Ratcheting/Shakedown Analysis of Cracked Structures

2011 ◽  
Author(s):  
R. Adibi-Asl ◽  
W. Reinhardt
Keyword(s):  
Numerical Schemes ◽  
Shakedown Analysis ◽  
Component Structure ◽  
Elastic Range ◽  
Cracked Structures ◽  
Elastic Shakedown ◽  
Plastic Shakedown ◽  
Time Invariant ◽  
Mean Time

The classical approaches in shakedown analysis are based the assumption that the stresses are eventually within the elastic range of the material everywhere in a component (elastic shakedown). Therefore, these approaches are not very useful to predict the ratcheting limit (ratchet limit) of a cracked component/structure in which the magnitude of stress locally exceeds the elastic range at any load, although in reality the configuration will certainly permit plastic shakedown. In recent years, the “Non-Cyclic Method” (NCM) was proposed by the present authors to predict the entire ratchet boundary (both elastic and plastic) of a component/structure by generalizing the static shakedown theorem (Melan’s theorem). The proposed method is based on decomposing the loading into mean (time invariant) and fully reversed components. The applicability of the NCM has been demonstrated for several uncracked components and structures using both analytical and numerical schemes. The present paper extends the NCM further to analyze plastic shakedown for two simple cracked components.

Local vs. Global Ratcheting in Cracked Structures

2014 ◽  
Author(s):  
R. Adibi-Asl ◽  
Wolf Reinhardt
Keyword(s):  
Cyclic Loading ◽  
Component Structure ◽  
Elastic Range ◽  
Cracked Structures ◽  
Elastic Shakedown ◽  
Plastic Shakedown ◽  
Time Invariant ◽  
Global And Local ◽  
Mean Time ◽  
Cracked Structure

The classical approaches in shakedown analysis are based on the assumption that the stresses are eventually within the elastic range of the material everywhere in a component (elastic shakedown). Therefore, these approaches are not very useful to predict the ratcheting limit (ratchet limit) of a cracked component/structure in which the magnitude of stress locally exceeds the elastic range at any load, although in reality the configuration will certainly permit plastic shakedown. The Non-Cyclic Method (NCM) has been proposed recently to determine both the elastic and the plastic ratchet boundary of a component or structure under cyclic loading by generalizing the static shakedown theorem (Melan’s theorem). The proposed method is based on decomposing the loading into mean (time invariant) and fully reversed components. When a cracked structure is subjected to cyclic loading, the crack and its vicinity behave differently (local) than the rest of the structure (global). The crack may propagate during the application of cyclic loading. This will affect both local and global behavior of the cracked structure. This paper investigates global and local ratcheting of the cracked structures using the NCM and fracture mechanic parameters.

Ratchet Boundary of a Beam With Arbitrary Cross Section

2013 ◽  
Author(s):  
R. Adibi-Asl ◽  
W. Reinhardt
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Arbitrary Cross Section ◽  
Fundamental Idea ◽  
Shakedown Analysis ◽  
Component Structure ◽  
Elastic Range ◽  
Bending Loads ◽  
Elastic Shakedown ◽  
Plastic Shakedown

The classical approaches in shakedown analysis are based the assumption that the stresses are eventually within the elastic range of the material everywhere in a component (elastic shakedown). Therefore, these approaches are not very useful to predict the ratcheting limit (ratchet limit) of a component/structure in which the magnitude of stress locally exceeds the elastic range at any load, although in reality the configuration will certainly permit plastic shakedown. In recent years, the “Non-Cyclic Method” (NCM) was proposed by the present authors to predict the entire ratchet boundary (both elastic and plastic) of a component/structure by generalizing the static shakedown theorem (Melan’s theorem). The fundamental idea behind the proposed method is to (conservatively) determine the stable and unstable boundary without going through the cyclic history. The method is used to derive the interaction diagrams for a beam subjected to primary membrane and bending with secondary bending loads. Various cross-sections including rectangular, solid circular and thin pipe are investigated.

Ratchet Limit Solution of a Beam With Arbitrary Cross Section

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
R. Adibi-Asl ◽  
W. Reinhardt
Keyword(s):  
Cross Sections ◽  
Arbitrary Cross Section ◽  
Fundamental Idea ◽  
Component Structure ◽  
Elastic Range ◽  
Limit Solution ◽  
Thin Walled Pipe ◽  
Bending Loads ◽  
Elastic Shakedown ◽  
Plastic Shakedown

The classical approaches in shakedown analysis are based the assumption that the stresses are eventually within the elastic range of the material everywhere in a component (elastic shakedown). Therefore, these approaches are not very useful to predict the ratcheting limit (ratchet limit) of a component/structure in which the magnitude of stress locally exceeds the elastic range at any load, although in reality the configuration will certainly permit plastic shakedown. In recent years, the “noncyclic method” (NCM) was proposed by the present authors to predict the entire ratchet boundary (both elastic and plastic) of a component/structure by generalizing the static shakedown theorem (Melan's theorem). The fundamental idea behind the proposed method is to (conservatively) determine the stable and unstable boundary without going through the cyclic history. The method is used to derive the interaction diagrams for a beam subjected to primary membrane and bending with secondary bending loads. Various cross-sections including rectangular, solid circular and thin-walled pipe are investigated.

