Pressurized Cylindrical Shell With a Rigid Circular Inclusion

1978 ◽  
Vol 100 (2) ◽  
pp. 158-163 ◽  
Author(s):  
D. H. Bonde ◽  
K. P. Rao
Keyword(s):  
Differential Equation ◽  
Cylindrical Shell ◽  
Shallow Shell ◽  
Circular Inclusion ◽  
Hankel Functions ◽  
Curvature Parameter ◽  
Shell Equations ◽  
Limiting Case ◽  
Rigid Circular Inclusion ◽  
Good Agreement

The effect of a rigid circular inclusion on stresses in a cylindrical shell subjected to internal pressure has been studied. The two linear shallow shell equations governing the behavior of a cylindrical shell are converted into a single differential equation involving a curvature parameter and a potential function in nondimensionalized form. The solution in terms of Hankel functions is used to find membrane and bending stressses. Boundary conditions at the inclusion shell junction are expressed in a simple form involving the in-plane strains and change of curvature. Good agreement has been obtained for the limiting case of a flat plate. The shell results are plotted in nondimensional form for ready use.

Stresses in a Spherical Shell With a Circular Elastic Inclusion

1974 ◽  
Vol 96 (3) ◽  
pp. 228-233
Author(s):  
P. Prakash ◽  
K. P. Rao
Keyword(s):  
Differential Equations ◽  
Spherical Shell ◽  
Elastic Inclusion ◽  
Circular Inclusion ◽  
Shallow Spherical Shell ◽  
Spherical Shells ◽  
Hankel Functions ◽  
Circular Elastic Inclusion ◽  
Rigid Circular Inclusion

The problem of a circular elastic inclusion in a thin pressurized spherical shell is considered. Using Reissner’s differential equations governing the behavior of a thin shallow spherical shell, the solutions for the two regions are obtained in terms of Bessel and Hankel functions. Particular cases of a rigid circular inclusion free to move with the shell and a clamped rigid circular inclusion are also considered. Results are presented in nondimensional form which will greatly facilitate their use in the design of spherical shells containing a rigid or an elastic inclusion.

Stress Concentration in a Cylindrical Shell Containing a Circular Hole

1971 ◽  
Vol 93 (4) ◽  
pp. 953-961 ◽  
Author(s):  
N. J. I. Adams
Keyword(s):  
Cylindrical Shell ◽  
Stress Concentration ◽  
Hole Radius ◽  
Axial Tension ◽  
State Of Stress ◽  
Curvature Parameter ◽  
Circular Cutout ◽  
Shell Equations ◽  
Plate Solution ◽  
Limiting Value

The state of stress in a cylindrical shell containing a circular cutout was determined for axial tension, torsion, and internal pressure loading. The solution was obtained for the shallow shell equations by a variational method. The results were expressed in terms of a nondimensional curvature parameter which was a function of shell radius, shell thickness, and hole radius. The function chosen for the solution was such that when the radius of the cylindrical shell approaches infinity, the flat-plate solution was obtained. The results are compared with solutions obtained by more rigorous analytical methods, and with some experimental results. For small values of the curvature parameter, the agreement is good. For higher values of the curvature parameter, the present solutions indicate a limiting value of stress concentration, which is in contrast to previous results.

An Efficient Computational Approach for a Large Opening in a Cylindrical Vessel

1986 ◽  
Vol 108 (4) ◽  
pp. 436-442 ◽  
Author(s):  
C. R. Steele ◽  
M. L. Steele ◽  
A. Khathlan
Keyword(s):  
Shallow Shell ◽  
Computer Calculation ◽  
Computational Approach ◽  
Cylindrical Vessel ◽  
Intersection Curve ◽  
High Harmonics ◽  
Large Opening ◽  
Shell Equations ◽  
Present Effort ◽  
Good Agreement

In our previous work, solutions of the shallow shell equations have provided the basis for efficient computer calculation for a reinforced opening in a cylindrical vessel. However, solutions are restricted to smaller nozzles and openings (d/D≤0.5). In the present effort, an approach for the large opening has been developed which retains computational efficiency and minimum user time. The total solution can be divided into “high” harmonics around the intersection curve, which are obtained from asymptotic analysis, and particular solutions and low harmonics of self-equilibrating loads, which are obtained as “cut” solutions. By this, the vessel is considered to be cut along the portion of the circumference inside the intersection curve. Appropriate discontinuities of stress and displacement on the cut provide the necessary solutions. Results for a rigid nozzle with external loadings show good agreement with the previous shallow shell calculations for d/D≤0.5 with a substantial divergence for larger values of d/D. The behavior at the limit of d/D = 1 remains to be clarified.

