Stresses In Hollow Cylinder Research Articles

Torsional wave dispersion in a bi-layered hollow cylinder with inhomogeneous initial stresses caused by internal and external radial pressures

The present paper studies the influence of the inhomogeneous initial stresses in the bi-layered hollow cylinder and it is assumed that these stresses are caused by the hydrostatic pressures acting on the interior and outer free surfaces of the cylinder. The study is made by utilizing the version of the three-dimensional linearized theory of elastic waves in bodies with initial stresses for which the initial stress-strain state in bodies is determined within the scope of the classical linear theory of elasticity. For the solution to the corresponding eigenvalue problem, the discrete-analytical method is employed. Numerical results are presented and analyzed for concrete selected pairs of materials. According to these results and their analyses, it is established that, unlike homogeneous initial stresses, the influence of the inhomogeneous initial stresses on the torsional wave dispersion has not only quantitative but also qualitative character. For instance, in particular, it is established that as a result of the initial stresses caused by the hydrostatic pressure acting in the interior free surface of the cylinder, the cut-off frequency appears for the fundamental dispersive mode and the values of this frequency increase with the intensity of this pressure.

Thermo-electro-elastic analysis of functionally graded piezoelectric shells of revolution: Governing equations and solutions for some simple cases

In this article, the three-dimensional multi-field equations of functionally graded piezoelectric (FGP) shells of revolution under thermo-mechanical loading are derived. First, the heat conduction equation for an FGP is derived and then, the displacement equations are developed considering thermal effects. The coupling is one-way, i.e. the temperature field affects the displacements and stresses while the back influence of the displacement on the temperature is disregarded. The Hamilton's principle is used to derive the governing equations of motion, in presence of system rotation effects, for thick shells of revolution with variable thickness and arbitrary curvature. Material properties are assumed to vary in various directions according to an arbitrary function. For the sake of simplicity and verification of derivation, the heat conduction and governing equations of motion have been reduced for a functionally graded piezoelectric cylindrical shell under thermal loading. In order for the general equations to be verified, two simple examples are investigated, i.e. thermal stresses in hollow cylinder and sphere. Correctness and generality of the present results can be justified given the capability of these equations for different geometries and material properties.

The effect of CNT volume fraction on the magneto-thermo-electro-mechanical behavior of smart nanocomposite cylinder

In this article, using analytical approach, the stress analysis of a long piezoelectric polymeric hollow cylinder reinforced with carbon nanotube (CNT) under combined magneto-thermo-electro-mechanical loading is investigated. Considering three combined loading conditions such as pressure-electric, pressure-electric magnetic and pressure-electric thermal, the governing equation of the problem is obtained. The rule of mixture and modified multiscale bridging model are used to predict effective properties of nanocomposite. The magneto-thermo-electro-mechanical stresses in hollow cylinder are discussed in detail. It can be concluded that increasing CNT volume fraction enhances strength of the nanocomposite cylinder. The results of this work could be useful in view of optimum design of the smart nanocomposite cylinder under magneto-thermo-electro-mechanical loadings and could also be as a reference for future related works.

Extensile Cracking in Porous Rock Under Differential Compressive Stress

Under differential compressive stress rocks exhibit nonlinear deformation that includes initial compaction, near-linear elastic behavior, and strain-hardening followed by strain-softening and dilation (or compaction in clastic rocks) and localization. This behavior derives largely from changes in the microstructure of the rocks. Much of it has been attributed to the growth of extensile microcracks. The stress-induced microstructural changes brought about by successively more complicated states of stress produced by uniaxial and triaxial compression of circular cylinders, axisymmetric stresses in hollow cylinders, and indentation by hemispheres in Indiana limestone and Berea sandstone have been preserved using Wood’s metal porosimetry. In this technique molten Wood’s metal at about 100°C is used as a pore fluid at a pressure of about 10 MPa, and the experiments are conducted using the concepts of effective stress. At the deformation state of interest, the temperature is lowered to solidify the metal, thereby preserving the microstructure as it exists under load and facilitating subsequent preparation of the specimen for microscopic study. Mode I microcrack growth is observed to occur by a variety of mechanisms such as bending, point loading and sliding cracks. The effects of this are analyzed using an elastic continuum within which Mode II displacement across microcracks and Mode I microcrack growth results from heterogeneous stress concentrations that produce local tensile stresses. While the continuum model replicates many of the observations, it fails to account for localization by en echelon arrays of extensile microcracks that precede macroscopic shear faulting. Using a “zero order” continuum approximation, the spatially stochastic distribution of grains in clastic rocks is shown to be important in the formation of the en echelon arrays of microcracks that form shear bands.

Thermoelastoplastic and Residual Stresses in a Hollow Cylinder With Temperature-Dependent Properties

Determination of residual stresses and the positive or negative effect that they may have on the component is an important consideration in design. Unexpected failure of components, latter determined to be attributable to residual stress, is not uncommon. In this paper, a theoretical study of the stresses in a long hollow circular cylinder subjected to rapid cooling of the exterior surface is presented. A quasi-static uncoupled thermoelastoplastic analysis, based on incremental theory of plasticity, is developed and a numerical procedure for successive approximation is formulated. For this analysis, it is assumed that the material has temperature-dependent properties and is characterized by linear strain hardening. The thermoelastoplastic and residual stress distributions are discussed in detail. The results are compared with related published work where a reasonable agreement is observed.

