# Shakedown analysis of elastic-plastic structures considering the effect of temperature on yield strength: theory, method and applications

Heng Peng, Yinghua Liu, Haofeng Chen

Research output: Contribution to journalArticle

### Abstract

According to the extended Melan's static theorem, theoretical and numerical aspects of the stress compensation method (SCM) are presented to perform shakedown analysis of elastic-plastic structures considering the effect of temperature on yield strength. Instead of constructing a mathematical programming formulation, this developed method consists of the two-level iterative scheme. The inner loop constructs the statically admissible self-equilibrating stress field, while the outer loop evaluates a sequence of decreasing load factors to approach to the shakedown limit multiplier. The yield strength considering temperature effect is updated based on the current temperature at each outer iteration, and the yield conditions are checked at all Gauss points. The numerical procedure is well incorporated into ABAQUS finite element code and used for calculating the shakedown limits of structures considering yield strengths as different functions of temperature under complex thermomechanical loading system. The method is validated by some plane stress and axisymmetric numerical examples with theoretical and numerical solutions, and subsequently applied to solve the practical shakedown problem of a pipe with oblique nozzle. The results demonstrate that the developed method is stable, accurate and efficient, and can effectively evaluate the shakedown limit of an elastic-plastic structure where the yield strength of material varies with temperature.
Language English 318-330 13 European Journal of Mechanics - A/Solids 73 25 Sep 2018 10.1016/j.euromechsol.2018.09.011 Published - 28 Feb 2019

### Fingerprint

yield strength
Yield stress
plastics
Plastics
mathematical programming
Temperature
plane stress
temperature
Mathematical programming
ABAQUS
multipliers
Thermal effects
stress distribution
nozzles
Strength of materials
iteration
temperature effects
Nozzles
theorems
Pipe

### Keywords

• shakedown analysis
• effect of temperature
• yield strength
• stress compensation method

### Cite this

@article{a13b7718fdea41b680084047b0da08be,
title = "Shakedown analysis of elastic-plastic structures considering the effect of temperature on yield strength: theory, method and applications",
abstract = "According to the extended Melan's static theorem, theoretical and numerical aspects of the stress compensation method (SCM) are presented to perform shakedown analysis of elastic-plastic structures considering the effect of temperature on yield strength. Instead of constructing a mathematical programming formulation, this developed method consists of the two-level iterative scheme. The inner loop constructs the statically admissible self-equilibrating stress field, while the outer loop evaluates a sequence of decreasing load factors to approach to the shakedown limit multiplier. The yield strength considering temperature effect is updated based on the current temperature at each outer iteration, and the yield conditions are checked at all Gauss points. The numerical procedure is well incorporated into ABAQUS finite element code and used for calculating the shakedown limits of structures considering yield strengths as different functions of temperature under complex thermomechanical loading system. The method is validated by some plane stress and axisymmetric numerical examples with theoretical and numerical solutions, and subsequently applied to solve the practical shakedown problem of a pipe with oblique nozzle. The results demonstrate that the developed method is stable, accurate and efficient, and can effectively evaluate the shakedown limit of an elastic-plastic structure where the yield strength of material varies with temperature.",
keywords = "shakedown analysis, effect of temperature, yield strength, stress compensation method, thermomechanical loading",
author = "Heng Peng and Yinghua Liu and Haofeng Chen",
year = "2019",
month = "2",
day = "28",
doi = "10.1016/j.euromechsol.2018.09.011",
language = "English",
volume = "73",
pages = "318--330",
journal = "European Journal of Mechanics - A/Solids",
issn = "0997-7538",

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In: European Journal of Mechanics - A/Solids, Vol. 73, 28.02.2019, p. 318-330.

Research output: Contribution to journalArticle

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T1 - Shakedown analysis of elastic-plastic structures considering the effect of temperature on yield strength

T2 - European Journal of Mechanics - A/Solids

AU - Peng, Heng

AU - Liu, Yinghua

AU - Chen, Haofeng

PY - 2019/2/28

Y1 - 2019/2/28

N2 - According to the extended Melan's static theorem, theoretical and numerical aspects of the stress compensation method (SCM) are presented to perform shakedown analysis of elastic-plastic structures considering the effect of temperature on yield strength. Instead of constructing a mathematical programming formulation, this developed method consists of the two-level iterative scheme. The inner loop constructs the statically admissible self-equilibrating stress field, while the outer loop evaluates a sequence of decreasing load factors to approach to the shakedown limit multiplier. The yield strength considering temperature effect is updated based on the current temperature at each outer iteration, and the yield conditions are checked at all Gauss points. The numerical procedure is well incorporated into ABAQUS finite element code and used for calculating the shakedown limits of structures considering yield strengths as different functions of temperature under complex thermomechanical loading system. The method is validated by some plane stress and axisymmetric numerical examples with theoretical and numerical solutions, and subsequently applied to solve the practical shakedown problem of a pipe with oblique nozzle. The results demonstrate that the developed method is stable, accurate and efficient, and can effectively evaluate the shakedown limit of an elastic-plastic structure where the yield strength of material varies with temperature.

AB - According to the extended Melan's static theorem, theoretical and numerical aspects of the stress compensation method (SCM) are presented to perform shakedown analysis of elastic-plastic structures considering the effect of temperature on yield strength. Instead of constructing a mathematical programming formulation, this developed method consists of the two-level iterative scheme. The inner loop constructs the statically admissible self-equilibrating stress field, while the outer loop evaluates a sequence of decreasing load factors to approach to the shakedown limit multiplier. The yield strength considering temperature effect is updated based on the current temperature at each outer iteration, and the yield conditions are checked at all Gauss points. The numerical procedure is well incorporated into ABAQUS finite element code and used for calculating the shakedown limits of structures considering yield strengths as different functions of temperature under complex thermomechanical loading system. The method is validated by some plane stress and axisymmetric numerical examples with theoretical and numerical solutions, and subsequently applied to solve the practical shakedown problem of a pipe with oblique nozzle. The results demonstrate that the developed method is stable, accurate and efficient, and can effectively evaluate the shakedown limit of an elastic-plastic structure where the yield strength of material varies with temperature.

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KW - yield strength

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