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.

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.

Elastic-Plastic Ring-Loaded Cylindrical Shells

1988 ◽  
Vol 55 (4) ◽  
pp. 761-766 ◽  
Author(s):  
Gregory N. Brooks
Keyword(s):  
Axisymmetric Problem ◽  
Shell Theory ◽  
Complete Solution ◽  
Yield Condition ◽  
Plastic Ring ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Small Deflection ◽  
Principal Directions ◽  
Long Cylindrical Shell

The elastic-plastic solution for an infinitely long cylindrical shell with an axisymmetric ring load is presented. Except for the material nonlinearity, the standard assumptions of small deflection shell theory were made. Because the principal directions are known for the axisymmetric problem, the Tresca yield condition wasused. This made it possible to obtain closed-form expressions for the elastic-plastic, moment-curvature relations, greatly simplfying the computational task. The actual stress distribution through the thickness was used, making these relations exact. Yielding was contained near the load. Thus, for the analysis the cylinder was divided along its axis into elastic-plastic and purely elastic regions. Solutions were obtained for each region which were then matched at their intersection to give the complete solution. All results are given in dimensionless form so that they may be applied to any shell.

Plastic Analysis of Rib-Reinforced Cylindrical Shells

1967 ◽  
Vol 34 (1) ◽  
pp. 37-42 ◽  
Author(s):  
Andre Biron ◽  
Antoni Sawczuk
Keyword(s):  
Cylindrical Shell ◽  
Yield Surface ◽  
Axial Load ◽  
Constant Pressure ◽  
Yield Condition ◽  
Mapping Method ◽  
Sample Problem ◽  
Strain Mapping ◽  
Tresca Yield Condition ◽  
Plastic Analysis

Using the strain-mapping method for the Tresca yield condition, the yield surface is derived for a cylindrical shell with a wall reinforced by longitudinal ribs on one side. Results are given for the case where the axial load is zero. As a sample problem utilizing this surface and as an appropriate method for solving nonlinear equations, the solution of a cantilever shell under constant pressure is obtained.

The Stability of an Axially–Loaded Continuous Beam

1955 ◽  
Vol 59 (535) ◽  
pp. 506-509
Author(s):  
A. M. Dobson
Keyword(s):  
Axial Load ◽  
Classical Method ◽  
Complete Solution ◽  
Critical Value ◽  
Continuous Beam ◽  
Independent Variables ◽  
A Value ◽  
Method Of Solution ◽  
Axially Loaded ◽  
The Stability

The Classical method of solution of the stability of an axially–loaded continuous beam is by means of the three moments equation, using the Berry Functions, which are functions of the axial load. As the axial load approaches a value equal to the critical value for a pin–jointed beam, the Berry Functions tend to infinity, and the use of the three moments equations —(i. e. treating the end fixing moments as the independent variables)—leads to certain difficulties in the complete solution of the problem.The major difficulty lies in the question of stability. The critical value is determined by the vanishing of the determinant of the coefficients of the fixing moments in the three moments equations. This value could be found by plotting the determinant against end load (c. f. Pippard and Pritchard). However, in a problem involving a large number of bays, the calculation necessary to do this is likely to be considerable, for there may be many branches to the curve.

scholarly journals Generalized Plane Strain Elasticity Problems

1995 ◽  
Author(s):  
A.H.-D. Cheng ◽  
J.J. Rencis ◽  
Y. Abousleiman
Keyword(s):  
Plane Strain ◽  
Elasticity Problems ◽  
Generalized Plane Strain

Dynamic Plastic Response of Cylindrical Shells Under Gaussian Impulse

1980 ◽  
Vol 24 (01) ◽  
pp. 24-30
Author(s):  
S. Anantha Ramu ◽  
K. J. Iyengar
Keyword(s):  
Cylindrical Shells ◽  
Yield Condition ◽  
Longitudinal Axis ◽  
Plastic Behavior ◽  
Plastic Response ◽  
Marine Structures ◽  
Impulsive Load ◽  
Tresca Yield Condition ◽  
Impulsive Loads

The determination of the inelastic response of cylindrical shells under general impulsive loads is of relevance to marine structures such as submarines, in analyzing their slamming damages. The present study is concerned with the plastic response of a simply supported cylindrical shell under a general axisymmetric impulsive load. The impulsive load is assumed to impart an axisymmetric velocity to the shell, with a Gaussian distribution along the longitudinal axis of the shell. A simplified Tresca yield condition is used. The shell response is determined for various forms of impulses ranging from a concentrated impulse to a uniform impulse over the entire length of the shell. Conclusions about the influence of geometry of the shell and the spatial distribution of impulse on the plastic behavior of cylindrical shells are presented.

Stresses and Displacements in an Elastic-Plastic Wedge

1957 ◽  
Vol 24 (1) ◽  
pp. 98-104
Author(s):  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Isotropic Material ◽  
Complete Solution ◽  
Normal Pressure ◽  
Stress Strain ◽  
Included Angle ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Domain ◽  
Elastic Perfectly Plastic

Abstract An elastic, perfectly plastic wedge of an incompressible isotropic material in the state of plane strain is considered, where the stress-strain relations of Prandtl-Reuss are employed in the plastic domain. For a wedge (with an included angle β) subjected to a uniform normal pressure on one boundary, the complete solution is obtained which is valid in the range 0 < β < π/2; this latter limitation is due to the character of the initial yield which depends on the magnitude of β. Numerical results for stresses and displacements are given in one case (β = π/4) for various positions of the elastic-plastic boundary.

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