scholarly journals Elastoplastic deformation of a rotating hollow cylinder with a rigid casing

2019 ◽  
pp. 120-135
Author(s):  
A N Prokudin ◽  
S V Firsov
Keyword(s):  
Plastic Flow ◽  
Hollow Cylinder ◽  
Outer Surface ◽  
Rotation Speed ◽  
Exact Analytical Solution ◽  
Plastic Region ◽  
Flow Rule ◽  
Elastoplastic Material ◽  
Plastic Deformations ◽  
Rotating Hollow Cylinder

A rotating hollow cylinder with fixed ends is considered, the inner surface of which is free of stresses, and the outer one is fixed from radial movements. It is assumed that the cylinder is made of an ideal isotropic elastoplastic material, and the deformations in it are small and represent the sum of elastic and plastic deformations. Stresses are associated with elastic deformations by Hooke's law. Plastic deformations are determined using the Tresca - Saint-Venant condition and the plastic flow rule associated with it. The cylinder rotation speed first monotonically increases to a maximum value, and then decreases to zero. By using the elastic solution, the dependence is found for the critical rotation speed at which the plastic flow begins. It is established that, depending on the thickness of the cylinder and the Poisson's ratio, plastic flow can begin, either on the inner or on the outer surface of the cylinder. In addition, 3 plastic regions appear in the cylinder at the loading stage, and 4 plastic regions appear at the unloading stage. These regions correspond to two faces and two edges of the Treska prism. For each plastic region, an exact analytical solution of the determining system of equations is found. The system of conditions at the boundaries between the regions providing continuity of the obtained solutions throughout the cylinder is given. Two cases are considered, i.e. the case with a plastic flow which starts first on the inner, and then on the outer surface of the cylinder. Analytical expressions are obtained for rotational speeds at which new regions appear. The relationship between the nucleation rates of the secondary and primary plastic flow is established. The value of the maximum rotation speed sufficient for a complete transition of the cylinder to the state of the secondary plastic flow was also found. It has been revealed that the adding of a rigid casing can significantly increase the resource of an exploited part.

Axially symmetric plastic deformations in soils

1961 ◽  
Vol 254 (1036) ◽  
pp. 1-45 ◽  
Keyword(s):  
Plastic Flow ◽  
Plane Surface ◽  
Velocity Fields ◽  
Natural Soil ◽  
Flow Rule ◽  
Foundation Engineering ◽  
Axially Symmetric ◽  
Plastic Deformations ◽  
Von Karman ◽  
Von Kármán

A theoretical investigation is given of quasi-static axially symmetric plastic deformations in soils.The mechanical behaviour of a natural soil is approximated by that of an ideal soil which obeys Coulomb’s yield criterion and associated flow rule, with restriction to rigid, perfectly plastic deformations. There are considerable variations in the structure of the associated stress and velocity field equations for the various plastic regimes, but it is noteworthy that real families of characteristics occur in all non-trivial cases. Attention is focused on those plastic régimes agreeing with the heuristic hypothesis of Haar & von Kármán as being seemingly of application to certain classes of problems, in particular to those of indentation. The stress and velocity fields are then hyperbolic with identical families of characteristics, and the stress field is statically determinate under appropriate boundary conditions. In applications of the theoretical analysis, attention is confined to situations involving only the Haar & von Kármán plastic regimes. First, possible velocity fields are obtained for the incipient plastic flow of a right circular cylindrical sample of soil subjected to uni-axial compressive stress parallel to its axis. Secondly, a complete solution is obtained for the incipient plastic flow in a semi-infinite region of soil, bounded by a plane surface, due to load applied through a flat-ended,smooth, rigid, circular cylinder; numerical results obtained for this problem include the variation of yield-point load with angle of internal friction of the ideal soil. These applications relate to problems of the mechanical testing of soil samples and of load-bearing capacity in foundation engineering.

scholarly journals The theory of combined plastic and elastic deformation with particular reference to a thick tube under internal pressure

1947 ◽  
Vol 191 (1026) ◽  
pp. 278-303 ◽  
Keyword(s):  
Stress Distribution ◽  
Internal Pressure ◽  
Plastic Flow ◽  
Plastic Region ◽  
Strain Diagram ◽  
Combined Stresses ◽  
Usual Theory ◽  
Plastic Components ◽  
Longitudinal Extension ◽  
Elastic Strains

In certain problems of plastic flow, for example, a thick tube expanded by internal pressure, it is important to consider changes in the elastic strain of material which is flowing plastically in order to deduce the correct stress distribution and deformation. The usual plastic theory which neglects elastic strains in the plastic region may lead to considerable errors in certain cases. In this paper we review the theory of the deformation of a material under combined stresses which involves both elastic and plastic components of strain. The relationship between stress and strain is represented on a plane diagram, the reduced stress-strain diagram, which facilitates discrimination between the elastic and plastic components of strain and aids considerably the solution of certain problems. The diagram can also be used to express the relationships governing the dissipation of energy during plastic flow under combined stresses. The theory is applied to the deformation of a long thick tube under internal pressure with zero longitudinal extension. The solution is compared with that based on the usual theory which neglects elastic strains in the plastic region, revealing an error which reaches a maxi­mum of over 60% in the longitudinal stress distribution. The significance of the differences between the two solutions is discussed in detail.

