Rigid-Plastic Response of Floating Plates

1988 ◽  
Vol 32 (03) ◽  
pp. 168-176
Author(s):  
John Anastasiadis ◽  
Paul C. Xirouchakis
Keyword(s):  
Rigid Body ◽  
Yield Condition ◽  
Body Motion ◽  
Phase Iii ◽  
Flow Rule ◽  
Rigid Plastic ◽  
Flexural Response ◽  
Tresca Yield Condition ◽  
Perfectly Plastic ◽  
R Ratio

This paper presents the exact formulation and solution for the static flexural response of a rigid perfectly plastic freely floating plate subjected to lateral axisymmetric loading. The Tresca yield condition is adopted with the associated flow rule. The plate response is divided into three phases: Initially the plate moves downward into the foundation as a rigid body (Phase I). Subsequently the plate deforms in a conical mode in addition to the rigid body motion (Phase II). At a certain value of the load a hinge-circle forms which may move as the pressure increases further (Phase III). The nature of the solution during the third phase depends upon the parameter α = a/R (ratio of radius of loaded area to the plate radius). When α = αs≅ 0.46 the hinge-circle remains stationary under increasing load. For α < αs the hinge-circle shrinks, whereas for α > αs the hinge-circle expands with increasing pressure. The application of the present results to the problem of laterally loaded floating ice plates is discussed.

Transient Thermal Stresses in Elasto-Plastic Discs

1969 ◽  
Vol 11 (4) ◽  
pp. 384-391 ◽  
Author(s):  
H. Odenö
Keyword(s):  
Temperature Distribution ◽  
Thermal Stresses ◽  
Plastic Material ◽  
Yield Condition ◽  
Transient Temperature ◽  
Flow Rule ◽  
Axially Symmetric ◽  
Exterior Surface ◽  
Tresca Yield Condition ◽  
Perfectly Plastic

A thin circular disc of elastic-perfectly plastic material, subjected to an axially symmetric transient temperature distribution, is treated analytically. All material parameters are assumed to be independent of the temperature. Poisson's ratio is taken to be one-half. The Tresca yield condition with associated flow rule is employed. The temperature distribution is that which appears when the outer rim surface of the disc receives a rapid temperature increase and it is solved approximately by the collocation method. The analysis shows that under certain circumstances, plastic deformation will occur in a moving annular region. This region starts to develop at the exterior surface and moves inward, while changing its width. After a certain finite time its width shrinks to zero. Except for a residual constant state of strain, the strain field is then again elastic. An application to the method of separating the ring and the shaft in a shrink-fit is carried out numerically. The residual stresses in the ring are calculated.

The Elastic, Plastic Bending of a Simply Supported Plate

1961 ◽  
Vol 28 (3) ◽  
pp. 395-401 ◽  
Author(s):  
G. Eason
Keyword(s):  
Yield Condition ◽  
Constant Load ◽  
Flow Rule ◽  
Plastic Bending ◽  
Simply Supported ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises

In this paper the problem of the elastic, plastic bending of a circular plate which is simply supported at its edge and carries a constant load over a central circular area is considered. The von Mises yield condition and the associated flow rule are assumed and the material of the plate is assumed to be nonhardening, elastic, perfectly plastic, and compressible. Stress fields are obtained in all cases and a velocity field is presented for the case of point loading. Some numerical results are given comparing the results obtained here with those obtained when the Tresca yield condition is assumed.

On the plastic theory of plates

1957 ◽  
Vol 241 (1225) ◽  
pp. 153-179 ◽  
Keyword(s):  
Plastic Material ◽  
Yield Condition ◽  
Middle Surface ◽  
Transverse Load ◽  
Flow Rule ◽  
Transverse Shear Strain ◽  
Elastic Plates ◽  
Field Equations ◽  
Rigid Plastic ◽  
Tresca Yield Condition

This paper presents a theory of the small deformations of a thin uniform plate under transverse load. The plate is made of non-hardening rigid-plastic material obeying the Tresca yield condition and associated flow rule. The basic assumptions are similar to those made in the conventional engineering theory of thin elastic plates, and the effects of transverse shear strain and rotatory inertia are neglected. Hitherto, the theory has been developed only under conditions of circular symmetry, and the object of the present paper is to remove this restriction. Attention is confined here to the derivation and classification of the field equations. The field equations involve the stress moments and the middle-surface curvature rates as the associated generalized stresses and strain rates. These equations are first referred to Cartesian co-ordinates. The condition of isotropy requires the coincidence of the directions of principal stress moment and curvature rate. One of these two families of directions is characteristic for the equations appropriate to certain plastic régimes. The field equations are therefore referred to curvilinear co-ordinates taken along these directions. A detailed study is made of discontinuities in the field quantities. The field equations are either parabolic or elliptic for the principal plastic régimes.

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.

