Stress Concentration in Nonlinear Creep of a Simple Shell

1966 ◽  
Vol 33 (2) ◽  
pp. 322-326 ◽  
Author(s):  
C. R. Calladine
Keyword(s):  
Cylindrical Shell ◽  
Stress Concentration ◽  
Strain Rate ◽  
Circular Cylindrical Shell ◽  
Bending Moment ◽  
Elastic Problem ◽  
Nonlinear Creep ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Plastic Analysis

A long, thin circular cylindrical shell is loaded at one edge by symmetrical radial shear Qx and bending moment Mx. (No interior pressure.) The shell is made of material which under applied stress creeps with a strain rate which is proportional to the rth power of the stress. Previous results are used to derive, approximately, the greatest stress in the shell for any Qx, Mx, and r. It is shown that for any load the greatest stress decreases as r increases, and is approximately a linear function of 1/r. The case r = 1 is exactly analogous to a linear elastic problem, and the case r → = ∞ corresponds exactly to a perfectly plastic problem. Results for any exponent r may thus be found approximately by simple interpolation between results obtained in linearelastic analysis and perfectly plastic analysis.

A Theoretical Study of the Elastic Behavior of Two Normally Intersecting Cylindrical Shells

1969 ◽  
Vol 91 (3) ◽  
pp. 563-572 ◽  
Author(s):  
J. W. Hansberry ◽  
N. Jones
Keyword(s):  
Cylindrical Shell ◽  
Theoretical Study ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Bending Moment ◽  
Pressure Vessels ◽  
Numerical Results ◽  
Elastic Behavior ◽  
Cylinder Diameter ◽  
Plane Transverse

A theoretical study has been made into the elastic behavior of a joint formed by the normal intersection of a right circular cylindrical shell with another of larger diameter. The wall of the larger cylinder is assumed to remain open inside the joint in order to give an arrangement which is encountered frequently in pressure vessels or pipeline intersections. An external bending moment which acts in the plane of the joint is applied to the nozzle cylinder and is equilibriated by moments of half this magnitude applied to either end of the parent cylinder. A solution for this loading has been obtained by assuming antisymmetric distributions of certain stresses across a plane transverse to the joint. The analysis presented is believed to be valid for nozzle to cylinder diameter ratios of less than 1:3. Numerical results are given for a number of cases having radius ratios of 1:10 and 1:4.

Stress Concentration in a Stretched Cylindrical Shell With Two Equal Circular Holes

1975 ◽  
Vol 42 (1) ◽  
pp. 105-109 ◽  
Author(s):  
P. Seide ◽  
A. S. Hafiz
Keyword(s):  
Cylindrical Shell ◽  
Stress Concentration ◽  
Stress Distribution ◽  
Circular Cylindrical Shell ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Wide Range ◽  
Circular Holes ◽  
Limiting Case ◽  
Infinite Set

In this investigation, the stress distribution due to uniaxial tension of an infinitely long, thin, circular cylindrical shell with two equal small circular holes located along a generator is obtained. The problem is solved by the superposition of solutions previously obtained for a cylinder with a single circular hole. The satisfaction of boundary conditions on the free surfaces of the holes, together with uniqueness and overall equilibrium conditions, yields an infinite set of linear algebraic equations involving Hankel and Bessel functions of complex argument. The stress distribution along the boundaries of the holes and the interior of the shell is investigated. In particular, the value of the maximum stress is calculated for a wide range of parameters, including the limiting case in which the holes almost touch and the limiting case in which the radius of the cylinder becomes very large. As is the case for a flat plate, the stress-concentration factor is reduced by the presence of another hole.

Uniaxial Constitutive Equation of Ice From Beam Tests

1985 ◽  
Vol 107 (4) ◽  
pp. 511-515 ◽  
Author(s):  
P. C. Xirouchakis ◽  
T. Wierzbicki
Keyword(s):  
Strain Rate ◽  
Direct Method ◽  
Elastic Beam ◽  
Bending Moment ◽  
Uniaxial Stress ◽  
Analytical Technique ◽  
Linear Elastic ◽  
Beam Depth ◽  
Tension And Compression ◽  
Extensional Strain

A method is proposed to obtain ice uniaxial stress, strain, strain-rate relations from beam tests. The basic advantage of the proposed analytical technique is that it is a direct method of reducing beam test data. So, no assumption is made with regard to the ice constitutive behavior. The proposed method is an extension of Gillis and Kelly’s procedure to account for different ice response in tension and compression. It is also an extension of the procedure reported by Mayville and Finnie to account for ice response dependence on strain rate. Furthermore, it is shown that the expressions presented by Mayville and Finnie are only valid when the bending moment, with respect to the zero strain axis, is assumed independent of the centroidal extensional strain. A simple example of a linear elastic beam with a Young’s modulus that varies linearly with the beam depth is worked out to show that these earlier given expressions are not applicable in that case.

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.

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