A numerical solution for axially symmetrical elasticity problems

An integral equation method is presented for the solution of axially symmetrical elasticity problems. The obtained integral equations are of second kind with regular (Fredholm) and singular kernel. The method is suited to the treament of both simply and multiply connected regions with irregular boundary shapes and any boundary load distribution which satisfies the equilibrium conditions. Numerical results are included.     

Structural symmetry and boundary conditions for nonlocal symmetrical problems

The paper deals with the determination of the symmetric model and proper boundary conditions for solving nonlocal elastic symmetric structures. The above concepts, in the context of nonlocal integral elasticity, turn out to be different with respect to the standard ones, classically applied when dealing with local elastic symmetric structures. Indeed, when only a symmetric portion of the structure is analyzed, the nonlocal effects induced by the remaining (cut) portions are lost, this necessitates the consideration of an enlarged symmetric model on which appropriate nonlocal boundary conditions have to be imposed. It has to be pointed out how the width of such an enlarged model depends on the nonlocal material parameters, while the correct unknown nonlocal boundary conditions are here obtained and enforced by an iterative procedure. The accuracy of the proposed approach in solving nonlocal structural symmetric problems is tested with the aid of two numerical examples.     

The axial symmetrical edge problems for thin-walled shells of revolution

In this paper, the uniformly valid asymptotic solutions for the axial symmetrical edge problems of thin-walled shells of revolution in bending are given.     

Some measurements in a binary gas jet

Simultaneous measurements of species volume concentration and velocities in a helium/air binary gas jet with a jet Reynolds number of 4,300 and a jet-to-ambient fluid density ratio of 0.64 were carried out using a laser/hot-wire technique. From the measurements, the turbulent axial and radial mass fluxes were evaluated together with the means, variances and spatial gradients of the mixture density and velocity. In the jet near field (up to ten diameters downstream of the jet exit), detailed measurements of u/ ₀ U ₀, v/ ₀ U₀, u v/ ₀ U ₀ ² , u ² / ₀ U ₀ ² and v ² / ₀ U ₀ ² reveal that the first three terms are of the same order of magnitude, while the last two are at least one order of magnitude smaller than the first three. Therefore, the binary gas jet in the near field cannot be approximated by a set of Reynolds-averaged boundary-layer equations. Both the mean and turbulent velocity and density fields achieve self-preservation around 24 diameters. Jet growth and centerline decay measurements are consistent with existing data on binary gas jets and the growth rate of the velocity field is slightly slower than that of the scalar field. Finally, the turbulent axial mass flux is found to follow gradient diffusion relation near the center of the jet, but the relation is not valid in other regions where the flow is intermittent.     

Large deformation symmetrical elasticity problems solved by the variational method

In this paper,based on the mathematical theory of classical mechanics and Chen‘s theorem,the variational method is used in the study of large deformation symmetrical elasticity problems.The generalized variational principles of potential energy and complementary energy,based on the instantaneous configuration are obtained,and the equivalence between the two principles is proved.Besides,the generalized variational principles of dynamical problems based on the instantaneous configuration are also given.     

Some non-classical thermoelasticity problems for a rectangular parallelepiped

Meccanica - In the Cartesian system of coordinates, thermoelastic equilibrium of an isotropic homogeneous rectangular parallelepiped is considered. On the lateral faces of a parallelepiped either...     

Some self-similar viscous gas flows in a channel

We consider the class of self-similar axisymmetric and two-dimensional laminar flows of a viscous gas in a long channel with smooth contour, in which the longitudinal component of the velocity and the gas temperature are functions of a single dimensionless transverse coordinate. Such flows correspond to exponential (axisymmetric flow) or linear (two-dimensional flow) increase of the radius or height of the channel and corresponding exponential or hyperbolic decrease of the static pressure along the channel.     

Some physical problems of cumulation

A review and analysis of some results related to the phenomenon of cumulation are given. The various models used to describe this phenomenon are considered. Lavrent’ev Institute of Hydrodynamics, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 10–26, September–October, 2000.     

