Shakedown analysis of structures made of materials with temperature-dependent yield stress

Vu, Duc Khôi; Staat, Manfred

doi:10.1016/j.ijsolstr.2006.11.038

Cited by 13 publications

(9 citation statements)

References 17 publications

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“…However, in many industrial domains, for example in boilers of nuclear power plants or in airplane and offshore structures and automotive motors, the structural elements are subjected to thermal cycles of large amplitude in such way that the dependence of the elastic coefficients with respect to the temperature cannot be neglected. The case for which the yield stress depend on the temperature is well understood (Prager, 1956;Borino, 2000) and many numerical algorithms where proposed for its resolution (Khôi Vu and Staat, 2007). However, when the compliance elastic tensor is temperature-dependent, the question of convergence of the elastic plastic evolution to a periodic asymptotic state remains open.…”

Section: Introductionmentioning

confidence: 99%

Inelastic responses of a two-bar system with temperature-dependent elastic modulus under cyclic thermomechanical loadings

Hasbroucq¹,

Oueslati²,

Saxcé³

2010

International Journal of Solids and Structures

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a b s t r a c tThis paper is concerned with the elastic plastic response of a two-bar system with temperature-dependent elastic coefficients under cyclic thermomechanical loadings. Such materials are characterized by lack of results concerning the asymptotic behaviors and conditions for shakedown occurrence. This study shows that the considered simple structure is sufficiently complex to experience different periodic long-term behaviors as in classical elastoplasticity. In order to understand how Melan-Koiter method works for such materials, the evolution of the structure's response until the stabilization of the plastic strain ('shakedown') or the asymptotic dissipative behavior ('alternating plasticity' or 'ratcheting') is analytically addressed and the Bree diagram is then constructed. The main result of this work is that the residual stress and strain fields are time-dependent even when shakedown occurs. Besides, we proved that Halphen's conjecture (Halphen, 2005) giving a sufficient condition for shakedown occurrence is not a necessary condition. Finally, numerical results performed by an incremental finite element procedure are presented.

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Section: Introductionmentioning

confidence: 99%

Inelastic responses of a two-bar system with temperature-dependent elastic modulus under cyclic thermomechanical loadings

Hasbroucq¹,

Oueslati²,

Saxcé³

2010

International Journal of Solids and Structures

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“…Many researchers have investigated the shakedown analysis considering the temperature-dependent material property (Prager, 1956;König, 1969;Vu and Staat, 2007;Peigney, 2014). The classical Melan's shakedown theorem was extended to include the variation of the yield strength with respect to temperature (Prager, 1956;Borino, 2000), where the constant residual stress field is required to be found.…”

Section: Introductionmentioning

confidence: 99%

“…Since Prager (1956) extended the classical static shakedown theorem of Melan to cover thermal loads and materials with the consideration of temperature effect on yield strength, some relevant studies have been reported (Naghdi, 1960;Bree, 1967;Gokhfeld and Charniavsky, 1980;Borino, 2000;Yan and Hung, 2001;Heitzer, 2004;Vu and Staat, 2007). Naghdi (1960) pointed out that, for the static approach to shakedown problem, the yield surface can be described by some parameters depending on the actual temperature of a material point, but the yield surface must be convex and the normality law should be applied.…”

Section: Introductionmentioning

confidence: 99%

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

Peng

Liu

Chen

2019

European Journal of Mechanics - A/Solids

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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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“…In recent years, there has been renewed interest in application of mathematical programming approaches to nonlinear mechanics problems [1][2][3][4][5][6], fueled by advances in optimization algorithms and solvers. These approaches build on generalizations of classical energy theorems [7][8][9][10][11], on the one hand, and upper-bound and lower-bound theorems [12][13][14][15][16][17][18][19] and shakedown theorems [20][21][22] on the other. They also represent confluence of nonsmooth mechanics, convex analysis and optimization [8,23].…”

Section: Introductionmentioning

confidence: 99%

A projected Newton algorithm for the dual convex program of elastoplasticity

Lotfian

Sivaselvan

2014

Numerical Meth Engineering

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SUMMARYIn this paper, we study a dual optimization problem that arises when taking a mathematical programming approach to incremental state update in nonlinear problems. The mathematical programming approach stems from energy-based descriptions of constitutive models. We describe a projected Newton algorithm to solve the dual optimization problem. This algorithm requires solution of an unconstrained optimization problem at the integration point level, rather than a constrained one as carried out by classical return-mapping schemes. Especially, implementation of multi-surface plasticity models is no more involved than that of single-surface models. We explore characteristics and performance of the projected Newton algorithm through numerical examples. Insights gained from such a further exploration of mathematical programming algorithms are likely to aid in development of successive convex programming approaches to geometric nonlinear and other non-convex problems such as non-associated flow models.

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Shakedown analysis of structures made of materials with temperature-dependent yield stress

Cited by 13 publications

References 17 publications

Inelastic responses of a two-bar system with temperature-dependent elastic modulus under cyclic thermomechanical loadings

Inelastic responses of a two-bar system with temperature-dependent elastic modulus under cyclic thermomechanical loadings

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

A projected Newton algorithm for the dual convex program of elastoplasticity

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