A theory for three-dimensional response of micropolar plates

Through combined applications of the transfer-matrix method and asymptotic expansion technique,we formulate a theory to predict the three-dimensional response of micropolar plates.No ad hoc assumptions regarding through-thickness assumptions of the field variables are made,and the governing equations are two-dimensional,with the displacements and microrotations of the mid-plane as the unknowns.Once the deformation of the mid-plane is solved,a three-dimensional micropolar elastic field within the plate is generated,which is exact up to the second order except in the boundary region close to the plate edge.As an illustrative example,the bending of a clamped infinitely long plate caused by a uniformly distributed transverse force is analyzed and discussed in detail.

Film Flow of Nano-Micropolar Fluid with Dissipation Effect

The physical problem of the thin film flow of a micropolar fluid over a dynamic and inclined substrate under the influence of gravitational and thermal forces in the presence of nanoparticles is formulated.Five different types of nanoparticle samples are accounted for in this current study,namely gold Au,silver Ag,molybdenum disulfide MoS_(2),aluminum oxide Al_(2)O_(3),and silicon dioxide SiO_(2).Blood,a micropolar fluid,serves as the common base fluid.An exact closed-form solution for this problem is derived for the first time in the literature.The results are particularly validated against those for the Newtonian fluid and show excellent agreement.It was found that increasing values of the spin boundary condition and micropolarity lead to a reduction in both the thermal and momentum boundary layers.A quantitative decay in the Nusselt number for a micropolar fluid,as compared to a Newtonian one for all the tested nanoparticles,is anticipated.Gold and silver nanoparticles(i)intensify in the flow parameter as the concentration of nanoparticles increases(ii)yield a higher thermal transfer rate,whereas molybdenum disulfide,aluminum oxide,and silicon dioxide exhibit a converse attitude for both Newtonian and micropolar fluids.The reduction in film thickness for fluid comprising gold particles,as compared to the rest of the nanoparticles,is remarkable.

Chemically Radiative MHD Flow of a Micropolar Nanofluid over a Stretching/ Shrinking Sheet with a Heat Source or Sink

This study examines the behavior of a micropolar nanofluidflowing over a sheet in the presence of a transverse magneticfield and thermal effects.In addition,chemical(first-order homogeneous)reactions are taken into account.A similarity transformation is used to reduce the system of governing coupled non-linear partial differ-ential equations(PDEs),which account for the transport of mass,momentum,angular momentum,energy and species,to a set of non-linear ordinary differential equations(ODEs).The Runge-Kutta method along with shoot-ing method is used to solve them.The impact of several parameters is evaluated.It is shown that the micro-rota-tional velocity of thefluid rises with the micropolar factor.Moreover,the radiation parameter can have a remarkable influence on theflow and temperature profiles and on the angular momentum distribution.

ANALYSES ON NONLINEAR COUPLING OF MAGNETO-THERMO-ELASTICITY OF FERROMAGNETIC THIN SHELL—II:FINITE ELEMENT MODELING AND APPLICATION

Based on the generalized vaxiational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established （see, Analyses on nonlinear coupling of magneto-thermo- elasticity of ferromagnetic thin shell--I）, the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell. The numerical modeling composes of finite element equations for three sub-systems of magnetic, thermal and deformation fields, as well as iterative methods for nonlinearities of the geometrical large-deflection and the multi-field coupling of the ferromagnetic shell. As examples, the numerical simulations on magneto-elastic behaviors of a ferromagnetic cylindrical shell in an applied magnetic field, and magneto-thermo-elastic behaviors of the shell in applied magnetic and thermal fields are carried out. The results are in good agreement with the experimental ones.

The Effects of Thermal Radiation and Viscous Dissipation on the Stagnation Point Flow of a Micropolar Fluid over a Permeable Stretching Sheet in the Presence of Porous Dissipation

In this paper,the effects of thermal radiation and viscous dissipation on the stagnation–point flow of a micropolar fluid over a permeable stretching sheet with suction and injection are analyzed and discussed.A suitable similarity transformation is used to convert the governing nonlinear partial differential equations into a system of nonlinear ordinary differential equations,which are then solved numerically by a fourth–order Runge–Kutta method.It is found that the linear fluid velocity decreases with the enhancement of the porosity,boundary,and suction parameters.Conversely,it increases with the micropolar and injection parameters.The angular velocity grows with the boundary,porosity,and suction parameters,whereas it is reduced if the micropolar and injection parameters become larger.It is concluded that the thermal boundary layer extension increases with the injection parameter and decreases with the suction parameter.

