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2019年 第40卷 第11期    刊出日期：2019-11-01

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论文

Modeling size-dependent thermo-mechanical behaviors of shape memory polymer Bernoulli-Euler microbeam

Bo ZHOU, Xueyao ZHENG, Zetian KANG, Shifeng XUE

2019, 40(11):  1531-1546.  doi:10.1007/s10483-019-2540-5

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The objective of this paper is to model the size-dependent thermo-mechanical behaviors of a shape memory polymer (SMP) microbeam. Size-dependent constitutive equations, which can capture the size effect of the SMP, are proposed based on the modified couple stress theory (MCST). The deformation energy expression of the SMP microbeam is obtained by employing the proposed size-dependent constitutive equation and Bernoulli-Euler beam theory. An SMP microbeam model, which includes the formulations of deflection, strain, curvature, stress and couple stress, is developed by using the principle of minimum potential energy and the separation of variables together. The sizedependent thermo-mechanical and shape memory behaviors of the SMP microbeam and the influence of the Poisson ratio are numerically investigated according to the developed SMP microbeam model. Results show that the size effects of the SMP microbeam are significant when the dimensionless height is small enough. However, they are too slight to be necessarily considered when the dimensionless height is large enough. The bending flexibility and stress level of the SMP microbeam rise with the increasing dimensionless height, while the couple stress level declines with the increasing dimensionless height. The larger the dimensionless height is, the more obvious the viscous property and shape memory effect of the SMP microbeam are. The Poisson ratio has obvious influence on the size-dependent behaviors of the SMP microbeam. The paper provides a theoretical basis and a quantitatively analyzing tool for the design and analysis of SMP micro-structures in the field of biological medicine, microelectronic devices and micro-electro-mechanical system (MEMS) self-assembling.



Influence of stretch and temperature on the energy density of dielectric elastomer generators

H. KHAJEHSAEID, H. BAGHSHOMAL AZAR

2019, 40(11):  1547-1560.  doi:10.1007/s10483-019-2539-7

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Application of dielectric elastomers (DE) has remarkably increased in mechatronics because they are suitable candidates for energy harvesting due to their low cost, light weight, and high energy density. The dielectric elastomer generators (DEGs) exhibit high performance regardless of the applications scale. However, functioning as a generator, a DE may lose its efficiency due to several failure modes including material rupture, loss of tension (LT), electrical breakdown (EB), and electromechanical instability (EMI). The failure modes confine the area of allowable states for generation process. Dielectric constant and dielectric strength of such elastomers depend on the amount of applied deformation and also working temperature, which are often ignored in theoretical simulations. In this paper, variations of the above-mentioned parameters are considered in mechanical and electrical modellings to investigate their effects on energy density and efficiency of generators. Obtained results show that, ignoring the variations of material dielectric constant and dielectric strength leads to overestimation of the specific energy. Furthermore, it is shown that, for an acrylic-based generator, the specific energy sharply decreases with temperature rise.

A well-posed Euler-Bernoulli beam model incorporating nonlocality and surface energy effect

Xiaowu ZHU, Li LI

2019, 40(11):  1561-1588.  doi:10.1007/s10483-019-2541-5

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This study shows that it is possible to develop a well-posed size-dependent model by considering the effect of both nonlocality and surface energy, and the model can provide another effective way of nanomechanics for nanostructures. For a practical but simple problem (an Euler-Bernoulli beam model under bending), the ill-posed issue of the pure nonlocal integral elasticity can be overcome. Therefore, a well-posed governing equation can be developed for the Euler-Bernoulli beams when considering both the pure nonlocal integral elasticity and surface elasticity. Moreover, closed-form solutions are found for the deflections of clamped-clamped (C-C), simply-supported (S-S) and cantilever (C-F) nano-/micro-beams. The effective elastic moduli are obtained in terms of the closed-form solutions since the transfer of physical quantities in the transition region is an important problem for span-scale modeling methods. The nonlocal integral and surface elasticities are adopted to examine the size-dependence of the effective moduli and deflection of Ag beams.

Mechanical analysis of C/C composite grids in ion optical system

Shuiqiang ZHANG, Aijun LI, Yuqin ZHENG, Dongsheng ZHANG

2019, 40(11):  1589-1600.  doi:10.1007/s10483-019-2527-9

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The ion thruster is an engine with high specific impulse for satellites and spacecrafts, which uses electric energy to boost the spacecraft. The ion optical system, also known as gate assemblies which consist of acceleration and screen grids, is the key component of the ion thruster. In this paper, the static mechanical properties of the C/C composite grids are evaluated based on the structural design. Representative volume element (RVE) is adopted to simplify the braded composite structure as a continuum material. The dynamical behavior of the 100 mm ion thruster optics in the launch environment (1 000g shock-load) is numerically modeled and simulated with the half-sine pulse method. The impact response of the C/C and molybdenum gate assemblies on the stress distribution and deformation is investigated. The simulated results indicate that the magnitudes of the normal displacement of the composite grids subject to the uniformly distributed load are on the same level as molybdenum grids although the normal stiffness of the composite grids is much smaller. When subject to impact loading, the stress distribution in the C/C composite grids is similar to molybdenum grids while the stress magnitude is much smaller. This finding shows that the C/C gate assemblies outperform molybdenum grids and meet the requirement of long lifetime service in space travel.