Nonstationary thermal stresses in a hollow cylinder with heat flux acting on the inside surface

Thermoelastic stresses in a long hollow cylinder are considered when a uniformly distributed heat flux is applied to the inside surface and the outside surface is heat-insulated.

Stresses in hollow cylinders with conical ends bonded to shell and shrunk

This paper deals with, the three-dimensional photoelastic analysis of stresses and strains in two long, hollow circular cylinders with conical ends of 45° and 60°. The cylinders were bonded to a steel casing on the outer surface. The stresses and strains due to restrained shrinkage have been determined at the interface. The maximum stress for both geometries was found to occur at the end of the bond, and to be about 40% higher in the 60° cylinder than in the 45° cylinder. A study was also made at the opposite end of the two cylinders, where a natural meniscus was formed. The results should be of interest in the design of solidpropellant rocket grains.

SYNOPTIC: Stresses in Hollow Cylinders with Conical Ends Bonded to Shell and Shrunk

This paper deals with the three-dimensional photoelastic analysis of stresses and strains in two long, hollow circular cylinders of epoxy resin with conical ends inclined at 45° and 60°. The cylinders were bonded to steel casings to simulate case-bonded propellant grains. The stresses and strains due to the restrained shrinkage of the cylinders were determined at the interface. A natural, toroidal meniscus was formed at the open end of each cylinder. The strains at the meniscus surface were also studied.

A contribution to the stress analysis of piston pins

The frozen stress photoelastic technique was used to study the stresses in hollow cylinders supported on a central lug and loaded through two outer lugs, simulating the loading of a piston pin by the connecting rod and pision. The loading was arranged so that the resultant piston thrust acted through the (exaggerated) gaps between the lugs. In addition to the surface stresses in the bore and on the outer surface of the pins, the distributions of orthogonal shear stresses on four (circular) cross-sections of one pin were determined and integrated to give the load transfer from the central lug into the pin. The orthogonal shear distribution in the gap was compared with Love's theoretical solution for the shear stresses in a thick walled tube.

Transient Thermal Stresses in Hollow Cylinders by the Rapid Heating with Special Application to the Heat Condition of a Hot Roll

A cast iron roll formed into a hollow cylinder closed at both ends is used to roll plastics and its inner surface is heated by steam. Recently, a roll was longitudinally cracked owing to the rapid heating. In this paper, it is assumed that the temperature of inner surface of an infinite hollow cylinder is linearly elevated to working temperature, and the transient thermal stresses in an infinite hollow cylinder are caluculated. If the allowable stress of material is given, the heat condition of rolls is determined. Also, when a hollow cylinder is closed at both ends, it is shown that the stresses in the cylinder near the ends become larger than the stresses in an infinite hollow cylinder. In an example, if the allowable tensile stress of material is 4 kg/mm2, it is found that a cylinder of inner radius 200 mm and outer radius 300 mm must be heated to 400°C in about 40 min.

Stresses in Hollow Cylinders Due to Asymmetrical Heat Generation

Equations are derived for the radial, tangential, shear, and axial stresses arising in nuclear reactor vessels, thermal shields, and so on, from internal heat generation caused by the absorption of gamma radiation. The heat generation considered behaves as a decaying exponential through the wall of the hollow cylinder and is an arbitrary function of the angle around the axis of the cylinder.

Thermal stresses in reactor shells due to γ-irradiation

This paper gives methods of calculating the temperatures and stresses in shells forming the pressure vessel or thermal shield of a nuclear reactor. It is assumed that the γ-ray currents are known on the inner surface of the shell. The heating and stress effects are considered, with particular reference to (a) Temperature boundary conditions, (b) Limitations of the flat slab approximation to the stresses in hollow cylinders and spheres.

Approximate Solution to Thermal-Shock Problems in Plates, Hollow Spheres, and Cylinders With Heat Transfer at Two Surfaces

Abstract An approximate method for computing transient thermal stresses in hollow cylinders, plates, and hollow spheres is presented. The method makes use of polynomial approximations to the temperature distribution by means of which the partial differential equation of the problem is reduced to a set of first-order ordinary differential equations. Nonuniform initial temperature distribution and heat transfer from both surfaces can be treated without difficulty making possible the practical solution of problems with relatively little labor for which an exact solution requires a great expenditure of labor and time. Several examples are presented and compare favorably with more accurate solutions.

An experimental investigation of residual stresses in hollow cylinders due to the creep produced by thermal stresses

The paper describes an investigation into the residual stresses produced in cast iron cylinders by the creep-relaxation of thermal stresses. The connexion of the work with failures of combustion chamber parts in large internal combustion engines is discussed. A series of thick-hollow cylinders were subjected to a radial flow of heat by heating the bore and water-cooling the outer diameter for a chosen period of time, during which the thermal stresses were relaxed by creep. The residual stresses due to relaxation were determined by slitting the cylinder and subsequently boring out concentric layers from the inside, the resulting changes in strain at the outside diameter being measured. The creep strains are confined to the inner layers of the wall and result in a steep residual stress gradient within those layers. The residual stress at the bore (in the extreme case) is 4 1 2 times that at the outside diameter. Creep in compression at the bore is the predominating factor in causing residual stresses on cooling.