60 results found
Mansour S, Silvestri S, Sadowski A, 2022, The ‘miniature silo’ test: a simple experimental set-up to estimate the effective friction coefficient between the granular solid and a horizontally-corrugated cylindrical metal silo wall, Powder Technology, Vol: 399, ISSN: 0032-5910
Corrugated walls are widely employed in the construction of metal silos. Despite the long history of testing to establish bulk material parameters for silo design, there does not appear to be an established test procedure to directly determine the effective friction coefficient for a corrugated wall other than an adaptation of a classical direct shear test. EN 1991-4: 2006 prescribes a simple weighted average formula for this coefficient based on the internal friction angle of the granular solid and a ‘flat’ wall friction coefficient. This paper describes a set of miniature-scale silo tests performed at the University of Bologna intended to establish a simple but useful procedure to directly estimate an average global friction coefficient between the granular solid and a corrugated silo wall. These ‘miniature silo’ tests are simple enough to be performed in any civil engineering laboratory with standard equipment.
Silvestri S, Mansour S, Marra M, et al., 2022, Shaking table tests of a full-scale flat-bottom manufactured steel silo filled with wheat: main results on the fixed-base configuration, Earthquake Engineering and Structural Dynamics, Vol: 51, Pages: 169-190, ISSN: 0098-8847
This paper reports on a series of shaking table tests on a full-scale flat-bottom steel silo filled with soft wheat, characterized by aspect ratio of around 0.9. The specimen was a 3.64-m diameter and 5.50-m high corrugated-wall cylindrical silo. Multiple sensors were used to monitor the static and dynamic response of the filled silo system, including accelerometers and pressure cells. Numerous unidirectional dynamic tests were performed consisting of random signals, sinusoidal inputs, and both artificial and real earthquake records. The objectives of this paper are (i) to provide a general overview of the whole experimental campaign and (ii) to present selected results obtained for the fixed-base configuration. The measured data were processed to assess the static pressures, the dynamic overpressures (related to the effective mass) and the accelerations of monitored points on the silo wall, and to identify the basic dynamic properties (fundamental frequency of vibration, damping ratio, dynamic amplification factors) of the filled silo. The main findings are discussed and compared with the predictions given by available theoretical models and code provisions. It is found that the fundamental frequency slightly decreases with increasing acceleration, while it slightly increases with increasing compaction of the granular material. For close-to-resonance input, the dynamic amplification (in terms of peak values of accelerations) increases along the height of the silo wall up to values of around 1.4 at the top surface of the solid content. The dynamic overpressures appear to increase with depth (differently from the EN1998-4 expectations), and to be proportional to the acceleration.
Sadowski AJ, Rotter JM, Nielsen J, 2021, A theory for pressures in cylindrical silos under concentric mixed flow, CHEMICAL ENGINEERING SCIENCE, Vol: 230, ISSN: 0009-2509
Sadowski A, Rotter JM, Nielsen J, 2020, A theory for pressures in cylindrical silos under concentric mixed flow, Chemical Engineering Science, Vol: 223, ISSN: 0009-2509
This paper presents a theory for the prediction of pressures in circular silos under concentric mixed flow, assuming an internal flow channel of conical profile with straight but inclined sides. The theory is based on a generalised application of the classical method of ‘slice equilibrium’ together with additional assumptions based on a treatment of the granular solid as a Coulombic material. Only one of the resulting pair of coupled linear ordinary differential equations may be solved in closed form, while both numerical and approximate closed-form solutions are explored for the other. The derivation of the theory is presented in full and a series of parametric studies explores the predictions and compares these with qualitative observations from experiments. In particular, the significant overpressure that is known to occur at the ‘effective transition’, where the internal flow channel intersects with the silo wall, may be estimated quantitatively for the first time.
Sadowski A, Wei Jun W, Simon Li SC, et al., 2020, Critical buckling strains in thick cold-formed circular hollow sections under cyclic loading, ASCE Journal of Structural Engineering, Vol: 146, Pages: 1-13, ISSN: 0733-9445
Contrary to the large dataset of test results exploring the monotonic bending response of steel tubes, the corresponding dataset of cyclic bending tests remains very small. Seven compact and semi-compact S355J2H cold-formed circular hollow sections with diameter to thickness (D/t) ratios between 20 to 60, representative of piles used in piers and wharves, were brought to failure in three-point cyclic bending tests. Digital Image Correlation was employed to estimate average cross-sectional curvatures, and hence the critical bending strains, during local buckling at the midspan plastic hinges. These estimates were compared against those from two simplified localised hinge models and differed by up to a factor of two. A parametric study was performed with a validated finite element model to ascertain the suitability of proposed design equations at predicting critical strains in piles with D/t from 20 to 60 under cyclic loading. Test and simulation data both show that critical buckling strains are lower under cyclic loading than under monotonic loading. This work can inform the future development of seismic design standards such as ASCE 61-14.