Effects of variable viscosity and temperature modulation on linear Rayleigh-Bénard convection in Newtonian dielectric liquid

P. G. SIDDHESHWAR, D. UMA, S. BHAVYA

2019, 40(11):  1601-1614.  doi:10.1007/s10483-019-2537-9

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The linear Rayleigh-Bénard electro-convective stability of the Newtonian dielectric liquid is determined theoretically subject to the temperature modulation with time. A perturbation method is used to compute the critical Rayleigh number and the wave number. The critical Rayleigh number is calculated as a function of the frequency of modulation, the temperature-dependent variable viscosity, the electric field dependent variable viscosity, the Prandtl number, and the electric Rayleigh number. The effects of all three cases of modulations are established to delay or advance the onset of the convection process. In addition, how the effect of variable viscosity controls the onset of convection is studied.

Carreau fluid flow due to nonlinearly stretching sheet with thermal radiation, heat flux, and variable conductivity

A. M. MEGAHED

2019, 40(11):  1615-1624.  doi:10.1007/s10483-019-2534-6

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A sophisticated theoretical and mathematical model is proposed. It is verified that this model can estimate and monitor the detailed behavior for the steady Carreau fluid flow past a nonlinear stretching surface and the predicted phenomena due to the presence of heat flux, thermal radiation, and viscous dissipation. Despite the fact that some properties of the fluid do not depend on the temperature, the fluid thermal conductivity is assumed to depend on the temperature. Based on accelerating the fluid elements, some of the kinetic energy for the fluid can be turned to the internal heating energy in the form of viscous dissipation phenomena. The contribution in this study is that a similar solution is obtained, in spite of the high nonlinearity of the Carreau model, especially, with the heat flux, variable conductivity, and viscous dissipation phenomena. Some of the major significant findings of this study can be observed from the reduction in the fluid velocity with enhancing the Weissenberg number. Likewise, the increase in the sheet temperature is noted with increasing the Eckert number while the reverse behavior is observed for increasing both the radiation parameter and the conductivity parameter. Finally, the accuracy and trust in the proposed numerical method are validated after benchmarking for our data onto the earlier results.

Numerical investigation on aerodynamic performance of a bionic flapping wing

Xinghua CHANG, Laiping ZHANG, Rong MA, Nianhua WANG

2019, 40(11):  1625-1646.  doi:10.1007/s10483-019-2532-8

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This paper numerically studies the aerodynamic performance of a bird-like bionic flapping wing. The geometry and kinematics are designed based on a seagull wing, in which flapping, folding, swaying, and twisting are considered. An in-house unsteady flow solver based on hybrid moving grids is adopted for unsteady flow simulations. We focus on two main issues in this study, i.e., the influence of the proportion of down-stroke and the effect of span-wise twisting. Numerical results show that the proportion of downstroke is closely related to the efficiency of the flapping process. The preferable proportion is about 0.7 by using the present geometry and kinematic model, which is very close to the observed data. Another finding is that the drag and the power consumption can be greatly reduced by the proper span-wise twisting. Two cases with different reduced frequencies are simulated and compared with each other. The numerical results show that the power consumption reduces by more than 20%, and the drag coefficient reduces by more than 60% through a proper twisting motion for both cases. The flow mechanism is mainly due to controlling of unsteady flow separation by adjusting the local effective angle of attack. These conclusions will be helpful for the high-performance micro air vehicle (MAV) design.

Numerical solution of oscillatory flow of Maxwell fluid in a rectangular straight duct

Xuyang SUN, Shaowei WANG, Moli ZHAO, Qiangyong ZHANG

2019, 40(11):  1647-1656.  doi:10.1007/s10483-019-2535-6

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A numerical analysis is presented for the oscillatory flow of Maxwell fluid in a rectangular straight duct subjected to a simple harmonic periodic pressure gradient. The numerical solutions are obtained by a finite difference scheme method. The stability of this finite difference scheme method is discussed. The distributions of the velocity and phase difference are given numerically and graphically. The effects of the Reynolds number, relaxation time, and aspect ratio of the cross section on the oscillatory flow are investigated. The results show that when the relaxation time of the Maxwell model and the Reynolds number increase, the resonance phenomena for the distributions of the velocity and phase difference enhance.

Two-grid methods for semi-linear elliptic interface problems by immersed finite element methods

Yang WANG, Yanping CHEN, Yunqing HUANG, Ying LIU

2019, 40(11):  1657-1676.  doi:10.1007/s10483-019-2538-7

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In this paper, two-grid immersed finite element (IFE) algorithms are proposed and analyzed for semi-linear interface problems with discontinuous diffusion coefficients in two dimension. Because of the advantages of finite element (FE) formulation and the simple structure of Cartesian grids, the IFE discretization is used in this paper. Two-grid schemes are formulated to linearize the FE equations. It is theoretically and numerically illustrated that the coarse space can be selected as coarse as H=O(h^1/4) (or H=O(h^1/8)), and the asymptotically optimal approximation can be achieved as the nonlinear schemes. As a result, we can settle a great majority of nonlinear equations as easy as linearized problems. In order to estimate the present two-grid algorithms, we derive the optimal error estimates of the IFE solution in the L^p norm. Numerical experiments are given to verify the theorems and indicate that the present two-grid algorithms can greatly improve the computing efficiency.

Asymptotical consensus of fractional-order multi-agent systems with current and delay states

Xuhui WANG, Xuesong LI, Nanjing HUANG, D. O'REGAN

2019, 40(11):  1677-1694.  doi:10.1007/s10483-019-2533-8

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In this paper, we study some new fractional-order multi-agent systems with current and delay states (FMASCD). Using the generalized Nyquist’s stability criterion and Gerschgorin’s circle theorem, we obtain the bounded input-bounded output (BIBO) stability and asymptotical consensus of the FMASCD under mild conditions. Moreover, we give some numerical examples to illustrate our main results.