Publications
198 results found
Wu K, Wadee MA, Gardner L, 2019, Stability and ultimate behaviour of prestressed stayed beam-columns, Engineering Structures, Vol: 201, ISSN: 0141-0296
The instability of beam-columns with crossarms and externally prestressed cable stays is studied analytically, where the combination of bending and compression is assumed to be derived from the system self-weight acting orthogonally to the applied axial load. Three principal zones of behaviour are identified with two of these each having two sub-zones that relate the critical buckling load to the initial prestressing force applied to the stay cables. The ultimate load-carrying capacity of the beam-columns is evaluated by conducting nonlinear finite element analysis within the commercial package ABAQUS. Results show that the analytically derived critical buckling loads generally provide safe predictions of the ultimate loads due to significant post-buckling strength. It is found that releasing the geometric double symmetry of the system can make for a significantly more efficient structure due to the effect of pre-cambering against the self-weight. The strength and efficiency of stayed beam-column systems opens up a range of potential applications, including lighter alternatives to conventional props to support wide excavations, which currently utilize very heavy steelwork.
Shen J, Wadee MA, 2019, Local-global mode interaction in thin-walled inelastic rectangular hollow section struts part 2: assessment of existing design guidance and new recommendations, Thin-Walled Structures, Vol: 145, ISSN: 0263-8231
The second part of the study on the local–global mode interaction in thin-walled inelastic rectangular hollow section struts focuses on design guidance. Based on the validated finite element (FE) model from the companion paper, a framework for fully automating FE model generation, submission and post-processing for geometric and material nonlinear analysis with imperfections is first presented. The ultimate load data for specimens with different cross-section aspect ratios, cross-sectional slenderness, global slenderness and welding options are generated. The current design rules for thin-walled welded RHS struts are assessed using the numerical results and existing experimental results from the literature by means of structural reliability analysis in accordance with the methodology presented in Annex D of Eurocode EN1990. A modified Direct Strength Method (DSM) relationship is then proposed and it is demonstrated to provide superior ultimate load predictions than the current guidelines.
Shen J, Wadee MA, 2019, Local-global mode interaction in thin-walled inelastic rectangular hollow section struts part 1: nonlinear finite element analysis, Thin-Walled Structures, Vol: 145, ISSN: 0263-8231
Mass efficient thin-walled rectangular hollow section (RHS) struts have been shown to be susceptible to local–global mode interaction and exhibit sensitivity to imperfections. Material nonlinearity may increase the imperfection sensitivity of such members further and affect the final failure mode. Nonlinear finite element (FE) models for welded inelastic thin-walled RHS struts with pre-defined local and global geometric imperfections alongside residual stresses are developed within the commercial package Abaqus and validated against two independent experimental studies. Based on the validated FE model, the effects of material nonlinearity and residual stresses from welding on the ultimate load, mechanical behaviour and the imperfection sensitivity of struts are investigated. A simplified method to determine the initial geometric imperfection amplitude introduced in the FE model with residual stresses explicitly modelled within the ECCS framework is proposed for the first time. The experimental and numerical results in conjunction with existing experimental results from the literature are employed in the companion paper for the assessment of the Effective Width Method and Direct Strength Method, which also forms the basis for a new set of design recommendations.
Hadjipantelis N, Gardner L, Wadee MA, 2019, Finite element modeling of prestressed cold-formed steel beams, Journal of Structural Engineering, Vol: 145, Pages: 04019100-1-04019100-19, ISSN: 0733-9445
The concept and structural benefits of prestressing cold-formed steel beams are explored in the present paper. In the proposed system, prestressing is applied by means of a high-strength steel cable located within the cross section of the beam at an eccentric location with respect to the strong geometric axis. The internal forces generated by the prestressing are opposite in sign to those induced under subsequent vertical loading. Hence, the development of detrimental compressive stresses within the top region of the cold-formed steel beam is delayed and thus the load-carrying capacity of the beam is enhanced. Owing to the precamber that is induced along the member during the prestressing stage, the overall deflections of the beam are also reduced significantly. In the present paper, finite-element (FE) modeling was employed to simulate the mechanical behavior of prestressed cold-formed steel beams during the prestressing and vertical loading stages. Following the validation of the FE modeling approach, a set of parametric studies was conducted, where the influence of the key controlling parameters on the structural benefits obtained from the prestressing process was investigated. The parametric results were utilized to determine how the benefits obtained from the addition of the prestressed cable can be maximized, demonstrating the significant enhancements in the performance of the cold-formed steel beam that can be achieved.
