Effect of partial elastic foundation on free vibration of fluid-filled functionally graded cylindrical shells

The free vibration characteristics of fluid-filled functionally graded cylindrical shells buried partially in elas- tic foundations are investigated by an analytical method. The elastic foundation of partial axial and angular dimen- sions is represented by the Pasternak model. The motion of the shells is represented by the first-order shear defor- mation theory to account for rotary inertia and transverse shear strains. The functionally graded cylindrical shells are composed of stainless steel and silicon nitride. Material prop- erties vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The governing equation is obtained using the Rayleigh-Ritz method and a variation approach. The fluid is described by the classical potential flow theory. Numerical examples are presented and compared with existing available results to validate the present method.

THE MECHANICAL METHOD OF CONSTRUCTING THE DISPLACEMENT FUNCTIONS IN ELASTICITY

In this Paper we have proven the general solution to the equations of linear operatorsAu=f as u=Cv+e . where v satisfies the equation Dv=g and D is adiagonal matrix. Basing on the consstructive proof of Hilbert Nullstellensat=. we haregiven the mechanical method of constucting C. D and e.and some of the mechanicalalgorithm displacement functions in elasticity are given by this method also .

Bolt support mechanism based on elastic theory

Mechanical model of anchorage surrounding rock considering tray effect was established based on elastic theory,in order to study the mechanism of bolt supporting.Elastic solutions of normal force at point in the interior of a semi-infnite solid were obtained by means of classical displacement function method in elasticity.The factors which influence stress of bolted surrounding rock,such as the length of bolt and tray effect,were analyzed.The absolute value of stress along bolt axes decreased rapidly with an increase in radical distance and the maximum appeared near ends of bolt.With increasing radical distance,the value of radical stress changed from positive to negative roughly and then increased to zero,with maximum at the middle of bolt.The evolution of hoop stress as radical distance increasing was similar with stress along bolt axes.With an increase in depth,the radical effect ranges of all normal stress components were reduced.These suggest that the effect from tray on stress along bolt axes of bolted surrounding rock could be neglected,except near surface of surrounding rock.

Pressure Effect on Elastic and Lattice Dynamic Properties of Beryllium Selenide from First Principles

The lattice dynamic, elastic, and thermodynamic properties of Be Se were investigated with first principles calculations. The phase transition pressure from the zinc blende（B3） to the nickel arsenide（B8） structure of Be Se was determined. The elastic stability analysis suggests that the B3 structure Be Se is mechanically stable in the applied pressure range of 0-50 GPa. Our lattice dynamic calculations show that the B3 structure is lattice dynamically stable under high pressure. Within the quasiharmonic approximation, the thermodynamic properties including the constant volume heat capacity and constant pressure heat capacity are predicted.

Statics of FGM circular plate with magneto-electro-elastic coupling:axisymmetric solutions and their relations with those for corresponding rectangular beam

This paper investigates the static behavior of a functionally graded circular plate made of magneto-electro-elastic（MEE） materials under tension and bending.The analysis is directly based on the three-dimensional governing equations for magnetoelectro-elasticity, with the boundary conditions on the upper and lower surfaces satisfied exactly and those on the cylindrical surface satisfied approximately（in the Saint Venant sense）. The analytical solutions, derived with a direct displacement method, are valid for any functionally graded material（FGM） with its properties varying independently in a continuous manner along the thickness direction. For homogeneous materials, these solutions are degenerated to the ones available in the literature. Interesting relations are also found between the solutions for a functionally graded magneto-electro-elastic（FGMEE） circular plate and those for an FGMEE rectangular beam, and even those for a functionally graded elastic beam when only the elastic displacements are considered. The beam solutions are also derived using a direct displacement method. Numerical examples are presented to verify the present analytical solutions, show the effects of material heterogeneity and multi-field coupling, and indicate the correspondence between the plate solutions and beam solutions.

Theoretical calculations of structural, electronic, and elastic properties of CdSe_(1-x)Te_x:A first principles study

The plane wave pseudo-potential method was used to investigate the structural, electronic, and elastic properties of Cd Se_（1-x）Te_x in the zinc blende phase. It is observed that the electronic properties are improved considerably by using LDA ＋ U as compared to the LDA approach. The calculated lattice constants and bulk moduli are also comparable to the experimental results. The cohesive energies for pure Cd Se and Cd Te binary and their mixed alloys are calculated. The second-order elastic constants are also calculated by the Lagrangian theory of elasticity. The elastic properties show that the studied material has a ductile nature.

