Free vibration of thermo-elastic microplate based on spatiotemporal fractional-order derivatives with nonlocal characteristic length and time

A fractional-order thermo-elastic model taking into account the small-scale effects of the thermo-elastic coupled behavior is developed to study the free vibration of a higher-order shear microplate. The nonlocal strain gradient theory is modified with the introduction of the fractional-order derivatives and the nonlocal characteristic length. The Fourier heat conduction is replaced by the non-Fourier heat conduction with the introduction of the fractional order and the memory characteristic tim...     

Biomechanical evaluation of heel elevation on load transfer — experimental measurement and finite element analysis

In spite of ill-effects of high heel shoes, they are widely used for women. Hence, it is essential to understand the load transfer biomechanics in order to design better fit and comfortable shoes. In this study, both experimental measurement and finite element analysis were used to evaluate the biomechanical effects of heel height on foot load transfer. A controlled experiment was conducted using custom-designed platforms. Under different weight-bearing conditions, peak plantar pressure, contact area and center of pressure were analyzed. A three-dimensional finite element foot model was used to simulate the high-heel support and to predict the internal stress distributions and deformations for different heel heights. Results from both experiment and model indicated that heel elevations had significant effects on all variables. When heel elevation increased, the center of pressure shifted from the midfoot region to the forefoot region, the contact area was reduced by 26% from 0 to 10.2 cm heel and the internal stress of foot bones increased. Prediction results also showed that the strain and total tension force of plantar fascia was minimum at 5.1 cm heel condition. This study helps to better understand the biomechanical behavior of foot, and to provide better suggestions for design parameters of high heeled shoes.     

Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations

A unified analysis is presented for the stabilized methods including the pres- sure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equa- tions. The existence and uniqueness of the solution and the optimal error estimates are proved.     

Pulsatile blood flow in large arteries: comparative study of Burton’s and McDonald’s models

To get a clear picture of the pulsatile nature of blood flow and its role in the pathogenesis of atherosclerosis, a comparative study of blood flow in large arteries is carried out using the two widely used models, McDonald＇s and Burton＇s models, for the pressure gradient. For both models, the blood velocity in the lumen is obtained analytically. Elaborate investigations on the wall shear stress （WSS） and oscillatory shear index （OSI） are carried out. The results are in good agreement with the available data in the literature. The superiority of McDonald＇s model in capturing the pulsatile nature of blood flow, especially the OSI, is highlighted. The present investigation supports the hypothesis that not only WSS but also OSI are the essential features determining the pathogenesis of atherosclerosis. Finally, by reviewing the limitations of the present investigation, the possibility of improvement is explored.     

A NONLINEAR MICROBEAM MODEL BASED ON STRAIN GRADIENT ELASTICITY THEORY

A micro scale nonlinear beam model based on strain gradient elasticity is developed.Governing equations of motion and boundary conditions are obtained in a variational framework.As an example,the nonlinear vibration of microbeams is analyzed.In a beam having a thickness to length parameter ratio close to unity,the strain gradient effect on increasing the natural frequency is predominant.By increasing the beam thickness,this effect decreases and geometric nonlinearity plays the main role on increasing the natural frequency.For some specific ratios,both geometric nonlinearity and size effects have a significant role on increasing the natural frequency.     

Effect of an adverse pressure gradient on the streamwise Reynolds stress profile maxima in a turbulent boundary layer

It is widely accepted that in a turbulent boundary layer （TBL） with adverse pressure gradient （APG） an outer peak usually appears in the profile of streamwise Reynolds stress. However, the effect of APG on this outer peak is not clearly understood. In this paper, the effect of APG is analysed using the numerical and experimental results in the literature. Because the effect of upstream flow is inherent in the TBL, we first analyse this effect in TBLs with zero pressure gradient on flat plates. Under the individual effect of upstream flow, an outer peak already appears in the profile of streamwise Reynolds stress when the TBL continues developing in the streamwise direction. The APG accelerates the appearance of the outer peak, instead of being a trigger.     

Blow-up rate estimate for degenerate parabolic equation with nonlinear gradient term

Abstract In this paper, the blow-up rate is obtained for a porous medium equation with a nonlinear gradient term and a nonlinear boundary flux. By using a scaling method and regularity estimates of parabolic equations, the blow-up rate determined by the interaction between the diffusion and the boundary flux is obtained. Compared with previous results, the gradient term, whose exponent does not exceed two, does not affect the blow-up rate of the solutions.     