Champneys AR, Dodwell TJ, Groh RMJ, et al., 2019, Happy catastrophe: Recent progress in analysis and exploitation of elastic instability, Frontiers in Applied Mathematics and Statistics, Vol: 5, Pages: 1-30, ISSN: 2297-4687
A synthesis of recent progress is presented on a topic that lies at the heart of both structural engineering and nonlinear science. The emphasis is on thin elastic structures that lose stability subcritically — without a nearby stable post-buckled state — a canonical example being a uniformly axially-loaded cylindrical shell. Such structures are hard to design and certify because imperfections or shocks trigger buckling at loads well below the threshold of linear stability. A resurgence of interest in structural instability phenomena suggests practical stability assessment require stochastic approaches and imperfection maps. This article surveys a different philosophy; the buckling process and ultimate post-buckled state are well described by the perfect problem. The significance of the Maxwell load is emphasised, where energy of the unbuckled and fully developed buckle patterns are equal, as is the energetic preference of localised states, stable and unstable versions of which connect in a snaking load-deflection path. The state of the art is presented on analytical, numerical and experimental methods. Pseudo15 arclength continuation (path-following) of a finite-element approximation computes families of complex localised states. Numerical implementation of a mountain-pass energy method then predicts the energy barrier through which the buckling process occurs. Recent developments also indicate how such procedures can be replicated experimentally; unstable states being accessed by careful control of constraints, and stability margins assessed by shock sensitivity experiments. Finally, the fact that subcritical instabilities can be robust, not being undone by reversal of the loading path, opens up potential for technological exploitation. Several examples at different length scales are discussed; a cable-stayed prestressed column, two examples of adaptive structures inspired by morphing aeroelastic surfaces, and a model for a functional auxetic material.
Hadjipantelis N, Gardner L, Wadee MA, 2019, Design of prestressed cold-formed steel beams, Thin-Walled Structures, Vol: 140, Pages: 565-578, ISSN: 0263-8231
Structural design rules for prestressed cold-formed steel beams, considering both the prestressing and imposed vertical loading stages, are presented herein. In the proposed approach, the cold-formed steel member is designed as a beam-column using linear interaction equations in conjunction with the Direct Strength Method (DSM), while the prestressed cable is designed by ensuring that its tensile capacity is not violated during the two loading stages. In the present paper, the design approach and the failure criteria, which define the permissible design zone for the prestressed system, are first introduced. The suitability of the design recommendations is then assessed by comparing a set of parametric finite element (FE) results for several combinations of prestress levels, beam geometries and cable sizes, with the corresponding design predictions. Finally, following reliability analysis, the implementation of the design recommendations is illustrated through a practical worked example.
Hadjipantelis N, Kyvelou P, Gardner L, et al., 2019, Numerical modelling of prestressed composite cold-formed steel flooring systems, Seventh International Conference in Structural Engineering, Mechanics and Computation, Publisher: CRC Press
A novel and highly-efficient prestressed composite flooring system comprising cold-formed steel joists and wood-based floorboards is introduced herein. The prestressing is applied by means of a high-strength steel cable housed within the bottom hollow flange of the steel joist, while the composite action is mobilised by making simple alterations to the currently employed fastening arrangements between the joist and the board. Geometrically and materially nonlinear finite element models with initial geometric imperfections have been developed to simulate the behaviour of the proposed system during the prestressing and vertical loading stages. The structural performance of the prestressed system is compared with that of conventional non-prestressed systems, demonstrating that substantial benefits can be achieved both in terms of load-carrying capacity and serviceability performance. Subsequently, a parametric study is conducted to investigate the effect of the steel section thickness on the ultimate moment capacity and bending stiffness of the system.
