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 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.

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.

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.

Interaction of Pressure, End Load, and Twisting Moment for a Rigid-Plastic Circular Tube

1963 ◽  
Vol 30 (3) ◽  
pp. 396-400 ◽  
Author(s):  
Joseph E. Panarelli ◽  
Philip G. Hodge
Keyword(s):  
Circular Cylinder ◽  
Shell Theory ◽  
Circular Tube ◽  
Plastic Material ◽  
Rigid Plastic ◽  
End Effects ◽  
Perfectly Plastic ◽  
Special Cases ◽  
Interaction Surface

A thick-walled circular cylinder acted on by pressure, axial end load, and twisting moment is analyzed under the assumption that end effects are negligible. The locus of all load points (interaction surface) for which unaccelerated flow of a perfectly plastic material can occur is found parametrically. Certain special cases are considered and the results compared with those of shell theory.

Effects of a Temperature Cycle on an Elastic-Plastic Shrink Fit with Solid Inclusion

2000 ◽  
Vol 16 (1) ◽  
pp. 23-30 ◽  
Author(s):  
Werner Mack ◽  
Manfred Plöchl ◽  
Udo Gamer
Keyword(s):  
Stress Distribution ◽  
Plastic Material ◽  
Yield Condition ◽  
Material Behavior ◽  
Temperature Cycle ◽  
Solid Inclusion ◽  
Flow Rule ◽  
Elastic Plastic ◽  
Elastic Plastic Material ◽  
Shrink Fit

ABSTRACTThe stress distribution in a shrink fit with solid inclusion subject to homogeneous heating and subsequent cooling is investigated. It is presumed that both components are in a state of plane stress and exhibit the same elastic-plastic material behavior. Based on Tresca's yield condition and the associated flow rule, the modification of the stress distribution is studied analytically. In particular, the reduction of the interface pressure — and therefore of the transferable moment — caused by the occurrence of plastic deformation is discussed, and the criteria for the avoidance of yielding of the inclusion or full plasticization of the hub are given.

scholarly journals A new displacement bound technique for rigid plastic continua subjectet to strong dynamic loading at large deflections II.

1987 ◽  
Vol 9 (3) ◽  
pp. 23-30
Author(s):  
Vu Van The ◽  
Tran Ba Tinh
Keyword(s):  
Space Variable ◽  
Shape Function ◽  
Plastic Material ◽  
Yield Condition ◽  
Time Function ◽  
Rigid Plastic ◽  
Perfectly Plastic ◽  
Previous Solution ◽  
Admissible Displacement ◽  
Strong Dynamic

The method developed in [ 1] is applied herein in order to obtain lower hound to large displacements of the hinge supported circular plate acted on by impulsively, uniformly distributed loading. The plate is made from rigid and perfectly plastic material which yields according to the yield condition shown in fig- 1· The lower bound (1.21) is obtained when the dynamically admissible displacement and velocity are chosen in separated variable form which is a scalar time function multiplied by a vector shape function of space variable (1.13). In the case when W, Ẇ * are chosen in form (1.22). [comparison of the obtained estimate Eq (1.24) with previous solution of the same problem [1], upper bound [2] and experimental date [3] are presented in fig. 2

An Application of Incremental Plasticity Theory to Fatigue Life Prediction of Steels

1991 ◽  
Vol 113 (4) ◽  
pp. 404-410 ◽  
Author(s):  
W. R. Chen ◽  
L. M. Keer
Keyword(s):  
Fatigue Life ◽  
Life Prediction ◽  
Kinematic Hardening ◽  
Yield Condition ◽  
Strain Curve ◽  
Fatigue Life Prediction ◽  
304 Stainless Steel ◽  
Flow Rule ◽  
Stress Strain ◽  
Von Mises

An incremental plasticity model is proposed based on the von-Mises yield condition, associated flow rule, and nonlinear kinematic hardening rule. In the present model, fatigue life prediction requires only the uniaxial cycle stress-strain curve and the uniaxial fatigue test results on smooth specimens. Experimental data of 304 stainless steel and 1045 carbon steel were used to validate this analytical model. It is shown that a reasonable description of steady-state hysteresis stress-strain loops and prediction of fatigue lives under various combined axial-torsional loadings are given by this model

scholarly journals The influence of pavement degradation caused by cyclic loading on its failure mechanisms

2016 ◽  
Vol 11 (3) ◽  
pp. 179-187 ◽  
Author(s):  
Marcin Gajewski ◽  
Stanisław Jemioło
Keyword(s):  
Yield Condition ◽  
Limit Load ◽  
Flow Rule ◽  
Smooth Approximation ◽  
Simple Method ◽  
Plastic Properties ◽  
The Road ◽  
Plastic Materials ◽  
Number Of Cycles ◽  
Elastic Plastic Materials

In this paper, a simple method is proposed to estimate capacity of multilayered road structure including the degradation of the elastic and plastic properties of the constituent materials. In the study boundary value problem modeling interaction of wheels with road surface layer in the frame of large deformation theory for elastic-plastic materials was formulated. Plastic properties of the material were described by the flow rule un-associated with yield condition. The Coulomb-Mohr yield condition was assumed and the potential for plasticity is its smooth approximation. In addition, in constitutive modeling the dependence of the Young’s modulus and cohesion of the material from the number of cycles is taken into account. This paper presents qualitative findings in relation to mechanical behavior of the road structure, i.e., for example, the development of plastic zones with increasing load for un-degraded and degraded materials. In addition, a parametric study of the influence of the degradation ratio of the elasticity and plasticity properties for road structure failure mechanism (limit load value) was made.

Stamping Rectangular Plates into Doubly-Curved Dies

1984 ◽  
Vol 198 (2) ◽  
pp. 109-125 ◽  
Author(s):  
T X Yu ◽  
W Johnson ◽  
W J Stronge
Keyword(s):  
Plastic Material ◽  
Rectangular Plates ◽  
Rigid Plastic ◽  
Punch Force ◽  
Plate Buckling ◽  
Rigid Plastic Material ◽  
Force Contact ◽  
Curvature Distribution ◽  
Doubly Curved ◽  
Deformation Modes

Shallow spheroidal shell segments have been press formed from rectangular plates by stamping between a die and matching punch that have two degrees of curvature. Experiments on mild steel, copper and aluminium plates that were not clamped in the die have measured the punch force, contact regions and final curvature distribution; and have observed plate buckling for a range of die curvature ratios and plate sizes. An analysis based on a rigid/plastic material idealization and decoupled in-plane forces and bending moments has been correlated with these experiments. The sequence of deformation modes has been identified; initially these are bending but in later stages, in-plane forces predominate.

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