Stability in Shells

Croll, James

doi:10.1007/s11071-006-0744-z

Cited by 14 publications

(7 citation statements)

References 13 publications

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“…The above reported studies have suggested that the axial load buckling behaviour of the isotropic cylinder can be viewed as simply a rather special case of the behaviour displayed by shells constructed from orthotropic fibre-reinforced composite materials. This echoes earlier suggestions that the behaviour of rib-reinforced cylinders could equally be seen as a generalization of the behaviour of the isotropic cylinder [1–6,31–32]. But what recent work exploiting the potential of ‘high-fidelity’ numerical experimentation shows, when interpreted within the framework of classical and its RS extension, is that this behaviour can be presented in a form of potential importance for design.…”

Section: Towards a Systematic Design Approachsupporting

confidence: 82%

Comments on effective use of numerical modelling and extended classical shell buckling theory

Croll

2023

Proc. R. Soc. A.

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This paper argues that in the understandable enthusiasm to use the now readily available high-fidelity numerical software allowing the analysis of the complexities of shell buckling, and especially the notorious case of the axially loaded cylinder, there has been insufficient consideration of classical shell buckling theory and its more recent reduced stiffness extension. If future design is to be able to effectively exploit the potential benefits of the use of advanced composite materials and/or the use of rib reinforcement, it is suggested that these numerically driven research programmes would benefit from more explicit integration within the framework of classically extended buckling theory. This suggestion is reinforced in what follows by highlighting the results from a longstanding research programme in which classically extended buckling theory has been demonstrably enhanced through its integration with reliable numerical experimentation. This enhancement has helped to resolve a number of important issues including: identification of the most critical forms of imperfection affecting the buckling loads; how the most critical knockdown factors are influenced by changes in the shells' geometric and material characteristics and how safe design might be more explicitly related to the prescribed levels of geometric tolerances. Recommendations are made as to how such integrated research programmes could in the future further enhance our ability to design materially efficient shells against buckling.

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Section: Towards a Systematic Design Approachsupporting

confidence: 82%

Comments on effective use of numerical modelling and extended classical shell buckling theory

Croll

2023

Proc. R. Soc. A.

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“…The lower bound is found when the membrane energy part is eliminated. In a series of papers for several cases [25,[62][63][64], the merits of the method were demonstrated. It was also shown [65] that the lower bounds determined by a slightly modified form of this method agree very well with experimental lower bounds.…”

Section: Postbuckling Behaviour and Lower Boundsmentioning

confidence: 99%

Buckling of metallic shells: Buckling and postbuckling behaviour of isotropic shells, especially cylinders

Edlund

2007

Struct. Control Health Monit.

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The large discrepancies between observed buckling loads for thin shells and the predictions of the classical theory have been a great challenge to many researchers since the 1920s. In this paper, the basic behaviour and characteristics are described and recent research, mainly from the last 10 years, is reviewed. The focus is on cylindrical shells and on the influence of initial imperfections on the buckling behaviour.Examples of recent surveys in the field, each with a certain bias, are [1][2][3][4]. The first and the last both deal with imperfections in real structures and numerical buckling analysis and simulation. The second one, by Rotter, focuses on cylindrical steel shell structures like silos and tanks with relationship to the Eurocode. The third one, by Schmidt, gives an outline of several problems for steel shells, especially on approaches to a numerically based stability design. The fourth relates to applications in aerospace structures, including composite shells and reliability-based design. For a specialized review on stochastic buckling or 'uncertain buckling', see [5]. For an outline of buckling phenomena, including shell types not covered by the present paper see [6].Books: The now classic books by Bushnell [7] on computerized shell buckling and by Yamaki [8] on buckling of elastic cylinders are recommended reading. The shell stability handbook [9] treats various important shell buckling problems of practical interest. The German compilation of stability problems for civil engineering shells of revolution [10] is in handbook style and mainly deals with cylindrical, conical and spherical shells. Volume 2 of the monumental work on experimental buckling of thin-walled structures by Singer et al. [11] contains two chapters devoted to shell buckling experiments and five chapters partly dealing with that subject. A recent book by 16 authors on the stability of thin metal shells [12] is certainly essential reading. It has a focus on cylindrical shells and covers several different aspects of buckling behaviour and applications to real civil engineering shell structures. The first chapter [13], by Teng and Rotter, is a comprehensive overview on the buckling of thin shells with almost 400 references.Eurocodes: As an example of codes, the Eurocode will be briefly discussed. The most recent editions of the European design code for metal shell structures are the Draft Eurocode 3, Part 1.6 (European Prestandard ENV) published in 1999 [2,3] and the thoroughly revised EN 1993-1-6, Eurocode 3, Part 1.6 issued in 2005 [14,15]. Rotter [2] also refers to older codes and standards both of the generic type, i.e. intended for a whole class of structures of a common form, and of the application type, i.e. intended for a certain structural type, such as tanks or silos. The new EN of 2005 [14] permits all forms of analysis and should be fully general for all kinds of thinwalled metal shells. The Eurocode defines two reference strengths: the 'elastic critical resistance' R cr , computed by a linear bifurcation analysis (...

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“…The Reduced Energy Analysis (REA) has been described by Croll and co-workers [27,28], and a slightly different formulation was given in Ref. [37].…”

Section: Reduced Energy Analysis (Rea)mentioning

confidence: 99%

“…The best readings reviewing the lower bound approach were presented by Croll as a design methodology [27,28] in which details of the motivations and achievements at each stage are discussed in an amenable way.…”

Section: Introductionmentioning

confidence: 99%

A penalty approach to obtain lower bound buckling loads for imperfection-sensitive shells

Godoy

Jaca

Sosa

et al. 2015

Thin-Walled Structures

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Stability in Shells

Cited by 14 publications

References 13 publications

Comments on effective use of numerical modelling and extended classical shell buckling theory

Comments on effective use of numerical modelling and extended classical shell buckling theory

Buckling of metallic shells: Buckling and postbuckling behaviour of isotropic shells, especially cylinders

A penalty approach to obtain lower bound buckling loads for imperfection-sensitive shells

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