Ultimate strength of submarine pressure hulls with failure governed by inelastic buckling

The analysis of submarine pressure hull assumes great importance among structural engineers due to the complexity involved in the collapse mechanism of stiffened shell structures. In most of the cases, the failure of stiffened shell structures occurs due to elastic buckling. But for some combinations of shell-stiffener geometry and material characteristics, the structure can fail by inelastic buckling, for which the methods of analysis are meagre. In this paper, the analysis of submarine pressure hull structure in which the failure gets governed by inelastic buckling is demonstrated. Three different approaches have been employed to investigate the ultimate strength of the ring stiffened submarine pressure hull structure with inelastic buckling modes of failure. The methods used are ‘Johnson–Ostenfeld inelastic correction’, ‘imperfection method’ and ‘finite element approach’. A typical submarine shell structure has been analysed for the inelastic buckling failure using these three approaches and the results are discussed.     

Buckling analysis of trapezoidally corrugated panels using spline finite strip method

Buckling of trapezoidally corrugated panels under in-plane loading is analyzed by a spline finite strip method. The influence on the elastic buckling load of various parameters, such as geometry. loading forms and boundary conditions, etc., is studied. It is found that: (1) for longitudinal compression the buckling load increases with the corrugation angle α, and for a given α the highest buckling load is achieved when the ‘proportion parameter’ γ = 1; (2) for shear loading the buckling load increases as α increases, and for a given α the highest buckling load is obtained when γ = 2; and (3) for a combined loading of compression and shear, interactive curves can be approximated by unit circles when α = 15°, 30°, 45°, 60° and 90°. However, when α = 75° a parabola seems to be a better approximation. Based on the numerical experiments, simplified formulae and interactive curves are suggested for practical design.     

GBT formulation to analyse the buckling behaviour of thin-walled members with arbitrarily ‘branched’ open cross-sections

This paper presents the derivation, validates and illustrates the application of a Generalised Beam Theory (GBT) formulation developed to analyse the buckling behaviour of thin-walled members with arbitrarily ‘branched’ open cross-sections. Following a brief overview of the conventional GBT, one addresses in great detail the modifications that must be incorporated into its cross-section analysis procedure, in order to be able to handle the ‘branching’ points — they concern mostly issues related to (i) the choice of the appropriate ‘elementary warping functions’ and (ii) the determination of the ‘initial flexural shape functions’. The derived formulation is then employed to investigate the local-plate, distortional and global buckling behaviour of (i) simply supported and fixed asymmetric E-section columns and (ii) simply supported I-section beams with unequal stiffened flanges. For validation purposes, several GBT-based results are compared with ‘exact’ values, obtained by means of finite strip or shell finite element analyses.     

Buckling behavior of cold-formed zed-purlins partially restrained by steel sheeting

This paper presents a study on the buckling behaviour of purlin-sheeting systems under wind uplift loading. The restraint provided by the sheeting to the purlin is modeled by using two springs representing the translational and rotational restraints. The analysis is performed using finite strip methods in which the pre-buckling stress is calculated based on the same model used for the buckling analysis rather than taken as the ‘pure bending’ stress. The results obtained from this study show that, for both local and distortional buckling, the restraints have significant influence on the critical loads through their influence on the pre-buckling stress rather than directly on the buckling modes. While for lateral-torsional buckling, the influence of the restraints on the critical loads is mainly due to their influence on the buckling modes rather than the pre-buckling stress.     

Some thoughtd on mode interaction in thin-walled columns under uniform compression

Interaction of nearly simultaneous buckling modes in the presence of imperfections is studied. The investigation is concerned with thin-walled trapezoidal columns under uniform compression. The asymptotic expansion established by Byskov and Hutchinson is also used here. The present paper is devoted to an improved study of the equilibrium path in the initial post-buckling behaviour of imperfect structures. The results obtained include the effect of interaction of the ‘primary’ local mode and a ‘secondary’ local mode having the same wavelength as the primary. In this paper the analysis of a few buckling mode interactions is presented.     

