An Analysis of the Yielded Compound Cylinder

1961 ◽  
Vol 83 (1) ◽  
pp. 43-47 ◽  
Author(s):  
S. J. Becker
Keyword(s):  
Plane Strain ◽  
Elastic Material ◽  
Plastic Range ◽  
Compound Cylinder ◽  
Concentric Cylinders

An analysis is made of the partially plastic range, restricted to plane strain, of the compound cylinder, made by shrinking together many concentric cylinders. An example is given using, for ease of illustration, a cylinder designed to yield simultaneously in all its components. A comparison is made between a structure with a compressible elastic material and one with an incompressible elastic material. Finally, an important auto-frettage formula, Equation (10), is developed.

Strain Hardening in the Yielded Compound Cylinder

1962 ◽  
Vol 84 (2) ◽  
pp. 220-224
Author(s):  
S. J. Becker ◽  
H. Kraus
Keyword(s):  
Plastic Deformation ◽  
Strain Hardening ◽  
Plane Strain ◽  
Yield Condition ◽  
Plastic Range ◽  
Linear Strain ◽  
Compound Cylinder ◽  
Small Strains ◽  
Tresca Yield Condition ◽  
Generalized Plane Strain

The theory of a previous paper which was designed for nonhardening plastic deformation of simple and compound cylinders in axisymmetric generalized plane strain is extended to include linear strain hardening in the plastic range. The method, which is limited to small strains, uses a modified Tresca yield condition and assumes incompressibility for both the plastic and the elastic ranges.

The Stress Field Due to a Line Load Acting on a Half Space of a Power-Law Hardening Material (A Comparison Between Plane Strain and Plane Stress)

1973 ◽  
Vol 40 (1) ◽  
pp. 288-290 ◽  
Author(s):  
C. Atkinson
Keyword(s):  
Exact Solution ◽  
Stress Field ◽  
Plane Strain ◽  
Half Space ◽  
Power Law ◽  
Elastic Material ◽  
Plane Stress ◽  
Strain Fields ◽  
Line Load ◽  
Hardening Material

The exact solution is given for a line load acting on a half space of a power-law elastic material under conditions of plane stress. This solution is compared with the corresponding solution under plane-strain conditions; see Aruliunian [1]. A marked difference is found between the plane-stress and plane-strain fields for different values of the hardening exponent.

The Yielded Compound Cylinder in Generalized Plane Strain

1961 ◽  
Vol 83 (4) ◽  
pp. 441-448 ◽  
Author(s):  
S. J. Becker
Keyword(s):  
Plane Strain ◽  
Axial Load ◽  
Axial Strain ◽  
Complete Solution ◽  
Yield Condition ◽  
Compound Cylinder ◽  
Elastic Zone ◽  
Tresca Yield Condition ◽  
Internal Pressures ◽  
Generalized Plane Strain

The theory of a previous paper [1], which was designed for plane strain of a compound cylinder, is extended to generalized plane strain, where the axial strain is a constant nonzero value for every radius and depends only on the external and internal pressures and any extraneous axial load. The method is limited to incompressible elastic material and is found to be completely solvable only if an elastic zone exists in each component. The assumed Tresca yield condition is verified in the process of obtaining the complete solution.

The Theory of the Ideal Design of a Compound Vessel

1960 ◽  
Vol 82 (2) ◽  
pp. 136-142 ◽  
Author(s):  
S. J. Becker ◽  
L. Mollick
Keyword(s):  
General Theory ◽  
Young’S Modulus ◽  
Elastic Moduli ◽  
Young's Modulus ◽  
Compound Cylinder ◽  
Concentric Cylinders ◽  
Elastic Design ◽  
The Ideal

A general theory for the elastic design of a compound cylinder made by shrinking together many concentric cylinders is described. Each cylinder may have entirely different strength and operate at any temperature under any pressure, internal or external. The only assumptions, in addition to the usual homogeneity and isotropy in each member, are that they have the same Young’s modulus, although even different elastic moduli could be accommodated, and that they are not so thin that stability becomes a problem.

Plane strain rotation moduli for soft elastic blocks

1979 ◽  
Vol 14 (1) ◽  
pp. 17-21 ◽  
Author(s):  
P B Lindley
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Plane Strain ◽  
Elastic Material ◽  
Analysis Data ◽  
Simple Relation ◽  
Theoretical Solution ◽  
The Other ◽  
Element Analysis ◽  
Poisson's Ratios

Making assumptions similar to these used to obtain compression moduli, a simple relation is developed for the plane strain rotation moduli for blocks of soft elastic material bonded to rigid end plates. The deformation arises when one plate rotates relative to the other plane about an axis along the centre of its width. The approximate theoretical solution compares well with finite-element analysis data for materials with Poisson's ratios of 0.333, 0.483 87 and 0.499 83 and blocks having width-to-thickness ratios between 0.25 and 64.

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