Shen J, Wadee MA, 2019, Sensitivity to local imperfections in inelastic thin-walled rectangular hollow section struts, Structures, Vol: 17, Pages: 43-57, ISSN: 2352-0124
Mass efficient inelastic thin-walled rectangular hollow section (RHS) struts practically always fail in a combination of local–global interactive buckling and material nonlinearity while also exhibiting high sensitivity to initial imperfections. Nonlinear finite element (FE) models for inelastic thin-walled RHS struts with pre-defined local and global geometric imperfections are developed within the commercial package Abaqus. Using a unified local imperfection measurement based on equal local bending energy, the effects of imperfect cross-section profiles, imperfection wavelength and the degree of localization in the longitudinal direction on the ultimate load and the nonlinear equilibrium path are investigated for four characteristic length struts at different material yielding stress levels. The corresponding most severe imperfection profiles are determined and are found to be qualitatively different to the linear eigenmodes in all cases. Moreover, it is found that the most severe purely periodic imperfections may be used to provide a safe approximation of the ultimate load when the corresponding amplitude is constrained to the manufacturing tolerance level. An extensive parametric study on the wavelength of the most severe periodic imperfection profile is conducted and a relationship for this is proposed in terms of the normalized local slenderness, which compares excellently with the FE results.
Wadee MA, Phillips ATM, Bekele A, 2019, From buckliphobes to buckliphiles: Recent developments in exploiting positive virtues of instability, 7th International Conference on Structural Engineering, Mechanics and Computation (SEMC), Publisher: CRC PRESS-BALKEMA, Pages: 455-461
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Hadjipantelis N, Gardner L, Wadee MA, 2018, Prestressed cold-formed steel beams – parametric studies and design recommendations, Hong Kong, China, Ninth International Conference on Advances in Steel Structures, Publisher: Hong Kong Institute of Steel Construction Limited
Owing to their enhanced load-carrying and serviceability performances, prestressed coldformed steel beams can potentially open up new applications within the construction industry. In theproposed concept, an eccentric prestressing force is applied to cold-formed steel beams by means of acable that is housed within a bottom hollow flange. During prestressing, tensile stresses are inducedwithin the top region of the beam, thus delaying the occurrence of local instabilities under subsequentvertical loading. Consequently, the moment capacity of the beam is enhanced. Furthermore, owing tothe prestressing, a pre-camber is also induced along the member, thus decreasing the overall verticaldeflections significantly. Following discussion of the mechanical behaviour of the proposed beams,design recommendations are developed by employing interaction equations alongside the DirectStrength Method. Subsequently, finite element (FE) analysis is employed to investigate the effects of theprestress level and the section slenderness of the steel beam on the benefits obtained from theprestressing process. The parametric FE results are then utilised to assess the design recommendations.
Zhang W, Gardner L, Wadee MA, et al., 2018, Analytical solutions for the inelastic lateral‑torsional buckling of I‑beams under pure bending via plate‑beam theory, International Journal of Steel Structures, Vol: 18, Pages: 1440-1463, ISSN: 1598-2351
The Wagner coefficient is a key parameter used to describe the inelastic lateral-torsional buckling (LTB) behaviour of the I-beam, since even for a doubly-symmetric I-section with residual stress, it becomes a monosymmetric I-section due to the characteristics of the non-symmetrical distribution of plastic regions. However, so far no theoretical derivation on the energy equation and Wagner’s coefficient have been presented due to the limitation of Vlasov’s buckling theory. In order to simplify the nonlinear analysis and calculation, this paper presents a simplified mechanical model and an analytical solution for doubly-symmetric I-beams under pure bending, in which residual stresses and yielding are taken into account. According to the plate-beam theory proposed by the lead author, the energy equation for the inelastic LTB of an I-beam is derived in detail, using only the Euler–Bernoulli beam model and the Kirchhoff-plate model. In this derivation, the concept of the instantaneous shear centre is used and its position can be determined naturally by the condition that the coefficient of the cross-term in the strain energy should be zero; formulae for both the critical moment and the corresponding critical beam length are proposed based upon the analytical buckling equation. An analytical formula of the Wagner coefficient is obtained and the validity of Wagner hypothesis is reconfirmed. Finally, the accuracy of the analytical solution is verified by a FEM solution based upon a bi-modulus model of I-beams. It is found that the critical moments given by the analytical solution almost is identical to those given by Trahair’s formulae, and hence the analytical solution can be used as a benchmark to verify the results obtained by other numerical algorithms for inelastic LTB behaviour.