DYNAMIC ANALYSIS OF A GRADIENT ELASTIC POLYMERIC FIBER

A dynamic analysis of an elastic gradient-dependent polymeric fiber subjected to a periodic excitation is considered.A nonlinear gradient elasticity constitutive equation with strain-dependent gradient coefficients is first derived and the dispersive wave propagation properties for its linearized counterpart are briefly discussed.For the linearized problem a variational formulation is also developed to obtain related boundary conditions of both classical(standard)and non-classical(gradient)type.Analytical solutions in the form of Fourier series for the fiber’s displacement and strain fields are provided.The solutions depend on a dimensionless scale parameter(the diameter to length radio d = D/L)and,therefore,size effects are captured.     

The singularity analysis of the stress and strain fields for Mode I fracture in elastic-plastic state

The stress and strain singularities of power hardening material for Mode I fracrure are analysed according to the fundamental equations of elastic-plastic mechanics. It is found that the singularities of all stress and strain components do not change in the thick direction, and neither the six stress components nor the six strain components have the same singularity.     

Poroelastic behaviors of the osteon: A comparison of two theoretical osteon models

In the paper, two theoretical poroelastic osteon models are presented to compare their poroelastic behaviors, one is the hollow osteon model (Haversian fluid is neglected) and the other is the osteon model with Haversian fluid considered. They both have the same two types of impermeable exterior boundary conditions, one is elastic restraint and the other is displacement constrained, which can be used for analyzing other experiments performed on similarly shaped poroelastic specimens. The obtained analytical pressure and velocity solutions demonstrate the effects of the loading factors and the material parameters, which may have a significant stimulus to the mechanotransduction of bone remodeling signals. Model comparisons indicate: (1) The Haversian fluid can enhance the whole osteonal fluid pressure and velocity fields. (2) In the hollow model, the key loading factor governing the poroelastic behavior of the osteon is strain rate, while in the model with Haversian fluid considered, the strain rate governs only the velocity. (3) The pressure amplitude is proportional to the loading frequency in the hollow model, while in the model with Haversian fluid considered, the loading frequency has little effect on the pressure amplitude.     

THE HLDER CONTINUITY FOR THE GRADIENT OF SOLUTIONS TO ONE-SIDED OBSTACLE PROBLEMS

The Hǒlder continuity is proved for the gradient of the solution to the one-sided obstacle problem of the following variational inequality in the case 1相似文献   

THE HLDER CONTINUITY FOR THE GRADIENT OF SOLUTIONS TO ONE-SIDED OBSTACLE PROBLEMS

The Hölder continuity is proved for the gradient of the solution Jo the one-sided obstacle problem of the following variational inequality in the case 1相似文献   

Effect of the size and pressure on the modified viscosity of water in microchannels

The phenomenon that flow resistances are higher in micro scale flow than in normal flow is clarified through the liquid viscosity. Based on the experimental results of deionized water flow in fused silica microtubes with the inner radii of 2.5 μm, 5 μm, 7.5 μm, and 10 μm, respectively,the relationship between water flow velocity and pressure gradient along the axis of tube is analyzed, which gradually becomes nonlinear as the radius of the microtube decreases.From the correlation, a viscosity model of water flow derived from the radius of microtube and the pressure gradient is proposed. The flow results modified by the viscosity model are in accordance with those of experiments, which are verified by numerical simulation software and the Hagen–Poiseuille equation. The experimental water flow velocity in a fused silica microtube with diameter of 5.03 μm, which has not been used in the fitting and derivation of the viscosity model,is proved to be comsistent with the viscosity model, showing a rather good match with a relative difference of 5.56%.     

Spatial relation between fluctuating wall pressure and near-wall streamwise vortices in wall bounded turbulent flow

A new view of the spatial relation between fluctuating wall pressure and near-wall streamwise vortices (NWSV) is proposed for wall bounded turbulent flow by use of the direct numerical simulation (DNS) database. The results show that the wall region with low pressure forms just below the strong NWSV, which is mostly associated with the overhead NWSV. The wall region with high pressure forms downstream of the NWSV, which has a good correspondence with the downwash of the fluids induced by the upstream NWSV. The results provide a significant basis for the detection of NWSV.     

Convergence analysis on Browder-Tikhonov regularization for second-order evolution hemivariational inequality

This paper studies the Browder-Tikhonov regularization of a second-order evolution hemivariational inequality (SOEHVI) with non-coercive operators. With duality mapping, the regularized formulations and a derived first-order evolution hemivariational inequality (FOEHVI) for the problem considered are presented. By applying the Browder-Tikhonov regularization method to the derived FOEHVI, a sequence of regularized solutions to the regularized SOEHVI is constructed, and the strong convergence of the whole sequence of regularized solutions to a solution to the problem is proved.     

