Optimality conditions for shakedown design of trusses

Giambanco, F.; Palizzolo, Luigi

doi:10.1007/bf00370559

Cited by 16 publications

(6 citation statements)

References 16 publications

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“…Few cycles after the beginning of the steady-state phase of the cyclic load, the steady-state phase of the behavioural variables begins. The residual horizontal and vertical node displacements of the top of column 13 (denoted as u r 13 and v r 13 ), as well as the vertical residual displacements of the middle points of beams 1, 3, 5 and 7 (denoted as v r 1 , v r 3 , v r 5 and v r 7 ) are reported in Table 2, together with the volume and the steady-state and transient plastic dissipation values. Although it has been adopted the reduced value ξ F c = 3.9 of Table 2 shows that, after ten cycles, frame (a) can be assumed as destroyed, being subjected to incremental collapse (Fig.…”

Section: Numerical Applicationsmentioning

confidence: 99%

“…In the framework of structural optimization many formulations, usually proposed as the search for the minimum volume structure, have been provided for the standard limit design [1][2][3][4][5][6][7][8], for the elastic optimal design [9] and for the shakedown optimal design [10][11][12][13][14][15], each one taking into account just a particular chosen resistance criterion and the corresponding structural limit design. Recently, in order to contemporaneously satisfy more resistance criteria, suitable multicriterion optimal design formulations have been proposed.…”

Section: Introductionmentioning

confidence: 99%

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Bounds on transient phase plastic deformations in optimal design of steel frames subjected to cyclic loads

2009

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A minimum volume multicriterion design of elastic perfectly plastic steel frames subjected to a combination of quasi-static fixed and cyclic loads, bounding the transient phase plastic deformations, is proposed. The problem is formulated according to a plastic shakedown criterion, so that incremental and instantaneous collapse are certainly prevented when the frame is subjected to very strongly amplified cyclic loads. The further condition that the structure must also behave elastically in serviceability conditions is imposed. Since the steady-state loading history is known it is possible to directly bound the steady-state plastic deformations. By applying a suitable own bounding theorem, it is also possible to indirectly bound the transient plastic deformations, whichever the unknown transient real loading history is. A numerical application confirms the fundamental role played by the transient phase plastic deformations both on the design as well as on the structural behaviour and the great performance of the proposed formulation

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Section: Numerical Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bounds on transient phase plastic deformations in optimal design of steel frames subjected to cyclic loads

2009

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“…The optimal shakedown design of beam structures using either the height or the width of the cross section as a design variable has recently been studied by , where comparisons are made by solving the problem using either the lower or the upper bound theorem. These results have been extended by the authors to the shakedown design of circular plates ) and trusses (Giambanco and Palizzolo 1995).…”

Section: Introductionmentioning

confidence: 96%

A fully automatic force method for the optimal shakedown design of frames

Spiliopoulos

1999

Computational Mechanics

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The paper presents a fully automatic way to handle the problem of the optimal shakedown design of planar frames. The evaluation of the elastic moments is essential for this design problem and due to the fact that they are design dependent, a classical iterative procedure is followed which updates these moments at the beginning of each iteration. A linear programming problem is then solved inside each iteration. The formulation adopted here is based on the force method which has computational advantages against the displacement method for this type of problems. Within the framework of the force method, the statical basis is provided by an easy to implement algorithm which selects a near minimal mesh basis for any planar graph. This basis is ef®ciently used, in a novel way, to ®nd the¯exibility matrix of the frame in a skyline form amenable to standard algorithms for its decomposition. The quickest way to the ground of each load is used to form the right hand side of the elastic compatibility equations for each load pattern. These equations are ef®-ciently solved by standard back-substitution algorithms and the elastic bending moments to be introduced at the beginning of each iteration is established. Examples of application are also included.

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“…You can find paper on the optimal design of truss based on the theory of shakedown with estimation of load capacity for shakedown. They mostly concern the model of elastic perfectly plastic material and static load, for example [6,8]. Other material models are also taken in the same way as at paper [11].…”

Section: Introductionmentioning

confidence: 99%

Elastic shakedown limit of a steel lattice girder

Brzuzy

2021

iboa

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This paper presents a solution for the problem concerning the behaviour of a steel lattice girder subjected to dynamic load pulses. The theory of shakedown is used in the analysis. It is assumed that such loads cause a non-elastic response which includes dissipation of energy causing deformations and residual forces developed in the structural members of the girder. At a certain intensity of these forces, the girder can react to subsequent load pulses without further dissipation of energy, behaving in the elastic region after shakedown. This condition is referred to as adaptation of the structure to assumed cyclic loading. Elastic shakedown limit is determined through a direct analysis of the girder's dynamic behaviour, i.e. by checking if energy dissipation decreases with loading cycles. This gives the number of load applications after which no further increase of the energy dissipation is observed. The existing permanent deformations persist and residual forces remain in the same state. The analysis takes into account the possibility that compressed members can buckle which may result in non-elastic, longitudinal and transverse vibrations of these members. Non-linear geometry of members is taken into account. Then a perfectly elastic-viscoplastic model of the material is used. The main goal is to determine the state of the non-elastic movements of the girder joints and the residual internal forces developed in the girder members after each load application. The values obtained in this way serve as the basis for describing the next loading cycle. It is possible to use the approach presented in the paper to evaluate the effects of accidental loads. Then it is checked whether a small number of repetitions of accidental load would result in exceeding the serviceability limit state criteria of the maximum permanent deformation or displacement and/or strain amplitudes. If so, the magnitude of accidental load is greater than the elastic shakedown limit. Some examples are given to illustrate the application of the theory of shakedown.

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Optimality conditions for shakedown design of trusses

Cited by 16 publications

References 16 publications

Bounds on transient phase plastic deformations in optimal design of steel frames subjected to cyclic loads

Bounds on transient phase plastic deformations in optimal design of steel frames subjected to cyclic loads

A fully automatic force method for the optimal shakedown design of frames

Elastic shakedown limit of a steel lattice girder

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