Wang J, Sadowski A, 2020, Elastic imperfect cylindrical shells of varying length under combined axial compression and bending, Journal of Structural Engineering, Vol: 146, Pages: 04020014-1-04020014-12, ISSN: 0733-9445
This paper presents a comprehensive computational investigation into the elastic nonlinear buckling response of near-perfect and highly imperfect uniform thickness thin cylindrical shells of varying length under combined uniform compression and bending. In particular, the elastic ovalisation phenomenon in cylindrical shell of sufficient length under combined compression and bending was systematically investigated with finite elements for the first time. The study considered a representative range of practical lengths up to very long cylinders where ovalisation is fully developed under uniform bending and Euler column buckling controls under uniform axial compression. The imperfection sensitivity of the system was also studied by introducing a single idealised axisymmetric weld depression imperfection at the midspan of the cylinder. The predictions permit an exploration of the nonlinear mechanics of the generally unfavourable interaction between bending and axial compression at the elastic nonlinear buckling limit state in thin long cylinders. The interaction is at its most unfavourable in cylinders where Euler column buckling is about to become critical, and is qualitatively very different from the favourable moment-force interaction at the reference plastic limit state of circular tubes. A simple closed-form algebraic characterisation of the interaction is proposed considering both imperfections and ovalisation.
Wang J, Fajuyitan OK, Orabi MA, et al., 2020, Cylindrical shells under uniform bending in the framework of Reference Resistance Design, Journal of Constructional Steel Research, Vol: 166, ISSN: 0143-974X
The resistance of cylindrical shells and tubes under uniform bending has received significant research attention in recent times, with a number of major projects aiming to characterise their strength through both experimental and numerical studies. However, the investigated cross-section slenderness ranges have mostly addressed low radius to thickness ratios where buckling occurs after significant plasticity and the influence of geometric imperfections is relatively minor. The behaviour under uniform bending of thinner imperfection-sensitive cylinders that fail by elastic buckling was largely omitted, as was the influence of finite length effects. The value of such resistance models that are only useful for thicker cylinders is therefore somewhat limited.This paper offers the most comprehensive known characterisation of the buckling and collapse resistance of isotropic cylindrical shells and tubes under uniform bending. Expressed within the modern framework of Reference Resistance Design (RRD), it holistically incorporates the effects of material plasticity, geometric nonlinearity and sensitivity to realistic and damaging weld depression imperfections. The characterisation was made possible by the authors' recently-developed novel methodology for mass automation of nonlinear shell buckling finite element analyses. A modification of the RRD formulation is proposed which facilitates its application to systems of low slenderness, and offers a compact algebraic characterisation of all potential imperfection amplitudes for this common shell structural condition. A reliability analysis is also performed.