Bai L, Yang J, Wadee MA, 2018, Cellular buckling from nonlinear mode interaction in unequal-leg angle struts, Thin-Walled Structures, Vol: 132, Pages: 316-331, ISSN: 0263-8231
A variational model based on total potential energy principles that describes the nonlinear mode interaction in thin-walled unequal-leg angle struts under pure axial compression is presented. The formulation, which combines continuous displacement functions and generalized coordinates, leads to the derivation of a system of differential and integral equations that describe the static equilibrium response of the strut. Solving the system of equations using numerical continuation techniques reveals, for the first time, progressive cellular buckling (or snaking) represented by a sequence of snap-back instabilities arising from the nonlinear interaction of the weak-axis flexural, strong-axis flexural and torsional buckling modes—the resulting behaviour being highly unstable. For verification purposes, a finite element (FE) model is also devised and the sequential snap-back instabilities are also captured within its framework. Moreover, once an initial geometric perturbation is incorporated within the variational model it compares very well with the FE model.
Hadjipantelis N, Gardner L, Wadee MA, 2018, Prestressed cold-formed steel beams: concept and mechanical behaviour, Engineering Structures, Vol: 172, Pages: 1057-1072, ISSN: 0141-0296
An innovative concept, whereby the load-carrying capacity and serviceability performance of cold-formed steel beams are enhanced by utilising prestressing techniques, is presented. The prestressing force is applied by means of a high-strength steel cable, which is housed at a location eccentric to the strong geometric axis within the bottom hollow flange of the cold-formed steel beam, inducing initial stresses in the beam that are opposite in sign to those introduced during the subsequent loading stage. As a consequence, the development of local instabilities during loading is delayed and thus the capacity of the beam is enhanced. Furthermore, the pre-camber induced during prestressing, as well as the contribution of the cable to the bending stiffness of the system, decrease the overall vertical deflections of the beam. The conceptual development of prestressed cold-formed steel beams and a study investigating the potential benefits are presented. The mechanical behaviour of the proposed beams in both the prestressing and imposed loading stages is described in terms of analytical expressions, while failure criteria for the design of the cold-formed steel beam and the cable are also developed by employing interaction equations in conjunction with the Direct Strength Method. Geometrically and materially nonlinear finite element analysis with imperfections is employed to simulate the behaviour of the proposed beams. Sample numerical results are presented and compared with the developed analytical expressions and failure criteria, demonstrating the substantial enhancement in moment capacity and serviceability performance offered by these beams.
Shen J, Wadee MA, 2018, Sensitivity of elastic thin-walled rectangular hollow section struts to manufacturing tolerance level imperfections., Engineering Structures, Vol: 170, Pages: 146-166, ISSN: 0141-0296
Finite element models for elastic thin-walled rectangular hollow section (RHS) struts with pre-defined local and global geometric imperfections are developed within the commercial package ABAQUS. A unified local imperfection measurement based on equal local bending energy is proposed. The effects of imperfect cross-section profiles, imperfection wavelength in the longitudinal direction and the degree of imperfection localization on the ultimate load and equilibrium path are investigated and the most severe imperfection profiles are determined. A parametric study on the wavelength of the most severe local imperfection profile is conducted and a semi-empirical equation to approximate the corresponding wavelength is proposed. Moreover, an equation to calculate the global buckling load of thin-walled RHS struts with tolerance level doubly-symmetric cross-section local imperfections is proposed.
Hadjipantelis N, Gardner L, Wadee MA, 2018, Prestressed cold-formed steel beams - conceptual development, Lisbon, Eight International Conference on Thin-Walled Structures
Shen J, Wadee MA, 2018, Length effects on interactive buckling in thin-walled rectangular hollow section struts, Thin Walled Structures, Vol: 128, Pages: 152-170, ISSN: 0263-8231
A variational model formulated using analytical techniques describing the nonlinear coupling between local and global buckling modes within an elastic thin-walled rectangular hollow section strut is presented. A system of nonlinear differential and integral equations subject to boundary conditions is derived and solved using numerical continuation techniques. The nonlinear behaviour of four representative lengths is investigated, which are characterized by the post-buckling equilibrium paths. The numerical results from the variational model are validated using a nonlinear finite element model and largely show excellent comparisons, particularly for the practically important ultimate load and the initial post-buckling behaviour. Boundaries for the four distinct length-dependent zones are identified and the most unstable zone is demonstrated to have a considerably narrower length range than previously determined for practical corner boundary conditions within the cross-section.
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.
