A linear programming approach to shakedown analysis of structures

Corradi, Leone; Zavelani, Adolfo

doi:10.1016/0045-7825(74)90041-3

Cited by 149 publications

(50 citation statements)

References 2 publications

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“…[2], [10], [12], such an approximation is frequently adopted to limit and shakedown analysis purposes, for computational convenience, see e.g. in [6]. Otherwise, Eqs.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Recourse to the LP dual problem and its processing, if advantageous, is automatically made in most LP software and provides further savings, see e.g. [6]. Clearly, the generation of PWL constitutive laws entails a computing cost, which is generally more than compensated by the savings entailed by the transition from convex nonlinear programming to LP.…”

Section: On Shakedown Analysismentioning

confidence: 99%

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Static shakedown theorems in piecewise linearized poroplasticity

Cocchetti

Maier

1998

Archive of Applied Mechanics (Ingenieur Archiv)

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A fully saturated two-phase solid or structure subjected to variable, in particular cyclic, external actions is described as a nonhardening poroelastoplastic material with piecewise linearized yield loci. With reference to a multi®eld ®nite element model, suf®cient and necessary conditions for shakedown are established by the static Melan's approach. Shakedown analysis by linear programming is brie¯y discussed.

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“…[2], [10], [12], such an approximation is frequently adopted to limit and shakedown analysis purposes, for computational convenience, see e.g. in [6]. Otherwise, Eqs.…”

Section: Problem Formulationmentioning

confidence: 99%

Section: On Shakedown Analysismentioning

confidence: 99%

Static shakedown theorems in piecewise linearized poroplasticity

Cocchetti

Maier

1998

Archive of Applied Mechanics (Ingenieur Archiv)

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“…Many structural components operate under complex variable or cyclic loading [4,9,10,12] . Usually, they are in normal conditions and work in elastic regime but sometimes suffer from external loading that cause partial yielding.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling for Shakedown Analysis of Offshore Structures

Fadaee¹,

Saffari²,

Tabatabaei³

2007

American J. of Applied Sciences

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Abstract:The shakedown analysis process of an offshore structure having elastic-plastic material presented. The finite element model of the structure has been developed first, and then a simple method has been applied for shakedown analysis using matrix tool. Simplifying the relationships together with applying the theory concepts of shakedown analysis is one of the characteristics of the presented method for practical problems. Here, shakedown analysis formulation discussed in four steps. First, the Morison equation adopted for converting the velocity and acceleration terms into resultant forces and it extended to consider arbitrary orientations of the structural members. Then the loads due to the waves have been calculated and they have been converted to specific repeating cyclic loads on the structure nodes. In the second step, the finite element model of the structure has been developed and considered under nodal loads resulted from the specific combined wave loads. Thirdly, the shakedown multiplier has been calculated using shakedown static theorem based upon the stress domain governing the problem. Finally, in the fourth step, a graph has been developed indicating the critical sea waves domain that cause the structure shakedown. The formulation has been applied for two types of offshore structures to verify the concept employed and its analytical capabilities.

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“…The assessment of the shakedown limit load for a given structure under a specified loading can be achieved by methods based on one of the basic shakedown theorems, namely the statical and kinematical theorems; related numerical procedures have been developed for various structural models and with different approximation levels (see e.g. Koiter 1960; Corradi and Zavelani Rossi 1974;Cohn and Maier 1977;Gokhfeld and Cherniavsky 1980;KSnig 1987). Since plastic deformations occurring in the initial phase of the structural response, although finite, may indeed exceed some tolerance limits (e.g.…”

Section: Introductionmentioning

confidence: 99%

Optimal shakedown design of beam structures

Giambanco

Palizzolo

Polizzotto

1994

Structural Optimization

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The optimal design of plane beam structures made of elastic perfectly plastic material is studied according to the shakedown criterion. The design problem is formulated by means of a statical approach on the grounds of the shakedown lower bound theorem, and by means of a kinematical approach on the grounds of the shakedown upper bound theorem. In both cases two different types of design problems are formulated: one searches for the minimum volume design whose shakedown limit load is assigned; the other searches for the design of the assigned volume whose shakedown limit load is maximum. The optimality conditions of the four problems above are found by the use of a variational approach; such conditions prove the equivalence of the two types of design problems, provide useful information on the structural behaviour in optimality conditions, and constitute a fifth possible way to determine the optimal design. Whatever approach is used, the strong non-linearity of the corresponding problem does not allow the finding of the analytical solution. Consequently, in the application stage suitable numerical procedures must be employed. Two numerical examples are given.

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A linear programming approach to shakedown analysis of structures

Cited by 149 publications

References 2 publications

Static shakedown theorems in piecewise linearized poroplasticity

Static shakedown theorems in piecewise linearized poroplasticity

Mathematical Modeling for Shakedown Analysis of Offshore Structures

Optimal shakedown design of beam structures

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