Meng X, Gardner L, Sadowski A, et al., 2020, Elasto-plastic behaviour and design of semi-compact circular hollow sections, Thin Walled Structures, Vol: 148, Pages: 1-12, ISSN: 0263-8231
Previous research has revealed shortcomings in the current Eurocode 3 (EC3) provisions for the design of semi-compact (Class 3) cross-sections. These shortcomings arise primarily from the lack of utilisation of partial plastification in bending, leading to a step in the design resistance function at the boundary between Class 2 and 3 cross-sections and an underestimation of the available capacity. This affects the accuracy of resistance predictions in bending and under combined loading, and applies at both cross-sectional and member level. To address this issue, the use of an elasto-plastic section modulus, which lies between the plastic and elastic section moduli, has been proposed and employed in the design of semi-compact I- and box sections. The aim of the present study is to develop new cross-section and member buckling design rules incorporating the elasto-plastic section modulus for semi-compact circular hollow sections (CHS), and to assess their accuracy against existing experimental and freshly generated numerical data. Firstly, an experimental database, consisting of previous cross-section and member buckling test results on steel CHS, was established. A comprehensive numerical simulation programme was subsequently carried out; in this programme, finite element (FE) models were developed, validated and used for parametric studies, where over 600 numerical structural performance data on semi-compact CHS were generated. New sets of cross-section and member buckling design expressions featuring elasto-plastic section properties were then proposed and assessed against the test and numerical data. The proposals were shown to offer improved accuracy and design efficiency over the elastic EC3 methods. The reliability of the proposed elasto-plastic design rules was then confirmed through statistical analyses in accordance with EN 1990, demonstrating their suitability for inclusion into the next revision of EN 1993
Kotsovinos P, Atalioti A, Rein G, et al., 2020, Analysis of the thermomechanical response of structural cables subject to fire, Fire Technology, Vol: 56, Pages: 515-543, ISSN: 0015-2684
Cable-supported structures such as bridges and stadia are critical for the surrounding community and the consequences arising from a major fire event can be substantial. Previous computational studies into the thermal response of cables often employed simplistic heat transfer models that assumed lump capacitance or cross-sectional homogeneity without proof of validity. This paper proposes a methodology for calculating the thermal response of a cable cross-section allowing for heat transfer by conduction through each strand contact surface and radiation across inter-strand cavities. The methodology has been validated against two experiments of cables subjected to radiant heating and an input sensitivity analysis has been undertaken for the heat transfer and material parameters. The approach is compared against simple heat transfer lumped methods for a parallel-strand cable where it is shown that these lumped models are not always conservative. The model is then coupled with a two-dimensional generalised plain strain model to study the likely effect of the cross-sectional temperature gradients on the mechanical response. The study considers three qualitatively different hydrocarbon jet fire scenarios, both with and without external insulation for fire protection. It is shown that the proposed methodology can reproduce realistic cross-sectional temperature distributions with up to 50% temperature difference at the cable external surface and can capture the phenomenon of load shedding in a gradually heated cable. It is also shown that assuming a lumped thermal mass neglects the possibility of moment-inducing temperature gradients which are not considered in the ambient design of cables that is driven by tensile capacities. The proposed model and its predictions contribute towards an improved understanding and a more informed structural design of cable-supported structures in fire.
Subsea pipelines and PIP systems experience large bending moments during installation andoperation. However, unlike single-walled pipelines, the behaviour of PIPs under bending hasbeen only marginally addressed. In the current study, the bending response of PIP systems withdiameter-to-thickness ratio (D/t) of 15 to 40 is investigated. Linear bifurcation analyses (LBA)and geometrically nonlinear analyses (GNA) are conducted on PIPs of varying lengths.Analytical expressions are provided to predict the classical and nonlinear limit moments ofPIPs, and are compared to existing expressions for single-walled pipelines. Ultimate bendingmoments of PIPs are obtained from physical four-point bending tests and are compared againstgeometrically and materially nonlinear analyses (GMNA). The finite element results show thatin PIPs with centralizers, the limit moments (GNA) drop slightly, however, the ultimatemoments (GMNA) remain unchanged. A parametric study of the effect of geometry andmaterial properties of the inner and outer pipes on the ultimate moment of PIPs is presented. Itis understood that the ultimate moments of PIPs with thick tubes are predominantly influencedby the material nonlinearities rather than ovalization of the tubes.
Sadowski A, 2019, On the advantages of hybrid beam-shell structural finite element models for the efficient analysis of metal wind turbine support towers, Finite Elements in Analysis and Design, Vol: 162, Pages: 9-33, ISSN: 0168-874X
Metal wind turbine support towers are very tall and slender shell structures designed to exhibit a stepwise varying distribution of optimised wall thicknesses, with strakes in the upper regions of the tower usually being much thinner than those in the lower regions. Each strake is an individual shell and potentially a critical location for failure, and as the failure location is rarely obvious in advance each strake in theory requires careful meshing in a finite element analysis. It is not unusual for over twenty individual strakes to be present in a design, and the computational cost involved in modelling such a structure with finite elements, particularly in nonlinear analyses, can quickly become prohibitive for execution on a personal workstation. Compromises in mesh resolution must often be made, usually to the detriment of the quality of the global solution.This paper explores a simple hybrid beam-shell modelling technique that permits an efficient and insightful analysis of multi-strake wind turbine support towers. It consists of modelling all but a handful of the strakes with beam elements or rigid bodies which have a negligible computational cost compared to shell elements, and to focus the deployment of expensive shell elements only on strakes of interest as part of a resistance assessment. As only strakes meshed with shell elements participate in a failure mechanism, the technique allows the realistic exploration of the relative criticality of all tower strakes. The technique is illustrated on a real design of a 1.5 MW 25-strake wind turbine tower.