Finite Elastic-Plastic Expansion of a Cylindrical Tube

1973 ◽  
Vol 2 (4) ◽  
pp. 216-222
Author(s):  
B. Slevinsky ◽  
J. B. Haddow
Keyword(s):  
Plastic Deformation ◽  
Yield Condition ◽  
Cylindrical Tube ◽  
Flow Rule ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
End Conditions ◽  
Cylindrical Tubes ◽  
Limiting Case ◽  
Plastic Flow Rule

A numerical method for the analysis of the isothermal elastic-plastic expansion, by internal pressure, of cylindrical tubes with various end conditions is presented. The Tresca yield condition and associated plastic flow rule are assumed and both non-hardening and work-hardening tubes are considered with account being taken of finite plastic deformation. Tubes which undergo further plastic deformation on unloading are also considered. Expansion of a cylindrical cavity from zero radius in an infinite medium is considered as a limiting case.

scholarly journals Rigid plastic plates at large deformations

1985 ◽  
Vol 7 (3) ◽  
pp. 18-23
Author(s):  
Vu Van The
Keyword(s):  
Large Deformations ◽  
Plastic Material ◽  
Plastic Hinge ◽  
Yield Condition ◽  
Rectangular Plates ◽  
Rigid Plastic ◽  
Hinge Line ◽  
Perfectly Plastic ◽  
Relationship Of ◽  
Line Patterns

The method developed in [8] is applied herein in order to obtain estimations of the load-deflection relationship of the hinge supported rectangular plates acted on by a uniformly distributed loading. The plate is made from rigid perfectly plastic material which yields according to the square yield condition and maximum normal yield condition. the plastic hinge line patterns shown  in figs. 1. 2. are chosen. The obtained results are presented in figs. 4, 5, 6, 8.

scholarly journals The yield condition strongly influences the formation of Dugdale plastic strips ahead of crack tips under tensile plane stress loading conditions

2012 ◽  
Vol 21 (1-2) ◽  
pp. 37-39
Author(s):  
David J. Unger
Keyword(s):  
Plane Stress ◽  
Plastic Material ◽  
Yield Condition ◽  
Loading Conditions ◽  
Element Analysis ◽  
Plastic Strip ◽  
Tresca Yield Condition ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises

AbstractA finite element analysis indicates a good correlation between the Dugdale plastic strip model and a linear elastic/perfectly plastic material under plane stress loading conditions for a flow theory of plasticity based on the Tresca yield condition. A similar analysis under the von Mises yield condition reveals no plastic strip formation.

The Influence of Blast Characteristics on the Final Deformation of Circular Cylindrical Shells

1956 ◽  
Vol 23 (4) ◽  
pp. 617-624
Author(s):  
P. G. Hodge
Keyword(s):  
Circular Cylindrical Shell ◽  
Plastic Material ◽  
Practical Importance ◽  
Yield Condition ◽  
Flow Rule ◽  
Analytic Approximation ◽  
Rigid Plastic ◽  
End Effects ◽  
Maximum Deformation ◽  
Method Of Solution

Abstract The final maximum deformation of a reinforced circular cylindrical shell caused by a briefly applied, intense loading is considered. The maximum deformation is obtained in a form which requires a double quadrature of the pressure where the limits of the integration are determined from side conditions. Attempts are made to find a simple analytic approximation, but the attempts are unsuccessful for loads of practical importance. A straightforward graphical-numerical method of solution is devised. Several examples are considered in support of the conclusions. The shell is assumed to be infinitely long, so that end effects may be neglected. The load is assumed to be applied to the entire shell simultaneously. The shell is assumed a perfect cylinder, and the reinforcements are taken as rigid. Finally, the shell is assumed to be made of an ideal rigid-plastic material which satisfies a certain simplified yield condition and the associated flow rule.

On the Use of Singular Yield Conditions and Associated Flow Rules

1953 ◽  
Vol 20 (3) ◽  
pp. 317-320
Author(s):  
William Prager
Keyword(s):  
Plastic Deformation ◽  
Closed Form ◽  
Circular Hole ◽  
Work Hardening ◽  
Yield Condition ◽  
Flow Rule ◽  
System Of Equations ◽  
Hardening Material ◽  
Perfectly Plastic ◽  
Yield Conditions

Abstract It is well known that the use of Tresca’s yield condition frequently leads to a simpler system of equations for the stresses in a plastic solid than the use of the yield condition of Mises. However, in most cases where Tresca’s yield condition has been used, the flow rule associated with the Mises condition has been retained. Following Koiter, it is shown that further simplification results from the use of the flow rule associated with the Tresca condition. The reason for this is discussed in connection with two examples concerning the finite enlargement of a circular hole in an infinite sheet of perfectly plastic or work-hardening material. The second example is probably the first nontrivial case in which a problem of finite plastic deformation of a work-hardening material has been treated in closed form by the use of incremental stress-strain relations.

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