A Study on Plastic Shakedown of Structures: Part II—Theorems

1993 ◽  
Vol 60 (2) ◽  
pp. 324-330 ◽  
Author(s):  
Castrenze Polizzotto
Keyword(s):  
Solid Body ◽  
Mechanical Load ◽  
Direct Determination ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Plastic Shakedown

For a continuous elastic-perfectly plastic solid body subjected to a combination of cyclic (mechanical and/or kinematical) load and of a steady (mechanical) load, two theorems of plastic shakedown are presented, one stating a necessary condition, another stating a sufficient condition. The problem of the direct determination of the plastic shakedown boundary is also briefly addressed.

A Study on Plastic Shakedown of Structures: Part I—Basic Properties

1993 ◽  
Vol 60 (2) ◽  
pp. 318-323 ◽  
Author(s):  
C. Polizzotto
Keyword(s):  
Solid Body ◽  
Mechanical Load ◽  
Basic Properties ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Plastic Shakedown

For a continuous elastic-perfectly plastic solid body subjected to a combination of cyclic (mechanical and/or kinematical) load and of a steady (mechanical) load such as to produce plastic shakedown (i.e., alternating plasticity), a number of characterizing properties are established and discussed. The conditions for the body’s transition from plastic shakedown to ratchetting are also addressed.

On the Conditions to Prevent Plastic Shakedown of Structures: Part I—Theory

1993 ◽  
Vol 60 (1) ◽  
pp. 15-19 ◽  
Author(s):  
Castrenze Polizzotto
Keyword(s):  
Mechanical Load ◽  
Plastic Material ◽  
Perfectly Plastic ◽  
Shakedown Theory ◽  
Elastic Perfectly Plastic ◽  
Plastic Shakedown ◽  
Steady Load

For a structure of elastic perfectly plastic material subjected to a given cyclic (mechanical and/or kinematical) load and to a steady (mechanical) load, the conditions are established in which plastic shakedown cannot occur whatever the steady load, and thus the structure is safe against the alternating plasticity collapse. Static and kinematic theorems, analogous to those of classical shakedown theory, are presented.

On the Conditions to Prevent Plastic Shakedown of Structures: Part II—The Plastic Shakedown Limit Load

1993 ◽  
Vol 60 (1) ◽  
pp. 20-25 ◽  
Author(s):  
Castrenze Polizzotto
Keyword(s):  
Mechanical Load ◽  
Plastic Material ◽  
Limit State ◽  
Limit Load ◽  
Companion Paper ◽  
Material Structure ◽  
Perfectly Plastic ◽  
Shakedown Limit ◽  
Elastic Shakedown ◽  
Plastic Shakedown

Following the results of a companion paper, the concept of plastic shakedown limit load is introduced for an elastic-perfectly plastic material structure subjected to combined cyclic (mechanical and/or kinematical) loads and steady (mechanical) load. Static and kinematic approaches are available for the computation of this load, in perfect analogy with the classic (elastic) shakedown limit load. The plastic shakedown limit state of the structure being in an impending alternating plasticity collapse is studied and a number of interesting features of it are pointed out.

Modelling plasticity in finite bodies containing stress concentrations by a distributed dislocation method

1998 ◽  
Vol 33 (4) ◽  
pp. 315-326 ◽  
Author(s):  
P M Blomerus ◽  
D A Hills
Keyword(s):  
Infinite Plane ◽  
Stress Concentrations ◽  
Reliable Prediction ◽  
Displacement Boundary ◽  
Perfectly Plastic ◽  
Distributed Dislocation ◽  
Edge Notch ◽  
Constant Displacement ◽  
Elastic Perfectly Plastic ◽  
Plastic Shakedown

An efficient method for the analysis of limited plasticity at stress raising features such as notches and holes in finite bodies has been developed. A network of stationary dislocations is used to simulate the plasticity and simple constant displacement boundary elements form the borders of the geometries. The notch or hole itself is implicitly included in the formulation by using specialized kernels for these features in an infinite plane, thereby improving the numerical efficiency. The cyclic plastic behaviour of an edge-notch in an infinite plane and a finite rectangular plate are analysed under elastic-perfectly plastic, plane strain conditions. Examples of the resulting stress state after stress redistribution and plastic shakedown are displayed which aid in the reliable prediction of component life.

A Simplified Approach to Elastic-Plastic Response to General Pulse Loads

1985 ◽  
Vol 52 (1) ◽  
pp. 115-121 ◽  
Author(s):  
P. S. Symonds ◽  
J. M. Mosquera
Keyword(s):  
Rate Sensitivity ◽  
Limit Load ◽  
Rigid Plastic ◽  
Short Pulses ◽  
Simplified Approach ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Mass Spring ◽  
Elastic Stage

The paper describes a method for estimating permanent and maximum (elastic plus plastic) deflections of a structure subjected to a force pulse loading of arbitrary shape and duration. The concept of artificially separating the response into purely elastic and purely plastic (i.e., rigid-plastic) stages is adopted. Previous applications have been to very short pulses. When the approach is applied to long pulses of only moderately large force compared to limit load magnitudes the interaction between elastic and plastic effects is more critical. The inclusion of plastic rate sensitivity and the determination of the duration of the initial elastic stage require new approaches. Insight is provided by studying a mass-spring (elastic-perfectly plastic) system of one degree of freedom. The duration of the elastic stage is chosen to maximize a specially defined work function. Comparisons are shown for examples of rate-independent and rate-sensitive frames between deflections given by the simple technique of the paper, final deflections obtained in laboratory tests, and maximum and final displacements furnished by the finite element code ABAQUS.

