Kinematical shakedown analysis with temperature-dependent yield stress

Yan, Aimin; Hung, Nguyen Dang

doi:10.1002/1097-0207(20010220)50:5<1145::aid-nme70>3.0.co;2-c

Cited by 19 publications

(15 citation statements)

References 29 publications

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“…Once the stress or displacement fields are approximated and the bound theorems applied, limit analysis becomes a problem of optimization involving either linear or nonlinear programming. Problems involving piecewise linear yield functions or nonlinear yield functions can respectively be solved using linear or non-linear programming techniques [13,14,5,15,16]. However, difficulty exists in the upper-bound optimization problem is that the objective function is convex, but not everywhere differentiable.…”

Section: Introductionmentioning

confidence: 99%

Upper and lower bound limit analysis of plates using FEM and second-order cone programming

Nguyen‐Xuan

Hung

2010

Computers & Structures

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Published paperLe, C.V., Nguyen-Xuan, H. and Nguyen-Dang, H. (2010) in which the pressure is equilibrated by corner loads only, ensuring that exact equilibrium relations associated with a uniform pressure can be obtained. Once the displacement or moment fields are approximated and the bound theorems applied, limit analysis becomes a problem of optimization. In this paper, the optimization problems are formulated in the form of a standard second-order cone programming which can be solved using highly efficient interior point solvers.The procedures are tested by applying it to several benchmark plate problems and are found good agreement between the present upper and lower bound solutions and results in the literature.Key words: Limit analysis, upper and lower bounds, displacement and equilibrium models, criterion of mean, second order cone programming

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Section: Introductionmentioning

confidence: 99%

Upper and lower bound limit analysis of plates using FEM and second-order cone programming

Nguyen‐Xuan

Hung

2010

Computers & Structures

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“…Yan and Nguyen (2001) used directly the formulation resulting from (15) and employed a nonlinear programming method to solve the problem. In their work, the yield stress function is updated at every iteration and the obtained solution becomes an approximation if the yield stress function is convex with respect to temperature.…”

Section: Existing Shakedown Theoremsmentioning

confidence: 99%

“…In other cases, only rough approximations can be obtained or global nonlinear programming tools must be used. For more details, see Gross-Weege and Weichert (1992), Xue et al (1997), Borino (2000), Vrankovic et al (2000), Yan and Nguyen (2001). In the following sections, we will introduce some restrictions on the thermal loading and, by using a linearized yield stress function, we will present new linearized versions of shakedown theorems.…”

Section: Introductionmentioning

confidence: 99%

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

Staat

2007

International Journal of Solids and Structures

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In this work, the shakedown of structures made of materials with temperature-dependent yield stress is considered. Under some restrictions on the thermal loading condition the yield stress is linearized and shakedown theorems are established. Based on these linearized shakedown theorems, the shakedown limit is formulated as a problem of convex optimization. An algorithm is built to compute shakedown limits. Numerical tests show good agreement with analytic solutions and experimental data.

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“…For perfectly plastic structures, the upper bound algorithm has been established by Yan and Nguyen Dang [15,16] and Yan et al [17]. The major numerical obstacle in this approach is the singular property of plastic dissipation function.…”

Section: Introductionmentioning

confidence: 99%

FEM-based shakedown analysis of hardening structures

Phạm

Staat

2014

Asia Pac. J. Comput. Engin.

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This paper develops a new finite element method (FEM)-based upper bound algorithm for limit and shakedown analysis of hardening structures by a direct plasticity method. The hardening model is a simple two-surface model of plasticity with a fixed bounding surface. The initial yield surface can translate inside the bounding surface, and it is bounded by one of the two equivalent conditions: (1) it always stays inside the bounding surface or (2) its centre cannot move outside the back-stress surface. The algorithm gives an effective tool to analyze the problems with a very high number of degree of freedom. Our numerical results are very close to the analytical solutions and numerical solutions in literature.

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Kinematical shakedown analysis with temperature-dependent yield stress

Cited by 19 publications

References 29 publications

Upper and lower bound limit analysis of plates using FEM and second-order cone programming

Upper and lower bound limit analysis of plates using FEM and second-order cone programming

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

FEM-based shakedown analysis of hardening structures

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