Liu Q, Sadowski AJ, Rotter JM, 2019, Ovalization restraint in four-point bending tests of tubes, Journal of Engineering Mechanics - ASCE, Vol: 145, ISSN: 0733-9399
Four-point bending tests have been a staple in many structural engineering experiments as a reliable way of assessing the bending resistance of circular hollow sections, tubes and cylindrical shells, and they continue to be widely performed. However, relatively little attention appears to have been paid to quantify the effects of different boundary conditions on the test outcome. In particular, the restraint or freedom given to the cross-section at the ends of the specimen to ovalize can have a significant impact when the specimen is in an appropriate length range. Ovalization is an elastic geometrically nonlinear phenomenon that is known to reduce the elastic bending resistance by as much as half in long tubes or cylinders. This paper presents a short distillation of some recent advances in understanding the buckling of cylindrical shells under uniform bending, identifying the strong influence of the cylinder length on cross-section ovalization. A sample set of three-dimensional load application arrangements used in existing four-point bending tests was simulated using finite elements, allowing an assessment of the differences caused by pre-buckling ovalization and its effect on the tested bending resistance. The study is limited to elastic behaviour to identify the effect of ovalization alone in reducing the stiffness without material nonlinearity. The outcomes demonstrate that maintaining circularity at the inner load application points by appropriate stiffening has a significant effect. With freedom to ovalize, a significant reduction in stiffness occurs, leading to much lower bending resistance at buckling than may be achievable in practical applications.
Fajuyitan OK, Sadowski AJ, 2018, Imperfection sensitivity in cylindrical shells under uniform bending, Advances in Structural Engineering: an international journal, Vol: 21, Pages: 2433-2453, ISSN: 1369-4332
Efforts are ongoing to characterise a comprehensive resistance function for cylindrical shells under uniform bending, a ubiquitous structural system that finds application in load-bearing circular hollow sections, tubes, piles, pipelines, wind turbine support towers, chimneys and silos. A recent computational study by Rotter et al. demonstrated that nonlinear buckling of perfect elastic cylinders under bending is governed by four length-dependent domains –‘short’, ‘medium’, ‘transitional’ and ‘long’– depending on the relative influence of end boundary conditions and cross-sectional ovalisation. The study additionally transformed its resistance predictions into compact algebraic relationships for use as design equations within the recently developed framework of reference resistance design. This article extends on the above to present a detailed computational investigation into the imperfection sensitivity of thin elastic cylindrical shells across the most important length domains, using automation to carry out the vast number of necessary finite element analyses. Geometric imperfections in three forms – the classical linear buckling eigenmode, an imposed cross-sectional ovalisation and a realistic manufacturing ‘weld depression’ defect – are applied to demonstrate that imperfection sensitivity is strongly length dependent but significantly less severe than for the closely related load case of cylinders under uniform axial compression. The axisymmetric weld depression almost always controls as the most deleterious imperfection. The data are processed computationally to offer an accurate yet conservative lower-bound algebraic design characterisation of imperfection sensitivity for use within the RRD framework. The outcomes are relevant to researchers and designers of large metal shells under bending and will appeal to computational enthusiasts who are encouraged to adopt the automation
Wang J, Sadowski AJ, Rotter JM, 2018, Influence of ovalisation on the plastic collapse of thick cylindrical tubes under uniform bending, International Journal of Pressure Vessels and Piping, Vol: 168, Pages: 94-99, ISSN: 0308-0161
An accurate assessment of the bending resistance of thick cylindrical metal tubes is necessary for the safe and efficient design of pipelines, piles, pressure vessels, circular hollow sections and other common tubular structures. Bending tests continue to be widely performed as part of many engineering research programmes, but despite their ubiquity they often generate results that are difficult to interpret. Discrepancies from the attainment of the classical full plastic moment are common and often attributed to a mixture of ovalisation, local buckling, imperfections and strain hardening. However, the effects of these phenomena are yet to be quantified in isolation, even for a system as classical as a cylinder under uniform bending.The goal of this computational study is to quantify the extent to which geometrically nonlinear effects, specifically ovalisation and bifurcation buckling, may depress the resistance of a thick perfect cylinder under uniform bending that would otherwise be expected to attain the full plastic moment. Simulations are performed using two- and three-dimensional finite element models with a simple ideal elastic-plastic material law that excludes the influence of strain hardening. Additionally, the study aims to arm designers of test programmes on the bending of tubulars with ‘rules of thumb’ to approximately quantify the likely influence of tube length on their results, recently shown to be an important parameter controlling geometric nonlinearity. For thick tubes, ovalisation at the plastic limit state under bending is found to be almost negligible.