Shen J, Wadee MA, 2018, Imperfection sensitivity of thin-walled rectangular hollow section struts susceptible to interactive buckling, International Journal of Non-Linear Mechanics, Vol: 99, Pages: 112-130, ISSN: 0020-7462
A variational model describing the interactive buckling of thin-walled rectangular hollow section struts with geometric imperfections is developed based on analytical techniques. A system of nonlinear differential and integral equilibrium equations is derived and solved using numerical continuation. Imperfection sensitivity studies focus on the cases where the global and local buckling loads are close. The equilibrium behaviour of struts with varying imperfection sizes, characterized by the equilibrium paths and the progressive change in local buckling wavelength, is highlighted and compared. The numerical results reveal that struts exhibiting mode interaction are very sensitive to both local and global imperfections. The results from the variational model are verified using the finite element method in conjunction with the static Riks method and show good comparisons. A simplified method to calculate the pitchfork bifurcation load where mode interaction is triggered for struts with a global imperfection is developed for the first time. The simplified method is calibrated to predict the ultimate load for struts with tolerance level global imperfections and combined imperfections based on the parametric study, which also reveals that local and global imperfections are relatively more significant where global and local buckling are critical respectively. Finally, the ultimate load for struts with tolerance level geometric imperfections is compared with the existing Direct Strength Method (DSM). Potential dangers of making unsafe load-carrying capacity predictions by the DSM are highlighted and an improved strength equation is proposed.
Bai L, Wang F, Wadee MA, et al., 2017, Nonlinear mode interaction in equal-leg angle struts susceptible to cellular buckling, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 473, Pages: 1-22, ISSN: 1364-5021
A variational model that describes the interactive buckling of a thin-walled equal-leg angle strut under pure axial compression is presented. A formulation combining the Rayleigh-Ritz method and continuous displacement functions is used to derive a system of differential and integral equilibrium equations for the structural component. Solving the equations using numerical continuation reveals progressive cellular buckling (or snaking) arising from the nonlinearinteraction between the weak-axis flexural buckling mode and the strong-axis flexural-torsional buckling mode for the first time - the resulting behaviour being highly unstable. Physical experiments conducted on 10 cold-formed steel specimens are presented andthe results show good agreement with the variational model.
Yu J, Wadee MA, 2017, Optimal prestressing of triple-bay prestressed stayed columns, Structures, Vol: 12, Pages: 132-144, ISSN: 2352-0124
A nonlinear finite element model of a triple-bay prestressed stayed column is developed within the commercial package ABAQUS. A linearly obtained 'optimal prestressing force' that maximizes the critical buckling load is investigated since this quantity has been demonstrated in previous work on single-bay prestressed columns to provide a lower bound to the actual maximum load carrying capacity when compared to experimental results and nonlinear modelling. The ratio of the crossarm to the overall column length, the diameter of the cable stays, the relative lengths of the individual crossarms and the ratio of the initial prestressing force to the aforementioned linear optimal prestress are varied. Measures for the relative efficiency of the main column and the stays are defined and the objective of the optimization study is for the efficiency to be maximized. It is found that the true optimal prestress is generally higher than the equivalent, linearly obtained, quantity but by a significantly reduced factor when compared to an equivalent study for single-bay prestressed stayed columns.
Lapira L, Wadee MA, Gardner L, 2017, Stability of multiple-crossarm prestressed stayed columns with additional stay systems, Structures, Vol: 12, Pages: 227-241, ISSN: 2352-0124
Prestressed stayed columns have an enhanced resistance to buckling through the effective use of crossarms and pretensioned stays when compared to conventional columns. An analytical derivation of the minimum, linear optimum and maximum initial pretension forces for configurations of prestressed stayed columns with multiple crossarms and additional stays is presented for the first time. The findings are validated through comparisons with finite element models developed in the commercial package ABAQUS. The influence of the initial pretension on the load-carrying capacity of the configurations considered is also analysed, providing insight into the actual optimum initial pretension force for the configurations accounting for the significance of geometric nonlinearities.
