interface between elastic solid and micropolar porous cubic crystal

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Applied Mathematics and Mechanics(English Edition) 2010年第5期31卷 605-616页

作者： Rajneesh KUMAR Meenakshi PANCHAL Department of Mathematics Kurukshetra University

The problem of reflection and transmission of plane periodic waves incident on the interface between the loosely bonded elastic solid and micropolar porous cubic crystal half spaces is investigated. This is done by assuming that the interface behaves like a dislocation, which preserves the continuity of traction while allowing a finite amount of slip. Amplitude ratios of various reflected and transmitted waves have been depicted graphically. Some special cases of interest have been deduced from the present investigation.

关键词： micropolar porous cubic crystal reflection coefficients transmission coefficients bonding parameter

Wave Propagation in a Magneto-micropolar Thermoelastic Medium with Two Temperatures for Three-Phase-Lag Model

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Computers, Materials & Continua 2016年第4期52卷 1-24页

作者： Samia M.Said Department of Mathematics Faculty of ScienceZagazig UniversityP.O.Box 44519ZagazigEgypt

The present paper is concerned with the wave propagation in a micropolar thermoelastic solid with distinct two temperatures under the effect of the magnetic field in the presence of the gravity field and an internal heat *** formulation of the problem is applied in the context of the three-phase-lag model and Green-Naghdi theory without *** medium is a homogeneous isotropic thermoelastic in the *** exact expressions of the considered variables are obtained by using normal mode *** are made with the results in the two theories in the absence and presence of the magnetic field as well as the two-temperature parameter.A comparison is also made in the two theories for different values of an internal heat source.

关键词： Green-Naghdi theory internal heat source magnetic field micropolar three-phase-lag model two-temperature

RESPONSE OF micropolar THERMOELASTIC SOLID WITH VOIDS DUE TO VARIOUS SOURCES UNDER GREEN NAGHDI THEORY

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Acta Mechanica Solida Sinica 2012年第2期25卷 197-209页

作者： Mohamed Ibrahim Ahmed Othman Sarhan Youssef Atwa Department of Mathematics Faculty of ScienceZagazig UniversityP.O.Box 44519ZagazigEgypt Higher Institute of Engineer Dept.of Eng.Math.and PhysicsShorouk AcademyEgypt Faculty of Science Department of mathematicsShaqra UniversityAL-QuwaiyahSaudi Arabia

Green-Naghdi （G-N） theory of thermoelasticity is employed to study the deformation of micropolar thermoelastic solid with voids considering the influence of various sources acting on the plane surface. The normal mode analysis is used to obtain the analytical expressions of the displacement components, force stress, coupled stress, variation of volume fraction field and temperature distribution. The computed results are presented graphically when the volume source is applied. Comparisons of type II and type III with and without micropolarity effect are made with the results predicted in the context of （G-N） theory.

关键词： micropolar thermoelastic solid volume fraction coupled stress energy dissipation,voids

A micropolar mixture theory of multi-component porous media

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Applied Mathematics and Mechanics(English Edition) 2009年第5期30卷 617-630页

作者：黄璐赵成刚 School of Civil Engineering and Architecture Beijing Jiaotong University

A mixture theory is developed for multi-component micropolar porous media with a combination of the hybrid mixture theory and the micropolar continuum theory. The system is modeled as multi-component micropolar elastic solids saturated with multi- component micropolar viscous fluids. Balance equations are given through the mixture theory. Constitutive equations are developed based on the second law of thermodynamics and constitutive assumptions. Taking account of compressibility of solid phases, the volume fraction of fluid as an independent state variable is introduced in the free energy function, and the dynamic compatibility condition is obtained to restrict the change of pressure difference on the solid-fluid interface. The constructed constitutive equations are used to close the field equations. The linear field equations are obtained using a linearization procedure, and the micropolar thermo-hydro-mechanical component transport model is established. This model can be applied to practical problems, such as contaminant, drug, and pesticide transport. When the proposed model is supposed to be porous media, and both fluid and solid are single-component, it will almost agree with Eringen＇s model.

关键词： hybrid mixture theory micropolar multi-component deforming porous media

Rotational Effect on the Propagation of Waves in a Magneto-micropolar Thermoelastic Medium

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Computers, Materials & Continua 2021年第10期69卷 205-220页

作者： A.M.Abd-Alla S.M.Abo-Dahab M.A.Abdelhafez A.M.Farhan Department of Mathematics Faculty of ScienceSohag UniversitySohagEgypt Department of Mathematics Faculty of ScienceSouth Valley University83523Egypt Department of Physics Faculty of ScienceJazan UniversityJazanSaudi Arabia Department of Physics Faculty of ScienceZagazig UniversityZagazigEgypt

The present paper aims to explore how the magnetic field,ramp parameter,and rotation affect a generalized micropolar thermoelastic medium that is standardized isotropic within the *** employing normal mode analysis and Lame’s potential theory,the authors could express analytically the components of displacement,stress,couple stress,and temperature field in the physical *** calculated such manners of expression numerically and plotted the matching graphs to highlight and make comparisons with theoretical *** highlights of the paper cover the impacts of various parameters on the rotating micropolar thermoelastic ***,the non-dimensional temperature is not affected by the rotation and the magnetic *** attention is paid to studying the impact of the magnetic field,rotation,and ramp parameter of the distribution of temperature,displacement,stress,and couple *** study highlighted the significant impact of the rotation,magnetic field,and ramp parameter on the micropolar thermoelastic *** conclusion,graphical presentations were provided to evaluate the impacts of different parameters on the propagation of plane waves in thermoelastic media of different *** study may help the designers and engineers develop a structural control system in several applied fields.

关键词： Magnetic field micropolar thermoelastic rotation ramp parameter normal mode analysis