A dual form for discretized kinematic formulation in shakedown analysis

Khoi, Vu Duc; Yan, Aimin; Hung, Nguyen Dang

doi:10.1016/j.ijsolstr.2003.08.013

Cited by 38 publications

(11 citation statements)

References 9 publications

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“…Let us remark that the presence of the term e eq ð _ e p k Þ implies a regularization based on the introduction of a small parameter as in Khoi et al (2004).…”

Section: Non-linear Kinematic Hardening Bound Problemsmentioning

confidence: 99%

Shakedown analysis: Comparison between models with the linear unlimited, linear limited and non-linear kinematic hardening

Bouby

Saxcé²,

Tritsch³

2009

Mechanics Research Communications

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“…Let us remark that the presence of the term e eq ð _ e p k Þ implies a regularization based on the introduction of a small parameter as in Khoi et al (2004).…”

Section: Non-linear Kinematic Hardening Bound Problemsmentioning

confidence: 99%

Shakedown analysis: Comparison between models with the linear unlimited, linear limited and non-linear kinematic hardening

Bouby

Saxcé²,

Tritsch³

2009

Mechanics Research Communications

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“…However, although the shakedown theories are proposed and extended, a bigger difficulty in practical engineering applications lies on the numerical method for solving the shakedown problem. Shakedown analysis based on the upper and lower bound theorem is mostly transformed as a mathematical programming problem [7,[17][18][19][20][21][22][23][24][25][26][27][28][29], which aims to minimize or maximize a goal function with plenty of independent variables and constraint conditions [17].…”

Section: Introductionmentioning

confidence: 99%

“…If the von Mises yield criterion is used, the mathematical programming formulation for shakedown analysis leads to a complicated nonlinear optimization problem. Over the last four decades, with the rapid development of numerical methods, some powerful algorithms such as the nonlinear Newton-type iteration algorithm [7,[20][21][22], the second order cone programming (SQCP) [23,24] and the interior point method (IPM) [25][26][27][28][29] have been developed to solve the nonlinear optimization problem. Besides, some other computational methods [30][31][32][33][34][35] of structural analysis instead of traditional finite element method have been combined with shakedown theory to solve the shakedown problem.…”

Section: Introductionmentioning

confidence: 99%

Shakedown analysis of engineering structures under multiple variable mechanical and thermal loads using the stress compensation method

Peng

Liu

Chen

et al. 2018

International Journal of Mechanical Sciences

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The determination of shakedown load or shakedown domain is an important task in structural design and integrity assessment. In this paper, a novel numerical procedure based on the Stress Compensation Method (SCM) is developed to perform shakedown analysis of engineering structures under multiple variable mechanical and thermal loads. By applying the compensation stress on the yield regions that occur at every load vertex of the prescribed loading domain to adjust the total stress to the yield surface and resolving the equilibrium equations, the statically admissible residual stress field for static shakedown analysis is constructed. A robust and effective iteration control technique with some convergence parameters is used to check the change of the compensation stress in the inner loop and to update the shakedown load multiplier in the outer loop. For the purpose of general use, the method is implemented into ABAQUS platform. The shakedown problems for the Bree plate, a square plate with a central circular hole and a practical thick vessel with nozzles under some two-dimensional and three-dimensional loading domains are effectively solved and analyzed. Both alternating plasticity mechanism and ratcheting mechanism to determine the shakedown boundary of these structures are revealed. Numerical applications show that the proposed method has good numerical stability, high accuracy and efficiency, and is well suited for shakedown analysis of large-scale practical engineering structures.

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“…In this work, we have achieved the full‐field plastic strain measurement of a plate with a central hole subjected to a cyclic loading. This specimen shape is a classical benchmark for either analytical or numerical shakedown studies [4–8]. The measurement was carried out during the 30th cycle for different values of the cyclic tensile force.…”

Section: Introductionmentioning

confidence: 99%

Electronic Speckle‐Pattern Interferometry Measurements of Structural Ratcheting Strain

Farge

Nazarov

Ayadi

2010

Strain

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Several tensile specimens with a central hole were subjected to a cyclic loading for which the Von Mises stress was beyond the initial yield stress in the vicinity of the hole. The tensile machine was fixed together with a phase-shifting electronic speckle-pattern interferometry measurement bench that makes it possible to perform strain measurement along the tensile axis. The plastic strain map corresponding to the 30th cycle was obtained. For the considered measurement field, the resolution of the strain measurement is close to 10 )5 . By varying the loading, it was possible to detect and observe the deformation corresponding to an early stage of the ratcheting phenomenon. The non-ratcheting cyclic plasticity behaviour was not observed during the 30th cycle. In the Discussion section, the experimental results were interpreted using Melans's theorem, which allowed us to determine an upper bound for the yield stress. Eventually, it is shown that the procedure followed in this work could be a way to obtain some interesting data related to the material behaviour laws.

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A dual form for discretized kinematic formulation in shakedown analysis

Cited by 38 publications

References 9 publications

Shakedown analysis: Comparison between models with the linear unlimited, linear limited and non-linear kinematic hardening

Shakedown analysis: Comparison between models with the linear unlimited, linear limited and non-linear kinematic hardening

Shakedown analysis of engineering structures under multiple variable mechanical and thermal loads using the stress compensation method

Electronic Speckle‐Pattern Interferometry Measurements of Structural Ratcheting Strain

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