Ummenhofer T, Sadowski AJ, 2018, Laudatio in honour of Professor J Michael Rotter's Honorary Doctorate awarded on Wednesday 25 July 2018 by the Karlsruhe Institute of Technology, ADVANCES IN STRUCTURAL ENGINEERING, Vol: 21, Pages: 2361-2363, ISSN: 1369-4332
Sadowski AJ, Pototschnig L, Constantinou P, 2018, The ‘panel analysis’ technique in the computational study of axisymmetric thin-walled shell systems, Finite Elements in Analysis and Design, Vol: 152, Pages: 55-68, ISSN: 0168-874X
Thin-walled shells of revolution under circumferentially uniform pre-buckling stress states are important fundamental systems, often serving as reference ‘base cases’ to which the behaviour of more complex unsymmetrical systems can be related. However, the same simplicity that often permits closed-form algebraic expressions for the critical buckling load is also often responsible for a lack of localisation and significant ambiguity in the critical buckling mode. The computation of the linear or nonlinear buckling loads requires the systematic trial of many potential buckling modes to identify the one which minimises the necessary strain energy. In times when researchers used custom-written tools usually based on circumferential Fourier series expansions, this operation was relatively straightforward. However, today's analysts using ‘general’ commercial 3D finite element packages must apply careful safeguards to correctly identify the correct buckling load and associated mode in axisymmetric shell systems.This paper presents a detailed computational strategy to accurately and efficiently investigate the correct buckling load and mode number of axisymmetric shell systems using the technique of a ‘panel analysis’. This is implemented in the ABAQUS finite element solver controlled by the SIMULIA™ Isight automation software and the Python object-oriented programming language. The methodology is illustrated on three classical benchmark problems from the scientific literature on the buckling of cylindrical shells under meridional compression, with special attention given to meshing considerations.
Boyez A, Sadowski AJ, Izzuddin BA, 2018, A ‘boundary layer’ finite element for thin multi-strake conical shells, Thin-Walled Structures, Vol: 130, Pages: 535-549, ISSN: 0263-8231
Multi-strake cylindrical and conical shells of revolution are complex but commonplace industrial structures which are composed of multiple segments of varying wall thickness. They find application as tanks, silos, circular hollow sections, aerospace structures and wind turbine support towers, amongst others. The modelling of such structures with classical finite elements interpolated using low order polynomial shape functions presents a particular challenge, because many elements must be sacrificed solely in order to accurately represent the regions oflocal compatibility bending, so-called ‘boundary layers’, near shell boundaries, changes of wall thickness and at other discontinuities. Partitioning schemes must be applied to localise mesh refinement within the boundary layers and avoid excessive model runtimes, a particular concern in incremental nonlinear analyses of large models where matrix systems are handled repeatedly. In a previous paper, the authors introduced a novel axisymmetric cylindrical shell finite element that was enriched with transcendental shape functions to capture the bending boundary layer exactly, permitting significant economies in the element and degrees of freedom count, mesh design and model generation effort. One element is sufficient per wall strake. This paper extends this work to conical geometries, where axisymmetric elements enriched with Bessel functions accurately capture the bending boundary layer for both ‘shallow’ and ‘steep’ conical strakes, which are characterised by interacting and independent boundary layers, respectively. The bending shape functions are integrated numerically, with several integration schemes investigated for accuracy and efficiency. The potential of the element is illustrated through a stress analysis of a real 22-strake metal wind turbine support tower under self-weight. The work is part of a wider project to desig
Wang J, Sadowski AJ, 2018, Elastic imperfect tip-loaded cantilever cylinders of varying length, International Journal of Mechanical Sciences, Vol: 140, Pages: 200-210, ISSN: 0020-7403
A number of recent publications have explored the crucial relationship between the length of a thin cylindrical shell and the influence of pre-buckling cross-sectional ovalisation on its nonlinear elastic buckling capacity under bending. However, the research thus far appears to have focused almost exclusively on uniform bending, with ovalisation under moment gradients largely neglected.This paper presents a comprehensive computational investigation into the nonlinear elastic buckling response of perfect and imperfect thin cantilever cylinders under global transverse shear. A complete range of practical lengths was investigated, from short cylinders which fail by shear buckling to very long ones which exhibit local meridional compression buckling with significant prior cross-section ovalisation. Two imperfection forms were applied depending on the length of the cylinder: the linear buckling eigenmode for short cylinders and a realistic weld depression imperfection for long cylinders. The weld depression imperfection was placed at the location where the cross-section of the perfect cylinder was found to undergo peak ovalisation under transverse shear, a location that approaches the base support with increasing length. Compact closed-form algebraic expressions are proposed to characterise the elastic buckling and ovalisation behaviour conservatively, suitable for direct application as design equations.This study contributes to complete the understanding of cylindrical structures of varying length where the dominant load case is global transverse shear, including multi-strake aerospace shells with short individual segments between stiffeners and long near-cylindrical wind-turbine support towers and chimneys under wind or seismic action.