Effect of Chinese Herbal Medicine for Calming Gan(肝) and Suppressing Hyperactive Yang on Arterial Elasticity Function and Circadian Rhythm of Blood Pressure in Patients with Essential Hypertension

Objective：To observe the effect of Chinese herbal medicine for calming Gan（肝） and suppressing hyperactive yang（平肝潜阳,CGSHY） on arterial elasticity function and the circadian rhythm of blood pressure in patients with essential hypertension（EH）.Methods：Adopting a parallel,randomized design,sixty-four patients with EH of stagesⅠandⅡwere randomly divided into two groups according to a random number table,with 32 in each group.The patients in the treatment group were treated with CGSHY and those in the control group were treated with Enalapril.All patients were given 24-h ambulatory blood pressure monitoring（ABPM） before and after a 12-week treatment.Trough/peak（T/P） ratios of systolic and diastolic blood pressure（SBP DBP） of each group were calculated.The circadian rhythm of their blood pressure was observed at the same time. The changes in elasticity of the carotid artery in the patients,including stiffness parameter（β）,pressure-strain elastic modulus（Ep）,arterial compliance（AC）,augmentation index（Al）,and pulse wave velocity（PVWβ） were determined by the echo-tracking technique before and after a 12-week treatment.In the meantime,their levels of nitric oxide（NO） and endothelin-1（ET-1） were measured respectively.Results：After treatment,all parameters in the 24-h ABPM and the elasticity of the carotid artery（β,Ep,AC and PVWβ） were markedly improved,the level of NO was increased,and ET-1 was decreased in both groups as compared with values before treatment （P0.05 or P0.01）.Further,the improvements in the ratio of T/P of SBP DBP and in the level of NO and ET-1 in the treatment group were more significant than those in the control group（P0.05）.There were no significant differences in all parameters in the ABPM monitoring and the elasticity of the carotid artery,the recovery of blood pressure circadian rhythm,and the therapeutic effect of antihypertension in EH patients between the two groups （P0.05）.Conclusions：Chinese herbal medicine for CGSHY may lower the blood pressure smoothly and recover the circadian rhythm of blood pressure in EH patients.They may also improve the carotid elasticity of EH patients similar to that of Enalapril.The mechanism of action of Chinese herbs on EH might be related to the regulation of vascular endothelium function.

Band structures of elastic SH waves in nanoscale multi-layered functionally graded phononic crystals with/without nonlocal interface imperfections by using a local RBF collocation method

A meshless radial basis function （RBF） collocation method based on the Eringen nonlocal elasticity theory is developed to calculate the band structures of ternary and quaternary nanoscale multi-layered phononic crystals （PNCs） with functionally graded （FG） interlayers. Detailed calculations are performed for anti-plane transverse waves propagating in such PNCs. The influences of FG and homogeneous interlayers, component number, nonlocal interface imperfections and nanoscale size on cut-off frequency and band structures are investigated in detail. Numerical results show that these factors have significant effects on band structures at the macroscopic and microscopic scales.

Dependence of Consumption Volume on the Labor-Force in One-Productive Models of Economic Dynamics

In the work one-productive model of economic dynamics the labor-force involved in production is investigated the case when or function with constant elasticity of substitution （CES） is studied. is considered. The dependence of the consumption volume on production function coincides with the Cobb-Douglas function

Approximate contact solutions for non-axisymmetric homogeneous and power-law graded elastic bodies:A practical tool for design engineers and tribologists

In two recent papers,approximate solutions for compact non-axisymmetric contact problems of homogeneous and power-law graded elastic bodies have been suggested,which provide explicit analytical relations for the force–approach relation,the size and the shape of the contact area,as well as for the pressure distribution therein.These solutions were derived for profiles,which only slightly deviate from the axisymmetric shape.In the present paper,they undergo an extensive testing and validation by comparison of solutions with a great variety of profile shapes with numerical solutions obtained by the fast Fourier transform(FFT)-assisted boundary element method(BEM).Examples are given with quite significant deviations from axial symmetry and show surprisingly good agreement with numerical solutions.

Thermal Buckling Analysis of Size-Dependent FG Nanobeams Based on the Third-Order Shear Deformation Beam Theory

In this paper,the thermal effects on the buckling of functionally graded（FG） nanobeams subjected to various types of thermal loading including uniform,linear and non-linear temperature changes are investigated based on the nonlocal third-order shear deformation beam theory.The material properties of FG nanobeam are supposed to vary gradually along the thickness direction according to the power-law form.The governing equations are derived through Hamilton＇s principle and solved analytically.Comparison examples are performed to verify the present results.Obtained results are presented for thermal buckling analysis of FG nanobeams such as the effects of the power-law index,nonlocal parameter,slenderness ratio and thermal loading in detail.