Dynamic shakedown analysis and bounds for elastoplastic structures with nonassociative, internal variable constitutive laws

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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“…In view of associative¯ow rule (3a) and von Mises' yield function (5), the plastic dissipation (4) is expressed by, [8,18] …”

Section: Assumptionsmentioning

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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“…A first line of research is concerned with extensions of the original theorem to various nonlinear behaviors, such as hardening plasticity (Pham, 2008;Nguyen, 2003), non standard plasticity (Corigliano et al, 1995;Bodovillé and De Saxcé, 2001), contact with friction (Ahn et al, 2008), phase-transformation (Peigney, 2010). A second (and complementing) line of research is concerned with the development of numerical methods for efficiently determining the shakedown domain in the space of load parameters (Zarka et al, 1988;Maitournam et al, 2002;Carvelli et al, 1999;Peigney andStolz, 2001, 2003;Simon and Weichert, 2012;Spiliopoulos and Panagiotou, 2012).…”

Section: Introductionmentioning

confidence: 99%

Shakedown of elastic-perfectly plastic materials with temperature-dependent elastic moduli

Peigney

2014

Journal of the Mechanics and Physics of Solids

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For elastic-perfectly plastic materials with constant properties, the well-known Melan's theorem gives a sufficient condition for shakedown to occur, independently on the initial state. It has been conjectured that Melan's theorem could be extended to temperature-dependent (or time-dependent) elastic moduli, but no theoretical result is available. This paper aims at providing results in that direction, with a special emphasis on time-periodic variations. If Melan's condition is satisfied, we show that shakedown indeed occurs provided the time fluctuations of the elastic moduli satisfy a certain condition (which in particular is fulfilled if the time fluctuations are not too large). We provide a counterexample which shows that setting such a constraint on the elastic moduli is necessary to reach path-independent theorems as proposed. A simple mechanical system is studied as an illustrative example.

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“…Our elastic-perfectly plastic model for the reinforced concrete plates has the advantage of simplicity and can be considered the ®rst approximation for the realistic behavior of practical reinforced plates, which generally should be much more complicated, especially, for dynamic processes. Some more re®ned features, such as hardening and nonassociativity effects, can also be included into more complicated schemes of shakedown analysis [2,3], other effects, like degradation of elastic and plastic properties or viscous effect, can hardly be treated within the framework of classical shakedown theory. Fig.…”

Section: Resultsmentioning

confidence: 99%

“…Alternative upper-bound approaches, based on the dual form of the static theorem, formulated by means of convex analysis, are developed in [4,9,13]. Perhaps the most striking feature of the shakedown analysis is that it applies to general dynamic problems, which lie outside the framework of the plastic limit design, [1,2,3,5,15,16]. Many practical structures are subjected not only to static and quasistatic loads, but also to certain dynamic¯uctuating ones called the quasiperiodic dynamic loads, see [15]), such as action of working machines and transport upon the structure.…”

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confidence: 99%

Failure of a circular reinforced concrete plate against dynamic fluctuating loads

Chinh

1998

Archive of Applied Mechanics (Ingenieur Archiv)

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The kinematic shakedown method is used to evaluate the dynamic cyclic collapse loads for a clamped reinforced concrete plate. The method, based on reduced kinematic formulae recently derived by the author, requires determination of the ®ctitious elastic ®elds within the plates, in particular ± their envelope corresponding to the external loads, and construction of potential incremental collapse mechanisms. The load amplitude-frequency diagrams constructed should help to choose the necessary reinforcements for the plate under given loading conditions.Key words Kinematic shakedown, reinforced plate, dynamic cyclic collapse, quasiperiodic load, incremental collapse, ®ctitious elastic ®eld IntroductionThe behaviour of many reinforced concrete plates subjected to simple¯exure can be described approximately by an elastic-perfectly plastic moment-curvature diagram. In particular, the simple Johansen yield criterion has been accepted for doubly reinforced concrete slabs, [7,12,17,21]. However, depending on the orientation and amount of the reinforcements, the particular values of the yield moment may locally differ in positive and negative bending, and depend on the bending direction in the plate's plane. This adds complexity to the engineering analysis of the structure, but makes its design more¯exible to meet the cost and load-bearing requirements. The plastic upper-bound kinematic method, involving construction of a collapse mechanism with yield curves and lines, has been developed successfully to evaluate the loadbearing capacity of a plate under static loads, [7,8,12,21]. Although for structures subjected to loading cycles the plastic limit design [20] is less conservative than the shakedown design [10,14,22], the latter is less often used in practice, mostly because of its mathematical complexity. Applications of the upper-bound kinematic approach in shakedown analysis of structures based on Koiter's theorem [10] have been attempted in a number of studies [6, 11, 15±19]. Recently, a reduced shakedown upper-bound kinematic theorem for reinforced plates, suitable for possible applications, has been formulated in [11]. This approach will be used in the present paper. Alternative upper-bound approaches, based on the dual form of the static theorem, formulated by means of convex analysis, are developed in [4,9,13]. Perhaps the most striking feature of the shakedown analysis is that it applies to general dynamic problems, which lie outside the framework of the plastic limit design, [1,2,3,5,15,16]. Many practical structures are subjected not only to static and quasistatic loads, but also to certain dynamic¯uctuating ones called the quasiperiodic dynamic loads, see [15]), such as action of working machines and transport upon the structure. As we shall see, at certain frequency ranges, the¯uctuating loads can become critical for a plate, even at relatively small amplitudes. In such cases, the plastic limit design should be replaced by the safer shakedown design, that is, the approach we follow in this work. 2The reduced ki...

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Dynamic shakedown analysis and bounds for elastoplastic structures with nonassociative, internal variable constitutive laws

Cited by 54 publications

References 38 publications

Shakedown analysis of defective pressure vessels by a kinematic approach

Shakedown analysis of defective pressure vessels by a kinematic approach

Shakedown of elastic-perfectly plastic materials with temperature-dependent elastic moduli

Failure of a circular reinforced concrete plate against dynamic fluctuating loads

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