Fajuyitan OK, Sadowski AJ, Wadee MA, et al., 2018, Nonlinear behaviour of short elastic cylindrical shells under global bending, Thin-Walled Structures, Vol: 124, Pages: 574-587, ISSN: 0263-8231
A recent computational study identified four distinct domains of stability behaviour at different lengths in thin elastic cylindrical shells under global bending. Cylinders of sufficient length suffer from fully-developed cross-sectional ovalisation and fail by local buckling at a moment very close to the Brazier prediction. Progressively shorter cylinders experience less ovalisation owing to the increasingly strong restraint provided by the boundary at the edges. Very short thin cylinders, however, restrain the formation of even a local buckle and fail through a limit point instability at moments and curvatures significantly in excess of the classical elastic prediction. This limit point behaviour is not caused by ovalisation but by the growth of a destabilising fold on the compressed meridian.The nonlinear behaviour of very short cylinders under global bending is investigated in detail herein, covering a wide range of lengths, radius to thickness ratios and boundary conditions with both restrained and unrestrained meridional rotations corresponding to ‘clamped’ and ‘simply-supported’ conditions respectively. Two types of imperfections are investigated, the critical buckling eigenmode and a realistic manufacturing-related ‘weld depression’. A complex insensitivity to these imperfections is revealed owing to a pre-buckling stress state dominated by local compatibility bending, and the cylinder length is confirmed as playing a crucial role in governing this behaviour. The study contributes to the characterisation of multi-segment shells with very short individual cylindrical segments, often found in the aerospace and marine industries as well as in specialised civil engineering applications such as LIPP® silos.
Fajuyitan OK, Sadowski AJ, Wadee MA, 2017, Buckling of short cylinders under under global bending: Elastic cylinders with weld depression imperfections, Eurosteel 2017
Rotter JM, Sadowski AJ, 2017, Development of circular tube slenderness classifications under axial and bending actions, Eurosteel 2017
Wang J, Sadowski AJ, 2017, Buckling of elastic cylindrical shells under symmetric but nonuniform bending moment distributions, Eurosteel 2017
Sadowski AJ, Rotter JM, Ummenhofer T, 2017, On recent characterisations of the post-yield properties of structural carbon steels, Eurosteel 2017
Fajuyitan OK, Sadowski AJ, Wadee MA, 2017, Buckling of very short elastic cylinders with weld imperfections under uniformbending, Steel Construction, Vol: 10, Pages: 216-221, ISSN: 1867-0539
The length-dependent behaviour domains of thin elastic cylindrical shells under uniform bending have recently received significant research attention. Ovalization is known to affect very long cylinders that undergo significant cross-sectional flattening before failing by local buckling. This effect is restrained by the end boundary conditions in shorter cylinders, which instead fail by local buckling at moments close to the classical analytical prediction. In very short cylinders, however, even this local buckling is restrained by the end boundary, and failure occurs instead through the development of a destabilizing meridional fold on the compressed side. Although this is a limit point instability under bending, ovalization does not play any role at all. This ‘very short’ length domain has only recently been explored for the first time with the aid of finite element modelling.A brief overview of the non-linear buckling behaviour of very short elastic cylinders under uniform bending is presented in this paper. Two types of edge rotational restraint are used to illustrate the influence of a varying support condition on the stability in this short length range. It is shown that short cylinders under bending do not suffer at all from local short-wave buckling. Additionally, when the meridional dimension of such cylinders becomes particularly short, the resulting numerical models may predict indefinite stiffening without a limit point, even when the shell is modelled using more complete 3D solid continuum finite elements. Idealized weld depressions, which are realistic representations of a systemic manufacturing defect, are used to demonstrate only a very mild sensitivity to geometric imperfections at such short lengths owing to a pre-buckling stress state dominated by local compatibility bending. The topic should be of interest to researchers studying shell problems dominated by local bending with computational tools and designers of multi-segment shells wi
Sadowski AJ, Fajuyitan OK, Wang J, 2017, A computational strategy to establish algebraic parameters for the Reference Resistance Design of metal shell structures, Advances in Engineering Software, Vol: 109, Pages: 15-30, ISSN: 0965-9978