Elastic wave propagation in 2D-FGM hollow cylinders with curved outer surface under moving shock loading using isogeometric analysis

2020 ◽  
pp. 095440622096076
Author(s):  
Ahmad Yavari ◽  
Mohammad Hossein Abolbashari ◽  
Behrooz Hassani
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Hollow Cylinder ◽  
Outer Surface ◽  
Material Properties ◽  
Shock Loading ◽  
Propagation Speed ◽  
Elastic Field ◽  
Functionally Graded ◽  
Elastic Wave Propagation

Analysis of elastic wave propagation in a hollow cylinder with two-dimensional (2D) functionally graded material (FGM) and the curved outer surface under internal moving shock loading is the subject of this study. In the proposed method, there is no restriction on the distribution of material properties, the shape of the outer surface, and the applied shock loading. They are treated with non-uniform rational B-spline (NURBS). The isogeometric approach is developed for solving the problem to ensure precise modeling of the geometry. Also, the Newmark approach is used for full discretization of the isogeometric equations. The distributions of all elastic field quantities are determined for two types of material distributions and shock loadings. The effects of shock loadings, the shape of the outer surface, and the material distribution on the elastic wave are thoroughly examined. Propagation, reflections, and propagation speed inside the hollow cylinder are investigated. It is found that the propagation speeds of elastic waves have a distribution associated with the distribution of the material properties. Also, the shape of the outer surface can affect the amplitude of the elastic wave and the locations of concentration stress. It is concluded that the sonic boom phenomenon occurs in the solids as well as in the air.

Convective Heat Transfer in a Rotating Hollow Cylinder with an End Wall

2020 ◽  
Vol 46 (7) ◽  
pp. 703-706
Author(s):  
V. A. Arkhipov ◽  
O. V. Matvienko ◽  
A. S. Zhukov ◽  
N. N. Zolotorev
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Hollow Cylinder ◽  
Convective Heat ◽  
Rotating Hollow Cylinder ◽  
End Wall

A new elastoplastic constitutive model for coarse granular aggregates incorporating particle breakage

2004 ◽  
Vol 41 (4) ◽  
pp. 657-671 ◽  
Author(s):  
Wadud Salim ◽  
Buddhima Indraratna
Keyword(s):  
Constitutive Model ◽  
Plastic Flow ◽  
Current Model ◽  
Particle Breakage ◽  
Flow Rule ◽  
Peak Strain ◽  
Stress Strain ◽  
Coarse Aggregates ◽  
Stress Changes ◽  
Plastic Flow Rule

A new elastoplastic stress–strain constitutive model is developed for granular coarse aggregates incorporating the degradation of particles during triaxial shearing. Coarse granular aggregates are subjected to breakage during excessive stress changes. Most of the available constitutive models do not consider the degradation of particles during shearing. In the current model, a plastic flow rule has been developed incorporating the energy consumption due to particle breakage during shear deformation. A non-associated flow and a kinematic type yield locus have been adopted in the model. A general formulation for the rate of particle breakage during shearing has been developed and incorporated in the plastic flow rule. The effects of particle breakage on the plastic distortional and volumetric deformations are incorporated in the current model. The stress–strain formulations are developed within the general critical state framework. The model can accurately predict the stress–strain and volume change behaviour of coarse granular aggregates. The plastic dilation and contraction features of coarse aggregates at various confining pressures are well captured, and the strain-hardening and post-peak strain-softening behaviour of coarse granular media is adequately represented. A particular feature of the model is its capability to predict the degree of particle breakage at any stage of shear deformation.Key words: constitutive modelling, coarse granular aggregates, particle breakage, dilatancy, non-associated flow, plasticity.

Generalized plastic flow rule

2005 ◽  
Vol 21 (2) ◽  
pp. 321-351 ◽  
Author(s):  
K HASHIGUCHI
Keyword(s):  
Plastic Flow ◽  
Flow Rule ◽  
Plastic Flow Rule

ANALYTICAL METHOD FOR DETERMINING THE THICKNESS OF DEPOSITS ON THE INTERNAL SURFACES OF HEAT EXCHANGERS

2019 ◽  
Vol 9 (1) ◽  
pp. 20-24
Author(s):  
Olga Yu. KURGANOVA ◽  
Igor V. KUDINOV ◽  
Ruslan M. KLEBLEEV ◽  
Ekaterina V. STEFANYUK ◽  
Tatiana E. GAVRILOVA
Keyword(s):  
Analytical Solution ◽  
Outer Surface ◽  
Analytical Method ◽  
Exact Analytical Solution ◽  
Large Diameter ◽  
Experimental Studies ◽  
Sediment Layer ◽  
Internal Surfaces ◽  
Pipeline Wall

Using the exact analytical solution of the stationary thermal conductivity problem for a two layer flat wall under inhomogeneous boundary conditions of the first and third kind, an analytical method for thickness determination of the sediment layer on the inner surface of the pipeline wall by the temperature known from the experiment on its outer surface is developed. The thickness of the deposits is found from the solution of the inverse problem by substituting the experimental value of the temperature of the outer surface of the wall into the formula of an accurate analytical solution. According to the results of theoretical studies, the thickness of the deposits was equal to 1.3 cm. Due to the large diameter of the pipeline (0.6 m) and the insignificant thickness of the two layer wall (0.016 m), it was assumed to be flat. The thickness of the deposits according to experimental studies was equal to 1.1 cm. Therefore, the discrepancy between the results of theoretical and experimental studies is 15.3%. The sequence of obtaining a solution to a similar problem for a cylindrical wall is also presented.

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