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.

Stresses Around a Rib-Reinforced Elliptic Hole in a Circular Cylindrical Shell Under Tension

1977 ◽  
Vol 99 (1) ◽  
pp. 12-16
Author(s):  
S. I. Chou ◽  
Om P. Chaudhary
Keyword(s):  
Cylindrical Shell ◽  
Stress State ◽  
Stress Concentration ◽  
Cross Section ◽  
Circular Cylindrical Shell ◽  
Elliptic Hole ◽  
Axial Tension ◽  
Bending Stresses ◽  
Curvature Parameter ◽  
Moduli Of Elasticity

The stress state around a rib reinforced elliptic hole in a circular cylindrical shell under axial tension at its ends is determined by perturbation in terms of a curvature parameter and the eccentricity of the elliptic hole. The reinforcing rib is assumed to be rectangular in cross section, and has extensional, flexural and torsional rigidities. Nondimensional membrane stresses and bending stresses around the hole are given for different values of E1/E1 where E1 and E are moduli of elasticity of the rib and the shell respectively. It is shown that the reinforcing rib substantially reduces the stress concentration around the hole.

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 Around an Elliptic Hole in a Cylindrical Shell

1969 ◽  
Vol 36 (1) ◽  
pp. 39-46 ◽  
Author(s):  
M. V. V. Murthy
Keyword(s):  
Cylindrical Shell ◽  
Stress Distribution ◽  
Theoretical Analysis ◽  
Circular Cylindrical Shell ◽  
Elliptic Hole ◽  
Major Axis ◽  
Axial Tension ◽  
Method Of Solution ◽  
Bending Stresses ◽  
Curvature Parameter

A theoretical analysis is presented for the membrane and bending stresses around an elliptic hole in a long, thin, circular cylindrical shell with the major axis of the hole parallel to the axis of the shell. The analysis has been carried out for the case of axial tension. The method of solution involves a perturbation in a curvature parameter and the results obtained are valid, if the hole is small in size compared to the shell. Formulas, from which the complete stress distribution at the hole can be calculated, are presented.

Stress Concentration in a Stretched Cylindrical Shell With Two Elliptical Holes

1978 ◽  
Vol 45 (4) ◽  
pp. 839-844 ◽  
Author(s):  
E. B. Hansen
Keyword(s):  
Integral Equation ◽  
Cylindrical Shell ◽  
Stress Concentration ◽  
Circular Cylindrical Shell ◽  
Integral Equation Method ◽  
Equation Method ◽  
Center Line ◽  
Axial Tension ◽  
Bending Stresses ◽  
Elliptical Holes

The circumferential membrane and bending stresses at the edges of two identical elliptical holes in a circular cylindrical shell loaded by axial tension are computed by means of an integral equation method. Pairs of holes of which the center line is along a generator of the shell, along a directrix, or in a direction forming an angle of 45° with the generators are considered. For each of these hole configurations results are presented for a number of hole distances, hole sizes, and axis ratios.

Stresses around a small circular cutout in a cylindrical shell subjected to asymmetric bending

1977 ◽  
Vol 12 (1) ◽  
pp. 53-61 ◽  
Author(s):  
J Pattabiraman ◽  
V Ramamurti
Keyword(s):  
Cylindrical Shell ◽  
Stress Concentration ◽  
Shear Force ◽  
Circular Cylindrical Shell ◽  
Pressure Vessels ◽  
Ball Mills ◽  
Edge Conditions ◽  
Circular Cutout ◽  
Asymmetric Load ◽  
Asymmetric Bending

The problem of stress concentration around cutouts in shells is an important one in the design of nuclear pressure vessels, boilers, pressure hulls of submarines, aircraft structures, pipe connections and tube and ball mills used in chemical industries. By using the finite-difference scheme suggested by Budiansky, the solution to the problem of a cylindrical shell without a cutout, subjected to an asymmetric load, is derived first. Then, the negatives of the stress resultants and stress couples at a given radius obtained from the above solution are combined with a transverse shear force to form the edge conditions for a circular cylindrical shell containing a circular cutout of radius a. The desired results are finally obtained by superposing these two solutions.