Towards a rationally based elastic-plastic shell buckling design methodology

The ‘reduced stiffness method’ for the analysis of shell buckling was developed to overcome a trend towards increasingly sophisticated analysis that has become divorced from its basically simple underlying physics. This paper outlines the developments of the reduced stiffness method from its origins in the late 1960s, through its experimental confirmation, generalisation and elaboration over the past 20 years, to its more recent consolidation using carefully controlled non-linear numerical experiments. It is suggested that the method has now reached a stage where it could profitably be adopted as a basis for an improved shell buckling design methodology.     

Buckling of wide struts/plates resting on isotropic foundations

Starting from an Airy stress function in plane strain a new solution is presented for the buckling of plates on elastic foundations with in-plane loading. Saint Venant's Principle is shown to play an important part in plate buckling behaviour when ‘deep’ foundations are present. Results are compared with those from Winkler's and Pasternak's models and they demostrate that, provided certain restrictions are satisfied, the latter can give reasonably accurate results.     

Numerical methods in rock mechanics

The purpose of this CivilZone review paper is to present the techniques, advances, problems and likely future development directions in numerical modelling for rock mechanics and rock engineering. Such modelling is essential for studying the fundamental processes occurring in rock, for assessing the anticipated and actual performance of structures built on and in rock masses, and hence for supporting rock engineering design. We begin by providing the rock engineering design backdrop to the review in Section 1. The states-of-the-art of different types of numerical methods are outlined in Section 2, with focus on representations of fractures in the rock mass. In Section 3, the numerical methods for incorporating couplings between the thermal, hydraulic and mechanical processes are described. In Section 4, inverse solution techniques are summarized. Finally, in Section 5, we list the issues of special difficulty and importance in the subject. In the reference list, ‘significant’ references are asterisked and ‘very significant’ references are doubly asterisked.     

Flexibility of mechanical fastenings of very thin-walled steel structures

Normal calculations of flexibility as a deformation characteristic of fastenings disregard the plastic response of screwed fastenings of very thin-walled steel structures. Preliminary tests have, however, shown that, unlike bolted fastenings in thick-walled steel structures, in screwed fastenings of very thin-walled steel structures the occurence of considerable plastic deformations can be observed from the beginning of loading. These should not be generally neglected in establishing the design characteristics of fastenings, i.e. design strength and design flexibility. This paper deals with cases in which an approximate value of ‘elastic flexibility’ can be used with sufficient accuracy, and how the analysis may be made more accurate by taking into account ‘elasto-plastic flexibility’.Extensive experimental research into the behaviour of screwed fastenings of very thin-walled steel structures subjected to non-repeated loading, repeated fluctuating and reversed loading, and multi-level loading simulating wind loading has been carried out, and ‘elastic flexibilities’ of selected fastenings have been established. At the same time, conditions for their application taking into account the elasto-plastic behaviour of fastenings subjected to repeated loading have been determined.     

The effects of connector spacing and distribution on the buckling behaviour of some single-cell and twin-cell box columns

Results are presented from a series of compression tests carried out on geometrically similar single-cell and twin-cell thin-walled box columns made by joining thin flat sheets together with rivet connectors. In particular a study has been made of the effect of changing the connectors' spacing and distribution on a column's initial buckling stress.The results show that the single-cell columns responded least to the changes and this appeared to be related to the geometry of the constituent plates. Significant differences were observed, however, with the twin-cell columns. Higher initial buckling loads were obtained from columns that had been made by using a ‘staggered’ connector distribution pattern as compared with those made by using a more ‘regular’ pattern. This result appeared to depend on the development of a skewed local buckling mode between the connectors.     

Fabrication of small models of large cylinders with extensive welding for buckling experiments

Cylindrical shells in large steel silos and tanks are commonly constructed from a large number of curved panels joined by many circumferential and meridional welds (referred to as the panel method hereafter). The extensive use of welding in these shells is a unique feature not previously studied in laboratory buckling experiments due to the great difficulty in fabricating realistic small-scale model shells. This paper presents an innovative technique for the fabrication of small models of such large steel cylindrical shells constructed from many welded panels. The experimental set-ups to implement this technique in the laboratory are also described. The new technique consists of two stages: (a) production of a high quality model by rolling two sheets (or a single sheet) and welding along the meridional seams; and (b) ‘welding’ in the form of controlled heat input in a required pattern of circumferential and meridional ‘welds’ on the central portion of the shell surface. The imperfections in an example specimen are also examined to show that they have a realistic pattern. The observed buckling behavior of this specimen is presented and discussed. The specimen buckled at a very low load, confirming that the welding-induced imperfections in such shells are severely detrimental to the buckling strength.     

