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.

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.

Impulsive Loading of a Simply Supported Circular Rigid Plastic Plate

1968 ◽  
Vol 35 (1) ◽  
pp. 59-65 ◽  
Author(s):  
Norman Jones
Keyword(s):  
Yield Condition ◽  
Impulsive Loading ◽  
Bending Moments ◽  
Circular Plates ◽  
Governing Equations ◽  
Rigid Plastic ◽  
Static Loads ◽  
Simply Supported ◽  
Experimental Values ◽  
Theoretical Procedure

It is clear from a survey of literature on the dynamic deformation of rigid-plastic plates that most work has been focused on plates in which either membrane forces or bending moments alone are considered important, while the combined effect of membrane forces and bending moments on the behavior of plates under static loads and beams under dynamic loads is fairly well established. This paper, therefore, is concerned with the behavior of circular plates loaded dynamically and with deflections in the range where both bending moments and membrane forces are important. A general theoretical procedure is developed from the equations for large deflections of plates and a simplified yield condition due to Hodge. The results obtained when solving the governing equations for the particular case of a simply supported circular plate loaded with a uniform impulsive velocity are found to compare favorably with the corresponding experimental values recorded by Florence.

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.

scholarly journals Plastic response of conical shells with stiffeners to blast loading

2020 ◽  
Vol 24 (1) ◽  
pp. 5-18
Author(s):  
Jaan Lellep ◽  
Ella Puman
Keyword(s):  
Time Moment ◽  
Yield Condition ◽  
Blast Loading ◽  
Theoretical Method ◽  
Initial Time ◽  
Conical Shells ◽  
Initial Time Moment ◽  
Circular Conical Shells ◽  
Load Intensity ◽  
The Impact

The inelastic response of circular conical shells to the blast loading is studied. The impact loading is applied at the initial time moment and it is removed at a certain instant of time. The load intensity depends of the coordinate of the shell. The material of the shell is a perfect plastic one obeying the Johansen yield condition and the associated flow law. It is assumed that the frustum of the cone is furnished with ring stiffeners made of the same material. A theoretical method for the evaluation of the stress strain state of the shell and for determination of maximal residual deflections is developed.

Dynamic Response of Blast-Loaded Stiffened Plates by Rigid-Plastic Analysis

2010 ◽  
Author(s):  
Ping Yang ◽  
Ying Peng
Keyword(s):  
Dynamic Response ◽  
Yield Curve ◽  
Bending Moment ◽  
Stiffened Plates ◽  
Flow Rule ◽  
Beam Model ◽  
Rigid Plastic ◽  
Perfectly Plastic ◽  
Load Intensity ◽  
Plastic Flow Rule

The dynamic response of one-way stiffened plates with clamped edges subjected to uniformly distributed blast-induced shock loading is theoretically investigated using a singly symmetric beam model. The beam model is based on the rigid-perfectly plastic assumption. The bending moment-axial force capacity interaction relation or yield curve for singly symmetric cross-section is derived and explicitly presented. The deflection condition that a plastic string response must satisfy is determined by the linearized interaction curve and associated plastic flow rule. Moreover, the possible motion mechanisms of the beam are discussed under different load intensity. Finally the dynamic response of a one-way stiffened plate is calculated theoretically and numerically. Good agreements are obtained between the presented theoretical results and those from numerical calculations of the FEM software ANSYS and ABAQUS/Explicit. It is concluded that the basic assumptions and approximations for simplifying calculations are reasonable and the beam model in theoretical analysis is adoptable. The example also shows that an arbitrary blast load can be replaced equivalently by a rectangular type pulse.

The Influence of Large Deflections on the Behavior of Rigid-Plastic Cylindrical Shells Loaded Impulsively

1970 ◽  
Vol 37 (2) ◽  
pp. 416-425 ◽  
Author(s):  
Norman Jones
Keyword(s):  
Cylindrical Shells ◽  
Dynamic Loads ◽  
Large Deflections ◽  
Finite Deflections ◽  
Shell Material ◽  
Governing Equations ◽  
Rigid Plastic ◽  
Perfectly Plastic ◽  
Dynamic Analyses ◽  
Circular Cylindrical Shells

A theoretical investigation is herein undertaken in order to examine the response of circular cylindrical shells subjected to dynamic loads of an intensity sufficient to cause large permanent deformations. The shell material is assumed to be rigid, perfectly plastic and the influence of finite deflections is retained in the governing equations. It emerges clearly from the study that geometry changes influence markedly the shell behavior even for quite small deflections and, therefore, they should be retained in any dynamic analyses of cylindrical shells with axial restraints.

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