Stress analysis of a cylindrical shell with a variable wall thickness

1987 ◽  
Vol 91 (908) ◽  
pp. 367-372
Author(s):  
D. S. Chehil ◽  
R. Jategaonkar ◽  
R. S. Dhaliwal
Keyword(s):  
Differential Equation ◽  
Cylindrical Shell ◽  
Differential Equations ◽  
Wall Thickness ◽  
Complete Solution ◽  
Complex Nature ◽  
Variable Wall Thickness ◽  
General Variation ◽  
Variable Wall ◽  
Good Agreement

Summary While the bending analysis of cylindrical containers with wall thickness varying linearly has attracted much attention, it seems the general variation in wall thickness has not been considered. This is because of the difficulties which have been encountered due to the complex nature of the differential equations involved. In this paper, the container’s wall thickness is chosen to be of general variation and the differential equation is perturbed to give rise to a sequence of differential equations. It is shown that this sequence can be easily solved when the form of variation in wall thickness is specified. A complete solution is obtained in a particular case when the wall thickness varies linearly and the tank is subjected to hydrostatic pressure. For this particular case the numerical results are compared with the ones available in the literature which seem to be in good agreement.

scholarly journals Stress Concentration in a Rubber Sheet Under Axially Symmetric Stretching

1967 ◽  
Vol 34 (4) ◽  
pp. 942-946 ◽  
Author(s):  
Wei Hsuin Yang
Keyword(s):  
Differential Equation ◽  
Phase Plane ◽  
Order Differential Equation ◽  
Outer Boundary ◽  
Circular Inclusion ◽  
Axially Symmetric ◽  
Rubber Sheet ◽  
First Order ◽  
Radial Loading ◽  
Rigid Circular Inclusion

A class of axially symmetric problems, concerning a highly elastic, circular rubber sheet with (a) a centered circular hole, (b) a rigid circular inclusion under outward radial loading at outer boundary, and (c) a rigid outer boundary and a concentric hole under inward radial loading around the hole, is solved. The solution of (a) has been obtained by Rivlin and Thomas [1] by solving simultaneously a set of differential equations numerically. In this paper, their equations are reduced to a single second-order differential equation governing the deformation function ρ(r). This is further reduced to two decoupled first-order equations after introducing the phase plane (λ1 – λ2 plane). The solutions are obtained conveniently in the phase plane by Picard’s method and by straightforward numerical integration.

Characteristics of Herringbone-Grooved, Gas-Lubricated Journal Bearings

1965 ◽  
Vol 87 (3) ◽  
pp. 568-576 ◽  
Author(s):  
J. H. Vohr ◽  
C. Y. Chow
Keyword(s):  
Differential Equation ◽  
Journal Bearing ◽  
Groove Depth ◽  
Radial Force ◽  
Journal Bearings ◽  
Speed Ratio ◽  
Plain Bearing ◽  
Relative Speed ◽  
Whirl Speed ◽  
Limiting Case

A differential equation is obtained for the smoothed “overall” pressure distribution around a herringbone-grooved, gas-lubricated journal bearing operating with a variable film thickness. The equation is based on the limiting case of an idealized bearing for which the number of grooves approaches an infinite number. A numerical solution to the differential equation is obtained valid for small eccentricities. This solution includes the case where the journal is undergoing steady circular whirl. In addition to the usual plain bearing parameters L/D, Λ, and whirl speed ratio ω3/(ω1 + ω2), the behavior of a grooved bearing also depends on four additional parameters: The groove angle β, the relative groove width α, the relative groove depth H0, and a compressibility number, Λs, which is based on the relative speed between the grooved and smooth members of the bearing. Results are presented showing bearing radial force and attitude angle as functions of β, α, H0, Λs, Λ, and whirl speed ratio.

scholarly journals CuO–Water Nanofluid Magnetohydrodynamic Natural Convection inside a Sinusoidal Annulus in Presence of Melting Heat Transfer

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
M. Sheikholeslami ◽  
R. Ellahi ◽  
C. Fetecau
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Melting Heat ◽  
Melting Heat Transfer ◽  
Limiting Case ◽  
Good Agreement ◽  
Melting Parameter

Impact of nanofluid natural convection due to magnetic field in existence of melting heat transfer is simulated using CVFEM in this research. KKL model is taken into account to obtain properties of CuO–H2O nanofluid. Roles of melting parameter (δ), CuO–H2O volume fraction (ϕ), Hartmann number (Ha), and Rayleigh (Ra) number are depicted in outputs. Results depict that temperature gradient improves with rise of Rayleigh number and melting parameter. Nusselt number detracts with rise of Ha. At the end, a comparison as a limiting case of the considered problem with the existing studies is made and found in good agreement.

Cylindrical Shells Under Line Load

1957 ◽  
Vol 24 (4) ◽  
pp. 553-558
Author(s):  
R. M. Cooper
Keyword(s):  
Cylindrical Shell ◽  
Radial Displacement ◽  
Circular Cylindrical Shell ◽  
Transverse Shear Deformation ◽  
System Of Equations ◽  
Principle Of Superposition ◽  
Line Load ◽  
Simply Supported ◽  
Shell Equations ◽  
Shell Geometry

Abstract The problem of a line load along a segment of a generator of a simply supported circular cylindrical shell is treated using shallow cylindrical shell equations which include the effect of transverse-shear deformation. The line load is first treated as a sinusoidally-varying edge load over the length of the shell, with boundary conditions prescribed along the loaded generator such that the continuity of the shell is maintained. The solution for the problem of a uniform line load over a segment of a generator is obtained from the preceding solution, using the principle of superposition. By means of a numerical example it is shown that the results predicted by the Donnell equations for the stresses are in excellent agreement with those obtained from the system of equations employed here. However, the radial displacement predicted by the Donnell equations is in error by as much as 20 per cent in the range of shell geometry considered.

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