ANALYSES ON NONLINEAR COUPLING OF MAGNETO-THERMO-ELASTICITY OF FERROMAGNETIC THIN SHELL—I:GENERALIZED VARIATIONAL THEORETICAL MODELING

Based on the generalized variational principle of magneto-thermo-elasticity of the ferromagnetic elastic medium, a nonlinear coupling theoretical modeling for a ferromagnetic thin shell is developed. All governing equations and boundary conditions for the ferromagnetic shell are obtained from the variational manipulations on the magnetic scalar potential, temperature and the elastic displacement related to the total energy functional. The multi-field couplings and geometrical nonlinearity of the ferromagnetic thin shell are taken into account in the modeling. The general modeling can be further deduced to existing models of the magneto-elasticity and the thermo-elasticity of a ferromagnetic shell and magneto-thermo-elasticity of a ferromagnetic plate, which are coincident with the ones in literature.

NCCT for Micropolar Solid and Fluid Media Based on Internal Rotations and Rotation Rates with Rotational Inertial Physics: Model Problem Studies

This paper presents model problem studies for micropolar thermoviscoelastic solids without memory and micropolar thermoviscous fluid using micropolar non-classical continuum theories (NCCT) based on internal rotations and rotation rates in which rotational inertial physics is considered in the derivation of the conservation and balance laws (CBL). The dissipation mechanism is due to strain rates as well as rotation rates. Model problems are designed to demonstrate and illustrate various significant aspects of the micropolar NCCT with rotational inertial physics considered in this paper. In case of micropolar solids, the translational and rotational waves are shown to coexist. In the absence of microconstituents (classical continuum theory, CCT) the internal rotations are a free field, hence have no influence on CCT. Absence of gradients of displacements and strains in micropolar thermoviscous fluid medium prohibits existence of translational waves as well as rotational waves even though the appearance of the mathematical model is analogous to the solids, but in terms of strain rates. It is shown that in case of micropolar thermoviscous fluids the BAM behaves more like time dependent diffusion equation i.e., like heat conduction equation in Lagrangian description. The influence of rotational inertial physics is demonstrated using BLM as well as BAM in the model problem studies.

VANISHING VISCOSITY LIMIT FOR THE 3D INCOMPRESSIBLE MICROPOLAR EQUATIONS IN A BOUNDED DOMAIN

In this paper,we investigate the vanishing viscosity limit of the 3D incompressible micropolar equations in bounded domains with boundary conditions.It is shown that there exist global weak solutions of the micropolar equations in a general bounded smooth domain.In particular,we establish the uniform estimate of the strong solutions for when the boundary is flat.Furthermore,we obtain the rate of convergence of viscosity solutions to the inviscid solutions as the viscosities tend to zero(i.e.,(ε,χ,γ,κ)→0).

Computational Dynamics of Stagnation Point Flow of Micropolar Fluid Past Vertical Porous Plates

This work examines the flow of a micropolar fluid over a vertical porous plate at the MHD stagnation point under viscous dissipation, convective boundary conditions, and thermal radiation. The governing partial differential equations and a set of similarity parameters were used to transform them into ordinary differential equations. The Runge-Kutta fourth-order algorithm is used in conjunction with the Newton Raphson shooting technique to numerically solve the generated self-similar equations. Results were tabulated both numerically and graphically, and examples for different controlling factors are quantitatively analyzed. According to the study, the vortex viscosity parameter (k) causes the velocity profiles to rise while the magnetic parameter, suction parameter, and radiation parameter cause them to fall. In contrast, as the flow’s suction and prandtl values rise, so do the magnetic parameter, radiation, and vortex viscosity, while the thickness of the thermal boundary layer decreases. .

Theory and Semi-Analytical Study of Micropolar Fluid Dynamics through a Porous Channel

In this work,We are looking at the characteristics of micropolar flow in a porous channel that’s being driven by suction or injection.The working of the fluid is described in the flowmodel.We can reduce the governing nonlinear partial differential equations(PDEs)to a model of coupled systems of nonlinear ordinary differential equations using similarity variables(ODEs).In order to obtain the results of a coupled system of nonlinear ODEs,we discuss a method which is known as the differential transform method(DTM).The concern transform is an excellent mathematical tool to obtain the analytical series solution to the nonlinear ODEs.To observe beast agreement between analytical method and numerical method,we compare our result with the Rung-Kutta method of order four(RK4).We also provide simulation plots to the obtained result by using Mathematica.Onthese plots,we discuss the effect of different parameters which arise during the calculation of the flow model equations.