Analysis on nonlinear effect of unsteady percolation in the inhomogeneous shale gas reservoir

The nonlinear effects of unsteady multi-scale shale gas percolation,such as desorption,slippage,diffusion,pressure-dependent viscosity,and compressibility,are investigated by numerical simulation.A new general mathematical model of the problem is built,in which the Gaussian distribution is used to describe the inhomogeneous intrinsic permeability.Based on the Boltzmann transformation,an efficient semi-analytical method is proposed.The problem is then converted into a nonlinear equation in an integral form for the pressure field,and a related explicit iteration scheme is constructed by numerical discretization.The validation examples show that the proposed method has good convergence,and the simulation results also agree well with the results obtained from both numerical and actual data of two vertical fractured test wells in the literature.Desorption,slippage,and diffusion have significant influence on shale gas flows.The accuracy of the usual technique that the product of viscosity and compressibility is approximated as its value at the average formation pressure is examined.     

Some problems of nonisothermal steady flow of a viscous fluid

The paper presents solutions to the problems of plane Couette flow, axial flow in an annulus between two infinite cylinders, and flow between two rotating cylinders. Taking into account energy dissipation and the temperature dependence of viscosity, as given by Reynolds's relation =₀ exp (–T) (₀, =const). Two types of boundary conditions are considered: a) the two surfaces are held at constant (but in general not equal) temperatures; b) one surface is held at a constant temperature, the other surface is insulated.Nonisothermal steady flow in simple conduits with dissipation of energy and temperature-dependent viscosity has been studied by several authors [1–11]. In most of these papers [1–6] viscosity was assumed to be a hyperbolic function of temperature, viz. =_m 1/1+²(T–T_m.Under this assumption the energy equation is linear in temperature and can he easily integrated. Couette flow with an exponential viscosity-temperature relation. =₀ e ^–T (₀, =const), (0.1) was studied in [7, 8]. Couette flow with a general (T) relation was studied in (9).Forced flow in a plane conduit and in a circular tube with a general (T) relation was studied in [10]. In particular, it has been shown in [10] that in the case of sufficiently strong dependence of viscosity on temperature there can exist a critical value of the pressure gradient, such that a steady flow is possible only for pressure gradients below this critical value.In a previous work [11] the authors studied Polseuille flow in a circular tube with an exponential (T) relation. This thermohydrodynamic problem was reduced to the problem of a thermal explosion in a cylindrical domain, which led to the existence of a critical regime. The critical conditions for the hydrodynamic thermal explosion and the temperature and velocity profiles were calculated.In this paper we treat the problems of Couette flow, pressureless axial flow in an annulus, and flow between two rotating cylinders taking into account dissipation and the variation of viscosity with temperature according to Reynolds's law (0.1). The treatment of the Couette flow problem differs from that given in [8] in that the constants of integration are found by elementary methods, whereas in [8] this step involved considerable difficulties. The solution to the two other problems is then based on the Couette problem.     

Some static problems for elastic bodies with a crust

Summary This paper studies the diffusion of stresses in a linear isotropic elastic body coated with a thin elastic shell called the ?crust?. Two static problems are considered. The first is that of the semi-infinite half-space covered by a thin plate subject to a point load at the origin. In the second problem a solid elastic sphere enveloped by a thin spherical elastic shell with two opposite point loads at the poles is investigated. Solutions for the displacement within the thin crust are obtained in the two problems by means of the Hankel transform and the Legendre polynomial respectively.

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Sommario Questo lavoro studia la diffusione degli sforzi in un corpo elastico, lineare, isotropo rivestito da un guscio elastico sottile denominato la ?crosta?. Sono considerati due problemi elastostatici. Il primo è quello di un semispazio coperto da una piastra sottile soggetta and un carico concentrato nell'origine. Nel secondo problema si studia una sfera solida elastica avvolta da un guscio sottile elastico con due carichi concentrati opposti nei poli. Nei due problemi le soluzioni in termini di spostamenti entro la crosta si ottengono rispettivamente mediante la trasformata di Hankel e i polinomi di Legendre.

     

Some nonlinear problems of groundwater flow through a porous medium

Self-similar solutions of the equation of groundwater gravity flow through a porous medium are given. The water flows from a basin into an underground permeable reservoir bounded from below by an impervious bed. A periodic problem of flow through a porous medium in which the water level in the basin periodically oscillates is considered. It is shown that in this case the water table elevation effect, i.e., water pumping into the aquifer, develops at a sufficient distance from the littoral zone. The invariant-group solutions of the problem of flow through a porous medium are investigated with allowance for evaporation from the groundwater surface.