Yield Conditions for Rotationally Symmetric Shells Under Axisymmetric Loading

1960 ◽  
Vol 27 (2) ◽  
pp. 323-331 ◽  
Author(s):  
P. G. Hodge
Keyword(s):  
Yield Surface ◽  
Yield Condition ◽  
Uniform Pressure ◽  
Stress Space ◽  
Reasonable Accuracy ◽  
Spherical Cap ◽  
Axisymmetric Loading ◽  
Tresca Yield Condition ◽  
Rotationally Symmetric ◽  
Yield Conditions

The yield condition for a rotationally symmetric shell may be represented as a surface in a four-dimensional stress space. The exact yield surface according to the Tresca yield condition is compared with various approximations. A new approximation is suggested which combines the advantages of mathematical simplicity and reasonable accuracy. The theory is illustrated with reference to a spherical cap under uniform pressure.

Crushing analysis of rotationally symmetric plastic shells

1982 ◽  
Vol 17 (4) ◽  
pp. 229-236 ◽  
Author(s):  
J G De Oliveira ◽  
T Wierzbicki
Keyword(s):  
Spherical Shell ◽  
Closed Form ◽  
Conical Shell ◽  
Point Load ◽  
Large Deflections ◽  
Uniform Pressure ◽  
Spherical Cap ◽  
Closed Form Solutions ◽  
General Methodology ◽  
Rotationally Symmetric

The crushing analysis of rotationally symmetric plastic shells undergoing very large deflections is presented. A general methodology is developed and simple closed-form solutions are derived for the case of a conical shell, a spherical shell under point load, a spherical shell crushed between rigid plates and under boss loading, and a spherical cap under external uniform pressure.

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 Significance of the Concentrated Load in the Limit Analysis of Conical Shells

1966 ◽  
Vol 33 (1) ◽  
pp. 93-101 ◽  
Author(s):  
John A. DeRuntz ◽  
P. G. Hodge
Keyword(s):  
Yield Condition ◽  
Point Load ◽  
Concentrated Load ◽  
Shallow Shells ◽  
Conical Shells ◽  
Simply Supported ◽  
Tresca Yield Condition ◽  
Wide Range ◽  
Limiting Case ◽  
Yield Conditions

The yield point load of a simply supported conical sandwich shell loaded at its vertex through a rigid central boss is found for a material obeying the Tresca yield condition. Exact solutions are found for a wide range of shell configurations ranging from thick shallow cones to thin steep ones, including large and small boss sizes. The results are compared with those for the limiting case of zero boss radius corresponding to a complete conical shell loaded with a concentrated load at its vertex. It is found that for thick shallow shells the concentrated-load solution is a good approximation to the solution for realistically small boss sizes, but that for thin and/or steep shells the agreement is so poor as to make the concentrated-load solution meaningless. It is shown that such behavior also can be expected for shells obeying more realistic yield conditions.

Analysis of Plastic Shallow Conical Shells

1963 ◽  
Vol 30 (2) ◽  
pp. 199-209 ◽  
Author(s):  
R. H. Lance ◽  
E. T. Onat
Keyword(s):  
Yield Surface ◽  
Digital Computer ◽  
Yield Condition ◽  
Shell Material ◽  
Rigid Plastic ◽  
Conical Shells ◽  
Simply Supported ◽  
State Of Stress ◽  
Load Intensity ◽  
Yield Conditions

The paper is concerned with simply supported shallow conical shells loaded through a central boss. The shell material is rigid-plastic and the relevant stress resultants are subject to a nonlinear yield condition. The critical load intensity at which the shell will begin to deform and the associated fields of stress resultants and plastic flow are to be determined. For this purpose, a problem concerned exclusively with stress resultants is formulated by using the equation of stress compatibility. The resulting nonlinear problem is solved, with the help of a digital computer, in cases where the yield-point state of stress is controlled, over the pertinent intervals covering the entire shell, by three distinct yield conditions, each corresponding to a given face of the appropriate four-dimensional nonlinear yield surface.

An Approximate Analysis of Circular Plates With Variable Thickness

1982 ◽  
Vol 104 (3) ◽  
pp. 533-535
Author(s):  
A. K. Naghdi
Keyword(s):  
Variable Thickness ◽  
Simple Technique ◽  
Bending Moment ◽  
The Other ◽  
Uniform Pressure ◽  
Approximate Analysis ◽  
Circular Plates ◽  
Numerical Examples ◽  
Classic Theory ◽  
Rotationally Symmetric

Based on classic theory of beams and certain modifications, a simple technique is derived in order to obtain an approximate value of the maximum bending moment in a rotationally symmetric circular plate with a variable thickness. It is assumed that one of the two concentric boundaries of the plate is clamped, and the other is free. Numerical examples for both cases of constant and variable thickness plates subject to uniform pressure or rim line loading are presented.