Unsteady Flow and Heat Transfer of a Casson Micropolar Nanofluid over a Curved Stretching/Shrinking Surface

We present the results of an investigation into the behavior of the unsteady flow of a Casson Micropolar nanofluid over a shrinking/stretching curved surface,together with a heat transfer analysis of the same problem.The body force acting perpendicular to the surface wall is in charge of regulating the fluid flow rate.Curvilinear coordinates are used to account for the considered curved geometry and a set of balance equations for mass,momentum,energy and concentration is obtained accordingly.These are turned into ordinary differential equations using a similarity transformation.We show that these equations have dual solutions for a number of different combinations of various parameters.The stability of such solutions is investigated by applying perturbations on the steady states.It is found that high values of the Micropolar and Casson parameters cause the flow to move more slowly.However,when compared to a shrunken surface,a stretched surface produces a greater Micro-rotation flux.

On complete and micropolar-based incomplete strain gradient theories for periodic lattice structures

The micropolar(MP) and strain gradient(SG) continua have been generally adopted to investigate the relations between the macroscopic elastic constants and the microstructural geometric parameters. Owing to the fact that the microrotation in the MP theory can be expressed in terms of the displacement gradient components, we may regard the MP theory as a particular incomplete SG theory called the MPSG theory,compared with the existing SG theories which are deemed complete since all the SGs are included. Taking the triangular lattice comprising zigzag beams as an example, it is found that as the angle of the zigzag beams increases, the bending of the beams plays a more important role in the total strain energy, and the difference between the results by the two theories gradually decreases. Finally, the models are verified with the pure bending and simple shear of lattices by comparing with the results obtained by the finite element method(FEM)-based structure analyses.

Strain localization of Mohr-Coulomb soils with non-associated plasticity based on micropolar continuum theory

To address the problems of strain localization, the exact Mohr-Coulomb (MC) model is used based on second-order cone programming (mpcFEM-SOCP) in the framework of micropolar continuum finite element method. Using the uniaxial compression test, we focused on the earth pressure problem of rigid wall segment involving non-associated plasticity. The numerical results reveal that when mpcFEM-SOCP is applied, the problems of mesh dependency can be effectively addressed. For geotechnical strain localization analysis involving non-associated MC plasticity, mpcFEM-SOCP in conjunction with the pseudo-time discrete scheme can improve the numerical stability and avoid the unreasonable softening issue in the pressure-displacement curves, which may be encountered in the conventional FEM. It also shows that the pressure-displacement responses calculated by mpcFEM-SOCP with the pseudo-time discrete scheme are higher than those calculated by mpcFEM-SOCP with the Davis scheme. The inclination angle of shear band predicted by mpcFEM-SOCP with the pseudo-time discrete scheme agrees well with the theoretical solution of non-associated MC plasticity.

带有分数阶耗散项的Magneto-Micropolar方程组的整体适定性

本文通过对三维磁场微极流方程组(Magneto-Micropolar fluid)的非线性结构进行细致分析并结合能量估计的方法,对一类带有分数阶耗散项的磁场微极流方程组解的整体适定性进行了研究,获得了当α≥5/2时磁场微极流方程组解的整体适定性.

颗粒土中剪切带临界状态数学描述及其完全解

为正确模拟土体涉及剪切带演化的后失效力学响应,需采用包含细观特征长度的高阶连续介质力学模型.笔者利用前期所建立的微极亚塑性模型,对颗粒土中剪切带的发展过程进行了分析推导,得到了剪切带临界状态条件下关键变量所满足的非线性微分方程.该文展示了上述非线性微分方程的简要推导,重点讨论了该非线性微分方程的主要性质、主要参数变化范围和求解途径;通过对剪切带进一步的力学分析补充建立了一个能量方程,使问题具有确定解.在此基础上,应用数值积分求出了剪切带厚度因子和剪切内应力、变形率分布及剪切速度分布的完全解.其中剪切带厚度因子对于微极亚塑性模型细观参数的确定具有重要作用.