The new Reference Resistance Design (RRD) method, recently developed by Rotter , for the manual dimensioning of metal shell structures effectively permits an analyst working with only a calculator or spreadsheet to take full advantage of the realism and accuracy of an advanced nonlinear finite element (FE) calculation. The method achieves this by reformulating the outcomes of a vast programme of parametric FE calculations in terms of six algebraic parameters and two resistances, each representing a physical aspect of the shell's behaviour.The formidable challenge now is to establish these parameters and resistances for the most important shell geometries and load cases. The systems that have received by far the most research attention for RRD are that of a cylindrical shell under uniform axial compression and uniform bending. Their partial algebraic characterisations required thousands of finite element calculations to be performed across a four-dimensional parameter hyperspace (i.e. length, radius to thickness ratio, imperfection amplitude, linear strain hardening modulus).Handling so many nonlinear finite element models is time-consuming and the quantities of data generated can be overwhelming. This paper illustrates a computational strategy to deal with both issues that may help researchers establish sets of RRD parameters for other important shell systems with greater confidence and accuracy. The methodology involves full automation of model generation, submission, termination and processing with object-oriented scripting, illustrated using code and pseudocode fragments.
Xu Z, Gardner L, Sadowski AJ, 2017, Nonlinear stability of elastic elliptical cylindrical shells under uniform bending, International Journal of Mechanical Sciences, Vol: 128-129, Pages: 593-606, ISSN: 0020-7403
Cylindrical metal shells with elliptical cross-sections are gaining increasing popularity as hollow sections due to their unique aesthetic appearance and different geometric properties about their two principal axes, with one axis exhibiting properties that are significantly more favourable than the other under flexure. However, in comparison with other hollow geometries, elliptical cross-sections have only recently begun receiving significant research attention. This is partly because even simple analytical treatments inevitably encounter cumbersome elliptical integrals that have no closed-form solutions, a problem now attenuated by powerful modern computing capabilities.A recent computational study investigated the nonlinear buckling resistance of perfect elastic circular cylindrical shells under uniform bending, establishing four distinct length-dependent domains of behaviour and characterising these in compact form using specially chosen dimensionless parameters. The present study extends this work to cylinders with elliptical cross-sections under bending about both principal axes. The same qualitative domains of length-dependent nonlinear elastic behaviour are found as for circular cylinders, but requiring a different algebraic characterisation that takes account of the varying elliptical radii. On the basis of computational results, a reference equation for the moment governing the ‘Brazier’ ovalisation cross-sectional failure mode for long elliptical thin-walled cylinders is deduced and presented for publication for the first time.
Sadowski AJ, Rotter JM, Stafford PJ, et al., 2016, On the gradient of the yield plateau in structural carbon steels, Journal of Constructional Steel Research, Vol: 130, Pages: 120-130, ISSN: 0143-974X
New design methodologies are being developed to allow stocky steel members to attain and exceed the full plastic condition. For theoretical validation, such methods require a characterisation of the uniaxial stress-strain behaviour of structural steel beyond an idealised elastic-plastic representation. However, the strain hardening properties of carbon steels are not currently guaranteed by the standards or by any steel manufacturer. Assumptions must thus be made on what values of these properties are appropriate, often based on limited information in the form of individual stress-strain curves. There is very little consistency in the choices made.This paper first illustrates, using an example elastic-plastic finite element calculation, that a stocky tubular structure can attain the full plastic condition at slendernesses comparable with those defined in current standards and supported by experiment when using only a very modest level of strain hardening, initiated at first yield. It is then hypothesised that the yield plateau in the stress-strain curve for structural carbon steels, classically treated as flat and with zero tangent modulus, actually has a small but statistically significant positive finite gradient. Finally, a robust set of linear regression analyses of yield plateau gradients extracted from 225 tensile tests appears to support this hypothesis, finding that the plateau gradient is of the order of 0.3% of the initial elastic modulus, consistent with what the finite element example suggests is sufficient to reproduce the full plastic condition at experimentally-supported slendernesses.
