A linear programming upper bound approach to the shakedown limit of thin shells subjected to variable thermal loading

Karadeniz, S.; Ponter, A. R. S.

doi:10.1243/03093247v194221

Cited by 35 publications

(12 citation statements)

References 11 publications

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“…In previous kinematic shakedown analyses, linear programming techniques were developed by using piece-wise linear (Tresca) or linearized yield criterion, e.g. [11,23]. The application of von Mises criterion leads to a nonlinear mathematical programming problem, the solution of which in practical engineering applications with complex structures and loading still represents a challenge.…”

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confidence: 99%

Shakedown analysis of defective pressure vessels by a kinematic approach

Carvelli

Cen

Liu

et al. 1999

Archive of Applied Mechanics (Ingenieur Archiv)

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In this paper, a kinematic approach and an iterative procedure, earlier proposed for\ud limit analysis, are adopted for shakedown analysis under variable repeated loading. Reference\ud is made to three-dimensional structures of engineering relevance, such as pressurized pipelines\ud and vessels with ¯uctuating pressure and with slot damages due, e.g. to pitting corrosion. The\ud numerical performance of the solution algorithm is investigated, and the cost-effectiveness of\ud the proposed direct shakedown analysis method is assessed and compared to that of timemarching\ud solutions by up-to-date codes

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confidence: 99%

Shakedown analysis of defective pressure vessels by a kinematic approach

Carvelli

Cen

Liu

et al. 1999

Archive of Applied Mechanics (Ingenieur Archiv)

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“…In what follows, the yield function values are sometimes denoted as : 1 5 4 38 9 8. The yield function is assumed to be strictly convex in the argument 4 3, and the inequality …”

Section: 65374mentioning

confidence: 99%

Shakedown, Integrity and Design of Elastic Plastic Damaged Structures as Subjected to Cyclic Loading

Druyanov

Roman

2006

Mathematics and Mechanics of Solids

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A method for direct design (i.e. without detailed investigation of the deformation process) of structures of elastic plastic isotropically damaged materials as subjected to cyclic loading is developed. The material is assumed to be stable. Shakedown and integrity conditions provide the possibility of obtaining the interval of safe values of a parameter 112 in design for which the structure preserves its safety. The damage process is assumed to be coupled with the plastic deformation development. Features of the post-adaptation stage lead to a min-max problem of mathematical programming, whose solution provides a relation between the limit values of the damage and hardening parameters. As the hardening parameter is assumed to be bounded, this relation issues in upper and lower bounds for the local actual limit values of the damage parameter admitted by the yield condition for the given loading program. The bounds result in a priori necessary and sufficient conditions of integrity. As the bounds depend on 1, the integrity conditions impose constraints to its safe values. A method for computing the purely elastic damaged response of the structure to the prescribed loading program is proposed. An example of the application of the developed method is given.Thus, fulfillment of the shakedown conditions is only necessary for the safety of solids subjected to cyclic loading. To guarantee its safety, the condition of local integrity at every point of the structure has to be satisfied, i.e. the parameters of the structure should be specified in such a way to assure the fulfillment both the shakedown and integrity conditions.Maier [1], Weichart and GrossWeege [2], Polizzotto et al. [3], Karadeniz and Ponter [4] and Zarka et al. [5] considered various aspects of applying the shakedown theory to problems of design. Giambanco et al. [6,7] employed the shakedown theory for the optimal design of certain structures, and investigated some related problems.The problem of application of the shakedown theory to the design of creeping elastic plastic mechanical systems has been the subject of the papers by Rose and White [8], Buckthorpe and White [9-11] and Toulios et al. [12].It is well known that the shakedown theory was originally developed for perfect elastic plastic materials [13][14][15]. Presently the question of extension of the shakedown theory to damaged elastic plastic solids is topical.Hachemi and Weichert [16] extended the static shakedown (Melan) theorem to elastic plastic isotropically damaged solids with unlimited linear kinematic strain hardening.Siemashko [17] developed a method of step-by-step inadaptation analysis for elasticplastic structures subjected to repeated loading, which accounts for nonlinear isotropic strain hardening, development of damage, and nonlinear geometrical effects.Polizzotto et al.[18] included the damage variable into a set of internal variables, and developed an elastic plastic damaged material model with associative constitutive relations and nonlinear elasticity. Employing the D-stability ...

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“…Only very few experimental results with cyclic thermal loading have been reported in Ponter (1983), Leers (1985) and Lang et al (2001). Numerical methods therefore have received much attention: Penny (1967, 1969), Sagar and Payne (1975), Goodman (1978), Karadeniz and Ponter (1984), Ponter and Karadeniz (1985a,b). If the yield stress is a linear or a concave function of temperature, linear or convex 0020-7683/$ -see front matter Ó 2006 Elsevier Ltd. All rights reserved.…”

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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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A linear programming upper bound approach to the shakedown limit of thin shells subjected to variable thermal loading

Cited by 35 publications

References 11 publications

Shakedown analysis of defective pressure vessels by a kinematic approach

Shakedown analysis of defective pressure vessels by a kinematic approach

Shakedown, Integrity and Design of Elastic Plastic Damaged Structures as Subjected to Cyclic Loading

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

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