平行板微通道中一类不可压缩微极性流体在高Zeta势下的时间周期电渗流

在高Zeta势下,研究平行板微通道中一类不可压缩微极性流体的时间周期电渗流.在不使用DebyeHüickel线性近似条件下,利用有限差分法数值求解非线性Poisson-Boltzmann方程和不可压缩微极性流体的连续性方程、动量方程、角动量方程及本构方程,在低Zeta势下将所得结果与使用Debye-Hückel线性近似得到的解析解比较,证明本文数值方法是可行的;讨论高Zeta势下电动宽度m、电振荡频率Ω、微极性参数k1等无量纲参数对不可压缩微极性流体的速度和微旋转效应的影响.研究表明:1)随着Zeta势的增大,微极性流体的速度、微旋转、体积流量、微旋强度以及剪切应力增大,说明与低Zeta势相比,高Zeta势对微极性流体电渗流有显著的促进作用.2)在高Zeta势下,随着微极性参数的增大,微极性流体的速度减小,但是对微旋转效应呈现先增强后减弱的趋势.3)在高Zeta势下,当电振荡频率较低(小于1)时,电动宽度的增大促进微极性流体的流动,但抑制其微旋转;当电振荡频率较高(大于1)时,电动宽度的增大抑制微极性流体的流动及微旋转,但促进体积流量快速增大并趋于恒定.4)在高Zeta势下,当电振荡频率较低(小于1)时,微极性流体电渗流速度和微旋转随着电振荡频率的变化呈现明显的振荡变化趋势,但是速度和微旋转的峰值、体积流量及微旋强度均保持不变;当电振荡频率较高(大于1)时,随着电振荡频率的增大,微极性流体电渗流速度和微旋转的幅值减小,体积流量及微旋强度减小直至趋于零.5)在高Zeta势下,壁面剪切应力σ21及σ12的幅值随电动宽度的增大而增大;当电振荡频率较低(小于1)时,壁面剪切应力σ21与σ12不随电振荡频率的增大而变化,均取恒定值,且微极性参数的取值不影响壁面剪切应力σ21的幅值;当电振荡频率较高(大于1)时,壁面剪切应力σ21及σ12的幅值随电振荡频率的增大而减小,且壁面剪切应力σ21的幅值随着微极性参数的增大而减小,而壁面剪切应力σ12的振幅随着微极性参数的增大而线性减小.

速度零耗散且温度分数阶扩散的二维微极Rayleigh-Bénard对流系统的全局正则性

该文研究速度零耗散,微旋转速度拉普拉斯耗散且温度分数阶扩散的二维微极Rayleigh-Bénard对流系统的全局正则性问题.通过构建两个组合量和使用Littlewood-Paley分解技术,该文建立了该系统解的全局正则性结果.

具有无穷磁雷诺数的三维磁微极流体方程的整体适定性

主要研究了具有无穷磁雷诺数的三维磁微极流体方程在T^(3)上的Cauchy问题的整体适定性,证明了当初始磁场很接近于背景磁场并且也满足丢番图条件时,该Cauchy问题是整体适定的.

二维有界区域内具Lions边值的magneto-micropolar系统解的存在性

在二维有界区域上研究u,h具Lions边值条件,m具齐次边值条件的magneto-micropolar方程,用Galerkin方法证明了其弱解和强解的存在唯一性.

芘稳态荧光法研究疏水碳原子数对两性型表面活性剂聚集行为的影响

为研究疏水碳原子数对两性型表面活性剂聚集行为的影响,笔者以疏水性芘为荧光探针,测定了疏水链碳原子数(m)分别为12、14、16、18的磺酸钠两性型表面活性剂(记作S_(m))的临界胶束浓度(CMC),并确定了合成样品的微极性。以373 nm与384 nm的荧光强度之比I1/I3与样品浓度的关系可知,样品S12~S18的CMC分别为7.90×10^(-4)mol/L、5.39×10^(-4)mol/L、4.72×10^(-4)mol/L、4.14×10^(-4)mol/L,平衡I1/I3分别为1.667、1.211、1.272、1.294。表明随着疏水链碳原子数的增加,合成样品形成有序聚集体的能力增强,所具有的表面活性随之增加,其中疏水碳原子数为14的样品S14形成聚集体的结构最为紧密。