Fajuyitan OK, Sadowski AJ, Wadee MA, 2017, Buckling of short cylinders under under global bending: Elastic cylinders with weld depression imperfections, Eurosteel 2017
Yu J, Wadee MA, 2017, Optimal prestressing of triple-bay prestressed stayed columns, Eurosteel 2017
Fajuyitan OK, Sadowski AJ, Wadee MA, 2017, 04.01: Buckling of very short elastic cylinders with weld imperfections under uniform bending, ce/papers, Vol: 1, Pages: 811-820, ISSN: 2509-7075
<jats:title>ABSTRACT</jats:title><jats:p>The length‐dependent domains of behaviour of thin elastic cylindrical shells under uniform bending have recently received significant research attention. Ovalisation is known to affect very long cylinders which undergo significant cross‐sectional flattening before failing by local buckling. This effect is restrained by the end boundary condition in shorter cylinders, which fail instead 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 destabilising meridional fold on the compressed side. Although this is a limit point instability under bending, ovalisation 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.</jats:p><jats:p>A brief overview of the nonlinear 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. Idealised 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 dom
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
Yu J, Wadee MA, 2017, Mode interaction in triple-bay prestressed stayed columns, International Journal of Non-Linear Mechanics, Vol: 88, Pages: 47-66, ISSN: 1878-5638
Prestressed stayed columns are an innovative type of structural system where the compressive load-carrying capacity can be enhanced through prestressed external cable stays. A nonlinear analytical model for prestressed stayed columns with multiple crossarm systems along the column length, based on the Rayleigh Ritz method, is presented that capture modal interactions for perfect geometries explicitly for the first time. It is demonstratedcthat the theoretical compressive strength enhancements under certain configurations canconly be obtained at the expense of triggering a sequence of destabilizing bifurcations. This can give rise to dangerously unstable interactive post-buckling behaviour inluding so-called "mode jumping" and "snaking" phenomena. Parametric spaces where the system is most susceptible to the modal interactions are identified and it is for those configurations that the system is likely to be highly sensitive to initial imperfections. The model is validated using a nonlinear nite element model formulated within the commercial code ABAQUS and excellent comparisons are obtained.
Liu EL, Wadee MA, 2016, Geometric factors affecting I-section struts experiencing local and strong-axis global buckling mode interaction, Thin-Walled Structures, Vol: 109, Pages: 319-331, ISSN: 0263-8231
A recent analytical model describing the post-buckling behaviour of an I-section strut experiencing strong axis global–local buckling interaction is extended to investigate the effects of modifying the strut geometry. Using a combination of analytical and finite element (FE) methods, the global and local slendernesses are varied parametrically, in turn, to determine the geometries leading to regions of interactive behaviour. The effect of stress relieved initial global imperfections are also investigated. It is observed that the strut can exhibit one of five distinct post-buckling behaviours, the geometries for which are identified. The strut can exhibit global buckling only, local buckling only, global–local buckling interaction with either the global or local mode being triggered first or the most severe case where both global and local buckling modes are triggered simultaneously. The strut is found to be highly sensitive to initial imperfections in the interactive region; the implications for imperfection sensitivity on the design and the practical use of such components are discussed.
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.
McCann F, Wadee MA, Pearson J, et al., 2016, Postbuckling behaviour of beams with discrete nonlinear restraints, Coupled Instabilities in Metal Structures (CIMS 2016), Publisher: CIMS
A beam with nonlinearly‐elastic lateral restraints attached at discrete points along its span is investigated via analytical and numerical methods. Previous results for the critical moment and the deflected shape based on an eigenvalue analysis of a similar beam with linearly‐elastic restraints are discussed, along with a validation of these results against an equivalent finite element model and results from numerical continuation. A beam with nonlinearly‐elastic restraints is then analysed with treatments for both quadratic and cubic restraint force-displacement relationships being provided. After formulation of the potential energy functionals, the governing differential equations of the system are derived via the calculus of variations and appropriate boundary conditions are applied. The equations are then solved using the numerical continuation software AUTO‐07p for a standard I‐section beam. The variation in elastic critical buckling moment with the linear component of the restraint stiffness is tracked via a two‐parameter numerical continuation, allowing determination of the stiffness values at which the critical buckling modes changes qualitatively. Using these stiffness values, subsequent analyses are conducted to examine the influence of the nonlinear component of the restraint stiffness, from which post‐buckling equilibrium paths and deformation modes are extracted. The results of these analyses are then compared with an equivalent Rayleigh–Ritz formulation whereby the displacement components are represented by Fourier series. Equilibrium equations are derived by minimizing the potential energy functional with respect to the amplitudes of the constituent harmonics of the Fourier series. The amplitudes are solved for in the post-buckling range by AUTO‐O7p and equilibrium paths are produced and compared to the equivalent solutions of the differential equations, with good agreement observed.
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