Project conceptualization using pragmatic methods

An important and difficult part of project management is the conceptualization stage – particularly when dealing with multiple powerful stakeholders and ‘messy’ situations. Pragmatism provides a way forward that makes central the ‘concepts’ being used to conceptualize the project (e.g. ‘timeliness’ or ‘sustainability’). This paper argues for a sequence of two approaches suggested in the literature that combine this pragmatism and soft systems thinking to conceptualize projects. These are Alexander’s ‘Synthesis’ [1] and Checkland’s ‘CATWOE’ [2]. The first identifies concepts or worldviews, the second uses these to draft a series of ‘what needs to be done’ statements. In the way of Pragmatic Systems Inquiry, these approaches suggested from the literature are then compared to a real case study: the LC-25 project.     

Numerical and experimental investigations of the response of aluminum cylinders with a cutout subject to axial compression

Understanding how a cutout influences the load bearing capacity and buckling behavior of a cylindrical shell is critical in the design of structural components used in automobiles, aircrafts, and marine applications. Numerical simulation and analysis of moderately thick and thin unstiffened aluminum cylindrical shells (D/t=45, 450 and L/D=2, 5, 10), having a square cutout, subjected to axial compression were systematically carried out in this paper. The investigation examined the influence of the cutout size, cutout location, and the shell aspect ratio (L/D) on the prebuckling, buckling, and postbuckling responses of the cylindrical shells.An experimental investigation on the moderately thick-walled shells was also carried out. A good correlation was observed between the results obtained from the finite element simulation and the experiments. Furthermore, empirical equations, in the form of a ‘buckling load reduction factor’ were developed using the least square regression method. These simple equations could be used to predict the buckling capacities of several specific types of cylindrical shells with a cutout.     

The application of ‘least-cost’ modelling as a functional landscape model

The growing awareness of the adverse effects of habitat fragmentation on natural systems has resulted in a rapidly increasing number of actions to reduce current fragmentation of natural systems as well as a growing demand for tools to predict and evaluate the effect of changes in the landscape on connectivity in the natural world. Recent studies used ‘least-cost’ modelling (available as a toolbox in GIS-systems) to calculate ‘effective distance’, a measure for distance modified with the cost to move between habitat patches based on detailed geographical information on the landscape as well as behavioural aspects of the organisms studied. We applied the method to a virtual landscape and a small scaled agricultural system subject to different scenarios in a land re-allotment project. We discuss the importance of technical aspects and ecological assumption underlying this modelling method. The model is shown to be a flexible tool to model functional connectivity in the study of the relation between landscape and mobility of organisms as well as in scenario building and evaluation in wild life protection projects and applied land management projects. Since ‘effective distance’ has the same units as Euclidean distance (m), this effective distance may be a straightforward way to include landscape and behavioural aspects in other models which include distance as a measure for isolation. We show the importance of the ‘ecological’ quality of the input maps and the choice of relevant landscape features and resistance values.     

Continuous accountability for acceptable building performance

Complexities in building technology when not fully understood, have resulted in a less than favorable aggregate impact on the building's environment. A surprisingly high portion of U.S. non-industrial buildings do not provide satisfactory task environments. Developments in computer technology have infused new thought processes in the way we plan, design, build and operate our buildings. This paper proposes a social and technical use of Knowledge-based-systems (KBS) for continuous accountability to assure healthy buildings. Diagnostics, as an emerging discipline in building design and operation, is also discussed. A proposed framework for such accountability and the resulting ‘chain of custody’, that draws on the medical paradigm and associated diagnostic procedures is presented. It is suggested that KBS also be used for the development and interpretation of criteria for evaluating building performance from initial conception through design, construction and operation. Thus, KBS is expected to aid in the analysis of ‘virtual’ and ‘actual’ buildings that may be ‘sick’ or ‘healthy’. It is proposed that for a building to provide satisfactory performance over its life-time, the ‘life-cycle’ concept must be modified in terms of the roles, responsibilities, and configuration of the building team, and in terms of its costing procedures.     