Detection of Ratcheting in Finite Element Calculations

2018 ◽  
Author(s):  
M. C. Messner ◽  
T.-L. Sham
Keyword(s):  
Finite Element ◽  
Fe Analysis ◽  
Design Methods ◽  
Finite Element Analyses ◽  
Perfectly Plastic ◽  
Ratcheting Strain ◽  
Small Cycle ◽  
Constitutive Response ◽  
Elastic Perfectly Plastic ◽  
Plastic Shakedown

The distinction between a ratcheting and non-ratcheting response is critical for many high temperature design methods. Non-ratcheting is generally considered safe — deformation remain bounded over the lifetime of the component — while ratcheting is undesirable. As a particular example, the elastic perfectly-plastic (EPP) design methods described in recent ASME Section III, Division 5 code cases require a designer to distinguish ratcheting from non-ratcheting for finite element analyses using a relatively simple, elastic perfectly-plastic constitutive response. However, it can be quite difficult to distinguish these two deformation regimes using finite element (FE) analysis particularly in the case where the actual ratcheting strain is small. In practice FE analysis of structures that are analytically in either the plastic shakedown or ratcheting regimes will result in small, cycle-to-cycle accumulated strains characteristic of ratcheting. Distinguishing false ratcheting — the structure is actually in the plastic shakedown regime — from true ratcheting can be challenging. We describe the characteristics of nonlinear FE analysis that cause these false ratcheting strains and describe practical methods for distinguishing a ratcheting from a non-ratcheting response.

Optimal Design of Trusses According to a Plastic Shakedown Criterion

2004 ◽  
Vol 71 (2) ◽  
pp. 240-246 ◽  
Author(s):  
Luigi Palizzolo
Keyword(s):  
Optimal Design ◽  
Optimization Problems ◽  
Limit Load ◽  
Truss Structures ◽  
Search Problem ◽  
Perfectly Plastic ◽  
Problem Formulations ◽  
Elastic Perfectly Plastic ◽  
Plastic Shakedown ◽  
Statical Approach

The optimal design of elastic-perfectly plastic truss structures subjected to quasi-statically loads variable within a given load domain is studied. The actions are given as the combination of fixed load and perfect cyclic load. Suitably chosen load multipliers are given. A minimum volume formulation of the design problem with assigned limit load multiplier is developed and it is provided on the grounds of a statical approach as well as of a kinematical approach. The incremental collapse (ratchetting) of the optimal structure is prevented, as long as the loads are not greater than some prescribed values, by special constraints suitably introduced in the search problem. The Kuhn-Tucker equations related to the above-described search problems are deduced and studied. The duality between the statical and the kinematical problem formulations is proved. A special iterative technique devoted to the solution of the above referred optimization problems is utilized for computational purposes. A numerical example concludes the paper. The comparison between different designs is effected.

Compression of elastic–perfectly plastic microcapsules using micromanipulation and finite element modelling: Determination of the yield stress

2011 ◽  
Vol 66 (9) ◽  
pp. 1835-1843 ◽  
Author(s):  
Ruben Mercadé-Prieto ◽  
Rachael Allen ◽  
David York ◽  
Jon A. Preece ◽  
Ted E. Goodwin ◽  
...  
Keyword(s):  
Finite Element ◽  
Yield Stress ◽  
Finite Element Modelling ◽  
Element Modelling ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Redundant Trusses of Elastic-Strain-Hardening Material

1958 ◽  
Vol 25 (2) ◽  
pp. 233-238
Author(s):  
Hans Ziegler
Keyword(s):  
Strain Hardening ◽  
Elastic Strain ◽  
Load Carrying Capacity ◽  
Hardening Material ◽  
Limit Loads ◽  
Perfectly Plastic ◽  
Load Carrying ◽  
Tension And Compression ◽  
Elastic Perfectly Plastic

Abstract W. Prager has given a geometric method for the determination of the load-carrying capacity of a redundant truss consisting of elastic, perfectly plastic bars. In the present paper this method is generalized for trusses consisting of elastic-strain-hardening bars with given limit loads in tension and compression.

Transient and Residual Stresses in Heat-Treated Plates

1958 ◽  
Vol 25 (4) ◽  
pp. 459-465
Author(s):  
H. G. Landau ◽  
J. H. Weiner
Keyword(s):  
Stress Distribution ◽  
Residual Stresses ◽  
Cooling Rate ◽  
Thermal Stresses ◽  
Heated Plate ◽  
Perfectly Plastic ◽  
Heat Treated ◽  
The Face ◽  
Elastic Perfectly Plastic

Abstract Equations are given for determining transient and residual thermal stresses in a heat-treated plate. The material of the plate is assumed to be elastic, perfectly plastic. The temperature is assumed uniform on any plane parallel to the faces of the plate but can vary arbitrarily in the direction normal to the face and in time. The stress distribution during the unloading period is determined exactly without the simplifying assumption of simultaneous unloading. Application is made to the determination of stresses during cooling of a uniformly heated plate. The stress-distribution sequence and residual stresses are calculated for several values of cooling rate and yield stress.

Sign in / Sign up

Export Citation Format

Share Document