Prismatic shells with hexagonal cross-section

A new discrete-continuous analytical model for prismatic shells with hexagonal cross-section is developed on the basis of the semimembrane shell theory. Final results for stresses are derived in form of simple expressions. The proposed analytical model is checked against test and finite element results. The accuracy is judged to be exceptionally good in all cases examined. Therefore, it appears that the method provides a simple but powerful tool in design of nuclear reactor subassembly ducts.     

Hele-Shaw flow with a small obstacle

Asymptotic analysis of the flow passing over a small obstacle in the Hele-Shaw cell is performed. The results are based on the asymptotic formulas for Green’s and Neumann functions recently obtained by Maz’ya and Movchan. Theoretical results are illustrated by the numerical simulations.     

Singular integral inequalities with several nonlinearities and integral equations with singular kernels

We deal with an integral inequality with a power nonlinearity on its left-hand side, n nonlinearities on its right-hand side, and weakly singular kernels. The obtained result is an extension of the Bihari, Henry, Pachpatte, and Pinto inequalities and results obtained by the author. Using these results, we prove sufficient conditions for the existence of global solutions of some nonlinear Volterra integral equations with singular kernels and n nonlinearities. Published in Neliniini Kolyvannya, Vol. 11, No. 1, pp. 71–80, January–March, 2007.     

The Blasius and Sakiadis flow with variable fluid properties

A theoretical study of the effect of variable fluid properties on the classical Blasius and Sakiadis flow is presented in this paper. The investigation concerns engine oil, water and air taking into account the variation of their physical properties with temperature. The results are obtained with the numerical simulation of the governing equations and cover large temperature differences. Velocity and temperature profiles are presented, as well as values of wall shear stress and wall heat transfer, for a variety of temperatures between the plate and the ambient fluid. It is found that the variation of fluid properties and especially viscosity have a strong influence on the results. The results of oil and water are, in general, similar and are generalized to liquids whereas air results are different and are generalized to gases. Except of the new results found in the present work some inaccurate results existing in the literature have been identified.     

Effective moduli of piezoelectric material with microcavities

The effective electroelastic moduli of microcavity-weakened piezoelectric plates are investigated by the dilute, self-consistent, Mori-Tanaka and differential micromechanics theories. The results of perturbed heat intensity, strain and electric field (SEF) due to the presence of voids are obtained for two-dimensional (2-D) piezoelectric plates with microcavities of various shapes, and then the above four micromechanics models can be established with the results. These models can be applicable to a wide range of microcavities such as ellipse, circle, crack, triangle, square and pentagon. Some numerical results are presented to illustrate the applicability of these models.     

A gas thrust bearing with pressurization

The Galerkin method was used to calculate a gas thrust bearing with pressurization. It is shown that, with an appropriate choice of approximating functions, the first approximation already gives satisfactory results. The data obtained are compared with the results of numerical integration.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 25–31, January–February, 1973.     

Forced convection with laminar pulsating flow in a tube

The heat transfer model of laminar pulsating flow in a tube in rolling motion is established. The correlations of velocity, temperature and Nusselt number are obtained. The effects of several parameters on Nusselt number are investigated. The theoretical results are consistent with experimental data. Then the results are evaluated with Nield and Kuznetsov’s results. It is found that Nield and Kuznetsov’s results are not applicable for the laminar pulsating flow in nuclear power systems in ocean environments.     

Generalized thermo-piezoelectric problems with temperature-dependent properties

The model of the equation of generalized thermo-piezoelectricity in an isotropic elastic medium with temperature-dependent mechanical properties is established. The modulus of elasticity is taken as a linear function of reference temperature. The state-space approach is adopted for the solution of one-dimensional problems in the absence or presence of heat sources. A numerical technique is employed to obtain the solution in the physical domain. The results are given and illustrated graphically. A comparison is made with results obtained in case of temperature-independent modulus of elasticity.     

Topological version of section theorems with applications

ＴＯＰＯＬＯＧＩＣＡＬＶＥＲＳＩＯＮＯＦＳＥＣＴＩＯＮＴＨＥＯＲＥＭＳＷＩＴＨＡＰＰＬＩＣＡＴＩＯＮＳＺｈａｎｇＳｈｉ－ｓｈｅｎｇ（张石生）（ＳｉｃｈｕａｎＵｎｉｖｅｒｓｉｔｙ,Ｃｈｅｎｇｄｕ）ＷｕＸｉａｎ（吴鲜）（ＺｈａｏｔｏｎｇＴｅａｃｈｅｒ’ｓ...     

High-order methods for differential equations with large first-derivative terms

A method is developed to solve elliptic singular perturbation problems. Examples are presented in one and two dimensions for both linear and non-linear problems. In particular, examples are presented for fluid flow problems with boundary layers. In the one-dimensional case an approximating equation is developed using just three points. The method first presented is a fourth-order approximation but is extended to become a higher-order method. Results are included for the fourth-, sixth-, eighth- and tenth-order methods. The results are first compared with results found by Segal in an article about elliptic singular perturbation problems. The elliptic singular perturbation problems are compared with a method by Il'in and also with central and backward difference schemes from Segal's article. There was only one case where the results in Segal's paper were as accurate as the results presented in this paper. However, in this case the method used by Segal did not give accurate values for a second problem presented. The results are also compared with results given by Spalding and by Christie. The method of this paper was also tested on the solution of some non-linear diffusion equations with concentration-dependent diffusion coefficients. The results were superior to results presented by Lee and by Schultz. Finally, the method is extended to several two-dimensional problems. The method developed in this paper is accurate, easy to use and can be generalized to other problems.     