Generalizing J 2 flow theory: Fundamental issues in strain gradient plasticity

It has not been a simple matter to obtain a sound extension of the classical J₂ flow theory of plasticity that in- corporates a dependence on plastic strain gradients and that is capable of capturing size-dependent behaviour of metals at the micron scale. Two classes of basic extensions of clas- sical J₂ theory have been proposed: one with increments in higher order stresses related to increments of strain gradi- ents and the other characterized by the higher order stresses themselves expressed in terms of increments of strain gra- dients. The theories proposed by Muhlhaus and Aifantis in 1991 and Fleck and Hutchinson in 2001 are in the first class, and, as formulated, these do not always satisfy ther- modynamic requirements on plastic dissipation. On the other hand, theories of the second class proposed by Gudmundson in 2004 and Gurtin and Anand in 2009 have the physical deficiency that the higher order stress quantities can change discontinuously for bodies subject to arbitrarily small load changes. The present paper lays out this background to the quest for a sound phenomenological extension of the rate- independent J₂ flow theory of plasticity to include a de- pendence on gradients of plastic strain. A modification of the Fleck-Hutchinson formulation that ensures its thermo- dynamic integrity is presented and contrasted with a compa- rable formulation of the second class where in the higher or- der stresses are expressed in terms of the plastic strain rate. Both versions are constructed to reduce to the classical J₂ flow theory of plasticity when the gradients can be neglected and to coincide with the simpler and more readily formulated J₂ deformation theory of gradient plasticity for deformation histories characterized by proportional straining.     

Optimization of multi-stage velocity gradients in a cylindrical fluidized bed flocculator

Flocculation time is conventionally believed to be proportional to the flocculation efficiency of a cylindrical fluidized bed flocculator.However,in a single-stage velocity gradient situation,the flocculation efficiency decreases when the optimal flocculation time is exceeded.A multi-stage velocity gradient was established in a cylindrical fluidized bed flocculator,based on the hydraulic classification theory.This multi-stage velocity gradient fluidized bed flocculator(MGF) created a more suitable environment for floc growth and protection,which was confirmed by the size distribution of flocs along the bed height.Correspondingly,the abatement efficiencies for Kaolin slurry and dyed wastewater treatment in the MGF were enhanced by5-10%,and by 7-20%,respectively,compared with those in the single-stage velocity gradient fluidized bed flocculators(SGFs).The initial bed height distribution ratio along the velocity gradients was an important factor for MGF optimization.     

ON THE STABILITY OF A FUNCTIONALLY GRADED RECTANGULAR MICRO-PLATE SUBJECTED TO HYDROSTATIC AND NONLINEAR ELECTROSTATIC PRESSURES

This article studies the stability of a functionally graded clamped-clamped micro-plate subjected to hydrostatic and electrostatic pressures. Equilibrium positions of the micro-plate are determined and shown in the state control space. To study the stability of the equilibrium positions, the motion trajectories are given for different initial conditions in the phase plane. Effects of the electrostatic and hydrostatic pressure changes on the deflection and stability of the micro-plate for some sample value of k are studied and values of the applied voltage and hydrostatic pressure leading system to unstable conditions by undergoing a saddle node and homoclinic bifurcations are determined.     

A UNIVERSAL CRACK EXTENSION CRITERION BASED ON THE EQUIVALENT STRESS GRADIENT:I.THEORY AND NUMERICAL VERIFICATION

In this contribution,the microscopic fracture mechanism and extension criterion for mixed type crack in ductile material under plane mixed mode loading are investigated in details.A universal extension...     

Fluctuation pressure on a bio-membrane confined within a parabolic potential well

A compliant bio-membrane with a nominally flatreference configuration is prone to random transverse deflec-tions when placed in water, due primarily to the Brownianmotion of the water molecules. On the average, these fluc-tuations result in a state of thermodynamic equilibrium be-tween the entropic energy of the water and the total free en-ergy of the membrane. When the membrane is in close prox-imity to a parallel surface, that surface restricts the fluctua-tions of the membrane which, in turn, results in an increasein its free energy. The amount of that increase depends onthe degree of confinement, and the resulting gradient in freeenergy with degree of confinement implies the existence ofa confining pressure. In the present study, we assume thatthe confinement is in the form of a continuous parabolic po-tential well resisting fluctuation. Analysis leads to a closedform expression for the mean pressure resulting from thisconfinement, and the results are discussed within the broadercontext of results in this area. In particular, the results pro-vide insights into the roles of membrane stiffness, number ofdegrees of freedom in the model of the membrane and othersystem parameters.