The Influence of Loads Superposition, Deterioration Due to Cracks and Residual Stresses on the Strength of Tubular Junction

2017 ◽  
Vol 68 (6) ◽  
pp. 1267-1273
Author(s):  
Valeriu V. Jinescu ◽  
Angela Chelu ◽  
Gheorghe Zecheru ◽  
Alexandru Pupazescu ◽  
Teodor Sima ◽  
...  
Keyword(s):  
Stress Concentration ◽  
Residual Stresses ◽  
Bending Moment ◽  
Combined Loading ◽  
Torsional Moment ◽  
Calculation Methods ◽  
State Of Stress ◽  
Cracked Structures ◽  
Total Participation ◽  
Theoretical Results

In the paper the interaction of several loads like pressure, axial force, bending moment and torsional moment are analyzed, taking into account the deterioration due to cracks and the influence of residual stresses. A nonlinear, power law, of structure material is considered. General relationships for total participation of specific energies introduced in the structure by the loads, as well as for the critical participation have been proposed. On these bases: - a new strength calculation methods was developed; � strength of tubular cracked structures and of cracked tubular junction subjected to combined loading and strength were analyzed. Relationships for critical state have been proposed, based on dimensionless variables. These theoretical results fit with experimental date reported in literature. On the other side stress concentration coefficients were defined. Our one experiments onto a model of a pipe with two opposite nozzles have been achieved. Near one of the nozzles is a crack on the run pipe. Trough the experiments the state of stress have been obtained near the tubular junction, near the tip of the crack and far from the stress concentration points. On this basis the stress concentration coefficients were calculated.

Stress concentrations due to axial tension and bending of loaded axisymmetric projections

1983 ◽  
Vol 18 (1) ◽  
pp. 7-14 ◽  
Author(s):  
T H Hyde ◽  
B J Marsden
Keyword(s):  
Stress Concentration ◽  
Diameter Ratio ◽  
The Finite Element Method ◽  
Stress Concentrations ◽  
Axial Tension ◽  
Bending Loads ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
D Values ◽  
Existing Data

The finite element method has been used to investigate the behaviour of axisymmetric loaded projections (e.g., bolts) subjected to axial tension and bending. The results show that existing data for stepped shafts, which have the axial tension and bending loads applied remote from the region of the step, cannot be applied to loaded projections with the same geometry. For h/d (head thickness to shank diameter ratio) values greater than 0.66 and 0.41 for axial tension and bending, respectively, the stress concentration factors are independent of h/d, load position, and D/d (head diameter to shank diameter ratio) for D/d in the range 1.5 ≤ D/d ≤ 2.0. Smaller h/d values result in large increases in the stress concentration factors due to dishing of the head.

Anisotropic Loading Functions for Combined Stresses in the Plastic Range

1955 ◽  
Vol 22 (1) ◽  
pp. 77-85
Author(s):  
L. W. Hu ◽  
Joseph Marin
Keyword(s):  
Plastic Flow ◽  
Biaxial Tension ◽  
Strain History ◽  
Test Results ◽  
Axial Tension ◽  
State Of Stress ◽  
Loading Function ◽  
Combined Stresses ◽  
Shift Of Origin ◽  
Tubular Specimens

Abstract A loading function is a relation between combined stresses for which the beginning of plastic flow takes place. The loading function for a given material is different depending upon the initial plastic strains produced. That is, the initial stress or strain history influences the subsequent loading function. This paper gives the results of an experimental investigation to determine the validity of certain loading functions proposed for anisotropic materials. The study reported was conducted for an aluminum alloy 24S-T and the state of stress covered was biaxial tension. These stresses were produced in the usual way by subjecting thin-walled tubular specimens to axial tension and internal pressure. The test results showed that none of the existing loading functions is adequate for interpreting the plastic stress-strain relations obtained. Tests also were made to determine the change in the loading function with increase in plastic flow. It was found that the loading function did not remain symmetrical with respect to the original function, nor was the new loading function the same as the original except for a shift of origin. However, the test results support in a qualitative way the concept of the so-called “yield corner.”

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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