Lower Bound Methods in Elastic-Plastic Shakedown Analysis

2010 ◽  
Author(s):  
Wolf Reinhardt ◽  
Reza Adibi-Asl
Keyword(s):  
Lower Bound ◽  
Plastic Material ◽  
Shakedown Analysis ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Efficient Calculation ◽  
Asme Code ◽  
Elastic Shakedown ◽  
Plastic Shakedown

Several methods were proposed in recent years that allow the efficient calculation of elastic and elastic-plastic shakedown limits. This paper establishes a uniform framework for such methods that are based on perfectly-plastic material behavour, and demonstrates the connection to Melan’s theorem of elastic shakedown. The paper discusses implications for simplified methods of establishing shakedown, such as those used in the ASME Code. The framework allows a clearer assessment of the limitations of such simplified approaches. Application examples are given.

Lower Bound Methods in Elastic-Plastic Shakedown Analysis

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Wolf Reinhardt ◽  
Reza Adibi-Asl
Keyword(s):  
Lower Bound ◽  
Plastic Material ◽  
Material Behavior ◽  
Shakedown Analysis ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Efficient Calculation ◽  
Asme Code ◽  
Elastic Shakedown ◽  
Plastic Shakedown

Several methods were proposed in recent years that allow the efficient calculation of elastic and elastic-plastic shakedown limits. This paper establishes a uniform framework for such methods that are based on perfectly-plastic material behavior, and demonstrates the connection to Melan's theorem of elastic shakedown. The paper discusses implications for simplified methods of establishing shakedown, such as those used in the ASME Code. The framework allows a clearer assessment of the limitations of such simplified approaches. Application examples are given.

A Non-Cyclic Method for Plastic Shakedown Analysis

2003 ◽  
Author(s):  
W. Reinhardt
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Computing Time ◽  
Strain Accumulation ◽  
Analysis Method ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Cyclic Phenomenon ◽  
Elastic Shakedown ◽  
Plastic Shakedown

Shakedown is a cyclic phenomenon, and for its analysis it seems natural to employ a cyclic analysis method. Two problems are associated when this direct approach is used in finite element analysis. Firstly, the analysis typically needs to be stabilized over several cycles, and the analysis of each individual cycle may need a considerable amount of computing time. Secondly, even in cases where a stable cycle is known to exist, the finite element analysis can show a small continuing amount of strain accumulation. For elastic shakedown, non-cyclic analysis methods that use Melan’s theorem have been proposed. The present paper extends non-cyclic lower bound methods to the analysis of plastic shakedown. The proposed method is demonstrated with several example problems.

An elastic–plastic shakedown analysis of fretting wear

Wear ◽  
2001 ◽  
Vol 247 (1) ◽  
pp. 41-54 ◽  
Author(s):  
S. Fouvry ◽  
Ph. Kapsa ◽  
L. Vincent
Keyword(s):  
Fretting Wear ◽  
Shakedown Analysis ◽  
Elastic Plastic ◽  
Plastic Shakedown

scholarly journals Shakedown of a Thick Cylinder With a Radial Crosshole

2006 ◽  
Author(s):  
Duncan Camilleri ◽  
Donald Mackenzie ◽  
Robert Hamilton
Keyword(s):  
Thermal Loading ◽  
Constant Pressure ◽  
Element Analysis ◽  
Cyclic Thermal Loading ◽  
Interaction Diagram ◽  
Thin Cylinder ◽  
Structural Discontinuity ◽  
Thick Cylinder ◽  
Elastic Shakedown ◽  
Plastic Shakedown

The shakedown behaviour of a thin cylinder subject to constant pressure and cyclic thermal loading is described by the well known Bree diagram. In this paper, the shakedown and ratchetting behaviour of a thin cylinder, a thick cylinder and a thick cylinder with a radial crosshole is investigated by inelastic finite element analysis. Load interaction diagrams identifying regions of elastic shakedown, plastic shakedown and ratchetting are presented. The interaction diagrams for the plain cylinders are shown to be similar to the Bree Diagram. Incorporating the radial crossbore in the thick cylinder significantly reduces the plastic shakedown boundary on the interaction diagram but does not significantly affect the ratchet boundary. The radial crosshole can therefore be regarded as a local structural discontinuity and neglected when determining the maximum shakedown or (primary plus secondary stress) load in Design by Analysis.

scholarly journals A Review of  Elasto-Plastic Shakedown Analysis with Limited Plastic Deformations and Displacements

2018 ◽  
Author(s):  
Majid Movahedi Rad
Keyword(s):  
Limit Analysis ◽  
Limit State ◽  
Variable Loading ◽  
Proportional Loading ◽  
Approximate Methods ◽  
Shakedown Analysis ◽  
Plastic Deformations ◽  
Analysis And Design ◽  
Residual Displacements ◽  
Plastic Shakedown

In classical plasticity the shakedown analysis is among the most important basic problems. The principles of shakedown analysis are counterparts to those of limit analysis in the sense that they provide static and kinematic approaches to the question of whether or not shakedown will occur for a body under multiple variable loading conditions. The principles of limit analysis provide static and kinematic approaches to the question of whether or not the plastic limit state will be reached by a body under proportional loading. The principles of shakedown analysis are, however, considerably more difficult to apply than those of limit analysis. In spite of these difficulties, shakedown analysis is a vital and developing topic in plasticity and a great number of applications have been made. At the application of the plastic analysis and design methods the control of the plastic behaviour of the structures is an important requirement. Since the shakedown analysis provide no information about the magnitude of the plastic deformations and residual displacements accumulated before the adaptation of the structure, therefore for their determination bounding theorems and approximate methods have been proposed.

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