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.

Thermodynamic-Based Modified Cam-Clay Constitutive Model Considering the Effect of Fabric

2011 ◽  
Vol 71-78 ◽  
pp. 1073-1078
Author(s):  
Xiao Xia Guo ◽  
Bo Ya Zhao
Keyword(s):  
Constitutive Model ◽  
Granular Materials ◽  
Yield Surface ◽  
True Stress ◽  
Stress Space ◽  
Volume Strain ◽  
Hardening Rule ◽  
Modified Cam Clay ◽  
Fabric Tensors ◽  
Cam Clay

In order to construct a constitutive model taking into the effect of both the fabric tensors and their evolution modes, this paper links modern ideas of thermomechanics opinion to the theory of fabric tensors. The anisotropic dissipation incremental function of modified Cam-clay constitutive model considering the effect of fabric characteristic can be obtained by establishing the relation between microstructure and plastic volume strain. After discussing the yield surfaces in the dissipative and the true stress space from the viewpoint of the evolution mode of the fabric tensors, the results indicate that the slope of the normal consolidation line and the critical state line will be governed by changes of void fabric. The model successfully captures most salient behaviors of granular materials related to fabric issues. In the dissipative stress space, the void of granular materials can rearrange and show more anisotropic. In the true stress space, fabric not only affects the deflection of the yield surface, but also affects the hardening rule.

Limit Analysis for Combined Edge and Pressure Loading on a Cylindrical Shell

1971 ◽  
Vol 93 (4) ◽  
pp. 998-1006
Author(s):  
H. S. Ho ◽  
D. P. Updike
Keyword(s):  
Cylindrical Shell ◽  
Velocity Field ◽  
Axial Force ◽  
Shear Force ◽  
Circular Cylindrical Shell ◽  
Yield Condition ◽  
External Pressure ◽  
Tresca Yield Condition ◽  
Stress States ◽  
Range Of Values

Equations describing the stress field and velocity field occurring in a circular cylindrical shell at plastic collapse are derived corresponding to stress states lying on each face of a yield surface for a uniform shell of material obeying the Tresca yield condition. They are then applied to the case of a shell under combined axisymmetric loadings (moment, shear force, and axial force) at one end and uniform internal or external pressure on the lateral surface. For a sufficiently long shell, complete solutions are obtained for a fixed far end, and for a certain range of values of axial force and pressure, they are obtained for a free far end. All the solutions are represented by either closed form or by quadratures. It is shown that in many cases the radial velocity field is proportional to the shear force.

A Theory of Multiaxial Anisotropic Viscoplasticity

1981 ◽  
Vol 48 (2) ◽  
pp. 276-284 ◽  
Author(s):  
M. A. Eisenberg ◽  
C.-F. Yen
Keyword(s):  
Yield Surface ◽  
Stress Space ◽  
Anisotropic Hardening ◽  
Surface Distortion ◽  
Induced Changes ◽  
Yield Surface Distortion

A theory of anisotropic viscoplasticity is developed. It is compared with and shown to reduce to existing theories under appropriate restrictions. The theory accommodates anisotropic hardening laws which, by means of Lagrangian mappings in stress space, incorporate experimentally observed yield surface distortion as well as kinematic and isotropic flow-induced changes. The theory is applied to the prediction of flow surfaces in tension-torsion space.

A Short Review of Shape Memory Alloys Thermomechanical Models

2008 ◽  
Vol 138 ◽  
pp. 355-366
Author(s):  
Christian Lexcellent ◽  
Elie Gibeau
Keyword(s):  
Phase Transformation ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Yield Surface ◽  
Short Review ◽  
Stress Space ◽  
Macroscopic Scale ◽  
Phenomenological Modeling ◽  
Strain Space

At first, some comments are made concerning the capacity of prediction of the microstructure for shape memory alloys by the Crystallographical Theory of Martensite. Secondly, the basic foundations of the phenomenological modeling of shape memory alloys behavior at the macroscopic scale are given. A special attention is devoted to the yield surface of phase transformation initiation in the stress space and its convex dual: the set of effective transformation strains in the strain space.

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