Rotter JM, Sadowski AJ, 2016, Full plastic resistance of tubes under bending and axial force: exact treatment and approximations, Structures, Vol: 10, Pages: 30-38, ISSN: 2352-0124
The full plastic resistance under a combination of bending and axial force of tubes of all possible wall thicknesses, from thin cylinders to circular solid sections, does not ever seem to have been thoroughly studied, despite the fact that this is a relatively simple analysis. The first part of this paper presents a formal analysis of the state of full plasticity under longitudinal stresses in a right circular tube of any thickness free of cross-section distortions. The derivation leads to relatively complicated algebraic expressions which are unsuitable for design guides and standards, so the chief purpose of this paper is to devise suitably accurate but simple empirical descriptions that give quite precise values for the state of full plasticity whilst avoiding the complexity of a formal exact analysis. The accuracy of each approximation is demonstrated. The two limiting cases of a thin tube (cylindrical shell) and circular solid section are shown to be simple special cases. The approximate expressions are particularly useful for the definition of the full plastic condition in tension members subject to small bending actions, but also applicable to all structural members and steel building structures standards, as well as to standards on thin shells where they provide the full plastic reference resistance. These expressions are also useful because they give simple definitions of the orientation of the plastic strain vector, which can assist in the development of analyses of the plastic collapse of arches and axially restrained members under bending.
Shen J, Wadee MA, Sadowski AJ, 2016, Interactive buckling in long thin-walled rectangular hollow section struts, International Journal of Non-Linear Mechanics, Vol: 89, Pages: 43-58, ISSN: 0020-7462
An analytical model describing the nonlinear interaction between global and local buckling modes in long thin-walled rectangular hollow section struts under pure compression founded on variational principles is presented. A system of nonlinear differential and integral equations subject to boundary conditions is formulated and solved using numerical continuation techniques. For the first time, the equilibrium behaviour of such struts with different cross-section joint rigidities is highlighted with characteristically unstable interactive buckling paths and a progressive change in the local buckling wavelength. With increasing joint rigidity within the cross-section, the severity of the unstable post-buckling behaviour is shown to be mollified. The results from the analytical model are validated using a nonlinear finite element model developed within the commercial package Abaqus and show excellent comparisons. A simplified method to calculate the local buckling load of the more compressed web undergoing global buckling and the corresponding global mode amplitude at the secondary bifurcation is also developed. Parametric studies on the effect of varying the length and cross-section aspect ratio are also presented that demonstrate the effectiveness of the currently developed models.
Boyez A, Sadowski AJ, Izzuddin BA, 2016, A novel 'boundary layer' finite element for the efficient analysis of thin cylindrical shells, Computers and Structures, Vol: 182, Pages: 573-587, ISSN: 0045-7949
Classical shell finite elements usually employ low-order polynomial shape functions to interpolate between nodal displacement and rotational degrees of freedom. Consequently, carefully-designed fine meshes are often required to accurately capture regions of high local curvature, such as at the ‘boundary layer’ of bending that occurs in cylindrical shells near a boundary or discontinuity. This significantly increases the computational cost of any analysis.This paper is a ‘proof of concept’ illustration of a novel cylindrical axisymmetric shell element that is enriched with rigorously-derived transcendental shape functions to exactly capture the bending boundary layer. When complemented with simple polynomials to express the membrane displacements, a single boundary layer shell element is able to support very complex displacement and stress fields that are exact for distributed element loads of up to second order. A single element is usually sufficient per shell segment in a multi-strake shell.The predictions of the novel element are compared against analytical solutions, a classical axisymmetric shell element with polynomial shape functions and the ABAQUS S4R shell element in three problems of increasing complexity and practical relevance. The element displays excellent numerical results with only a fraction of the total degrees of freedom and involves virtually no mesh design. The shell theory employed at present is kept deliberately simple for illustration purposes, though the formulation will be extended in future work.
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