Design procedure for the buckling analysis of reinforced concrete shells

The paper presents a simple procedure to establish the buckling load of shell structures. It is essentially based on the assumption that the various factors influencing buckling can be assessed as multipliers of the ‘classical’ critical load.

These factors are: imperfections, creep, plasticity, cracks and the steel reinforcement. The paper gives the values of these factors, thus establishing a method which can be used in practical design.     

Stochastic imperfection modelling in shell buckling studies

One possible avenue that may improve design against buckling is to recognise and account for the random nature of initial geometric imperfections introduced by manufacturing. This paper presents the application of a probabilistic methodology to the design and analysis of cylindrical shells under axial compression. Results from two cases are presented and compared: the first involves stringer-stiffened steel cylinders failing elastoplastically, whereas the second examines unstiffened composite cylinders buckling elastically. In both cases, the method is underpinned by statistical analysis of imperfections measured on nominally identical specimens. Nonlinear FE analysis is used for strength assessment and the results of the statistical analysis are introduced in the imperfection modelling. It is demonstrated that the method has advantages over code design based on ‘lower bound’ curves, in terms of the calculated buckling loads but also in offering a systematic and rational way by which randomness in imperfections can be assessed.     

Optimum stiffened panel design with fundamental frequency constraint

A generic analysis/design method for prismatic plate assemblies, using exact plate stiffnesses which are transcendental functions of loading and/or vibration frequency, has long been validated by the established program . Hitherto vibrations were permitted only in analysis because design uses the Wittrick–Williams algorithm to modify the design predicted by a linear optimiser to be ‘just stable’ by scaling all layer thicknesses by F. This works because buckling loads, unlike the fundamental frequency f₁, vary monotonically with F. The paper considers additionally scaling all plate breadths by F^α such that the buckling loads and f₁ all vary monotonically with F. Theoretical consideration of simple limiting cases establishes bounds on the permitted values of α as 0.1≤α≤0.4. Then results for typical stiffened panels demonstrate the method to be correct and are used to investigate the value of α which is most effective in returning stabilised designs of least mass and with least computation.     

Recent research advances on ECBL approach.: Part I: Plastic–elastic interactive buckling of cold-formed steel sections

The objective of this two parts paper is to present some recent developments and applications of erosion of critical bifurcation load (ECBL) approach for the interactive buckling. Two different types of problems are analysed: (1) plastic–elastic interactive buckling which implements into the Ayrton–Perry interaction formula the plastic strength of the stub columns evaluated by means of local plastic mechanism analysis, and (2) elastic–elastic interactive buckling for members with perforations.The first part of the paper analyses the occurrence of local plastic mechanisms in cold-formed steel sections in compression, and how they can be implemented in the ultimate limit state analysis of the members. Actually, the failure of thin-walled cold-formed members in compression always occurs with a local plastic mechanism. Starting from this observation, the authors suggest to use in the interactive local-overall buckling analysis the sectional plastic mechanism strength instead of traditional ‘effective section’. The ECBL approach is used to implement the proposed interactive buckling model. Results are compared with those of other two recent methods, namely the direct strength method and plastic effective width approach. Relevant tests are used to evaluate the three methods. Comparisons with European and American design codes are also presented in the paper.     

An investigation into non-linear interaction between buckling modes

This paper is a contribution to the understanding of the interaction between overall lateral-torsional buckling and local buckling of a beam under transverse loading. It concentrates on the case where the critical load for local buckling is smallest. Three approaches have been used: numerical analysis using the asymptotic theory; a qualitative analysis using an a priori simple discrete model; and experiments. The study suggests that just three modes in the asymptotic analysis are adequate to describe the interactive behaviour. The resulting reduced potential energy expression is quite similar to that of the a priori simple discrete model and provides insight into the destabilizing phenomenon. The experiments confirm these results.