Incompressible Flows with Piecewise Constant Density

We investigate the incompressible Navier–Stokes equations with variable density. The aim is to prove existence and uniqueness results in the case of discontinuous initial density. In dimension n = 2,3, assuming only that the initial density is bounded and bounded away from zero, and that the initial velocity is smooth enough, we get the local-in-time existence of unique solutions. Uniqueness holds in any dimension and for a wider class of velocity fields. In particular, all those results are true for piecewise constant densities with arbitrarily large jumps. Global results are established in dimension two if the density is close enough to a positive constant, and in n dimensions if, in addition, the initial velocity is small. The Lagrangian formulation for describing the flow plays a key role in the analysis that is proposed in the present paper.     

Crack problem for superconducting strip with finite thickness

The inclined crack problems are considered for a thin strip and a strip with finite thickness in a perpendicular magnetic field. The critical current density is assumed to be a constant. The crack orientation is varied and the effect of crack on the magnetic field distribution is neglected. Based on the analytical results and variational inequality, the field and current distributions are computed for both thin strip and strip with finite thickness cases, respectively. Then, the stress intensity factors at the crack tip are determined using the finite element method for magnetic field loads. The numerical results are presented for different inclined crack angles, magnetization processes and geometry parameters of the strip. The results show that the fracture behavior of the strip with finite thickness is more complicated than that of the thin strip. With the numerical results, we can predict the largest possibility of cracking as the strip is in an external field.     

Coaxial turbulent jets with strong central blowing

The results of solving the problem of the initial section of isothermal coaxial jets with strong central blowing, when the transverse pressure gradient has only a slight effect and there is no circulation zone in the central jet are given. The problem is solved by the integral relation method with allowance for jet interference and the presence of a cocurrent flow. The results of an experimental investigation of these jets over a wide range of the geometric and regime parameters are also given. The results of the calculations made using the formulas obtained are compared with the experimental data.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 52–59, May–June, 1996.     

Hopf bifurcation in general Brusselator system with diffusion

The general Brusselator system is considered under homogeneous Neumann boundary conditions. The existence results of the Hopf bifurcation to the ordinary differential equation (ODE) and partial differential equation (PDE) models are obtained. By the center manifold theory and the normal form method, the bifurcation direction and stability of periodic solutions are established. Moreover, some numerical simulations are shown to support the analytical results. At the same time, the positive steady-state solutions and spatially inhomogeneous periodic solutions are graphically shown to supplement the analytical results.     

压电体椭圆孔边的力学分析

基于复变函数的方法,以PZT-4材料为例,分别采用精确电边界条件和非导通电边界条件进行了远场均匀载荷作用下的横观各向同性压电体椭圆孔的力学分析并与相关结果进行对比。结果表明当椭圆孔退化为圆孔时,无论在远场作用力载荷或电载荷,两种电边界条件下的结果均能完全吻合。随着椭圆孔的愈加尖锐化,非导通电边界条件逐渐不能适用。     

Comparison of heat transfer performance of tube bank fin with mounted vortex generators to tube bank fin with punched vortex generators

The results obtained from naphthalene sublimation heat/mass analogy experiments in selecting the optimum geometrical parameters of tube bank fin heat exchanger with fins mounted with vortex generators are compared with the results obtained from the condensing experiments of the real heat exchangers with vortex generators punched out on the fins. The results declare that VGs pouched or mounted on fin surfaces have only limited effects on heat transfer performance in the studied configurations; naphthalene sublimation method can be used to select fin patterns with reasonable reliability.     

Brachistochrone on a surface with Coulomb friction

The problem of brachistochronic motion of a particle on a surface with the simultaneous action of gravity and Coulomb friction has been solved. Analytical solutions of the problem in special cases have been found. In the case of a cylindrical surface, it is shown that the solutions found includes, as a special case, all well-known results which refer to the brachistochronic motion of a particle. The results are illustrated with a series of concrete examples.     

INTERACTIONS BETWEEN TWO SEDIMENTING PARTICLES WITH DIFFERENT SIZES

IntroductionParticulateflowsarecommonlyencounteredinvariousnaturalphenomenaandindustrialprocesses,suchasinthechemicalandpetroleumindustries,thesedimentationofparticlesisawayofseparatingparticlesfromfluid ,aswellasawayofseparatingparticleswithdifferentsettlingspeedsfromeachother[1].Animportantaspectoftheseflowsisparticlepairinteraction ,whichisfundamentalmechanismsthatenterstronglyintoallpracticalapplicationsofparticulateflows.Problemofthesedimentationoftwoequalparticleshasbeenpreviouslystudied…