Imperial College London

Professor M Ahmer Wadee

Faculty of EngineeringDepartment of Civil and Environmental Engineering

Professor of Nonlinear Mechanics
 
 
 
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Contact

 

+44 (0)20 7594 6050a.wadee Website

 
 
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Assistant

 

Ms Ruth Bello +44 (0)20 7594 6040

 
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Location

 

421Skempton BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

147 results found

Bai L, Wang F, Wadee MA, Yang Jet 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: 20170583-20170583, 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.

JOURNAL ARTICLE

Fajuyitan OK, Sadowski AJ, Wadee MA, 2017, Buckling of very short elastic cylinders with weld imperfections under uniform bending, STEEL CONSTRUCTION-DESIGN AND RESEARCH, Vol: 10, Pages: 216-221, ISSN: 1867-0520

JOURNAL ARTICLE

Fajuyitan OK, Sadowski AJ, Wadee MA, 2017, Buckling of short cylinders under under global bending: Elastic cylinders with weld depression imperfections, Eurosteel 2017

CONFERENCE PAPER

Lapira L, Wadee MA, Gardner L, 2017, Stability of Multiple-crossarm Prestressed Stayed Columns With Additional Stay Systems, Structures, Vol: 12, Pages: 227-241

© 2017 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.

JOURNAL ARTICLE

Shen J, Wadee MA, 2017, Length effects on interactive buckling in thin-walled rectangular hollow section struts, Thin-Walled Structures, ISSN: 0263-8231

© 2017 Elsevier Ltd. 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.

JOURNAL ARTICLE

Shen J, Wadee MA, 2017, Imperfection sensitivity of thin-walled rectangular hollow section struts susceptible to interactive buckling, International Journal of Non-Linear Mechanics, 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.

JOURNAL ARTICLE

Shen J, Wadee MA, Sadowski AJ, 2017, Interactive buckling in long thin-walled rectangular hollow section struts, INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, Vol: 89, Pages: 43-58, ISSN: 0020-7462

JOURNAL ARTICLE

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.

JOURNAL ARTICLE

Yu J, Wadee MA, 2017, Optimal prestressing of triple-bay prestressed stayed columns, Structures, Vol: 12, Pages: 132-144, ISSN: 2352-0124

JOURNAL ARTICLE

Yu J, Wadee MA, 2017, 05.23: Optimal prestressing of triple-bay prestressed stayed columns, Pages: 1225-1234, ISSN: 2509-7075

CONFERENCE PAPER

Bai L, Wadee MA, 2016, Slenderness effects in thin-walled I-section struts susceptible to local-global mode interaction, ENGINEERING STRUCTURES, Vol: 124, Pages: 128-141, ISSN: 0141-0296

JOURNAL ARTICLE

Gosaye J, Gardner L, Wadee MA, Ellen MEet al., 2016, Compressive behaviour and design of prestressed steel elements, Structures, Vol: 5, Pages: 76-87, ISSN: 2352-0124

JOURNAL ARTICLE

Li P, Wadee MA, Yu J, Christie NG, Wu Met al., 2016, Stability of prestressed stayed steel columns with a three branch crossarm system, JOURNAL OF CONSTRUCTIONAL STEEL RESEARCH, Vol: 122, Pages: 274-291, ISSN: 0143-974X

JOURNAL ARTICLE

Liu EL, Wadee MA, 2016, Mode interaction in perfect and imperfect thin-walled I-section struts susceptible to global buckling about the strong axis, THIN-WALLED STRUCTURES, Vol: 106, Pages: 228-243, ISSN: 0263-8231

JOURNAL ARTICLE

Liu EL, Wadee MA, 2016, Imperfection sensitivity in i-section struts experiencing local and strong-axis global buckling mode interaction, Pages: 732-737

© 2016 Taylor & Francis Group, London. An extension of recent work on strong axis global-local buckling mode interaction in thin-walled I-section struts is presented. The variational model is extended to include initial geometric, stress-relieved, local imperfections. An imperfection sensitivity study of the strut reveals a decreased load carrying capacity with increasing magnitudes of local imperfections and a particular sensitivity to localized imperfection shapes. An identical strut is constructed and analysed using the commercial finite element software Abaqus, showing excellent comparisons especially in the initial stages of the post-buckling path.

CONFERENCE PAPER

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.

JOURNAL ARTICLE

Liu EL, Wadee MA, 2016, Geometric factors affecting I-section struts experiencing local and strong-axis global buckling mode interaction, Coupled Instabilities in Metal Structures, Publisher: CIMS

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 slenderness is varied parametrically to determine the regions of interactive behaviour. The effects of stress relieved initial global imperfections are also investigated. It is observed that the strut can exhibit one of five distinctive post-buckling behaviours, the geometries for which are identified. The strut can exhibit local buckling only, global buckling only, global–local buckling interaction with either the global or the local buckling mode being triggered first, or the critical 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, and the implications that this has on the design and the practical use of such components are discussed.

CONFERENCE PAPER

McCann F, Wadee MA, Gardner L, 2016, Harmonic analysis of elliptical hollow section tubes in bending, EMI/PMC 2016

CONFERENCE PAPER

McCann F, Wadee MA, Pearson J, Gardner Let 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.

CONFERENCE PAPER

Shen J, Wadee MA, Sadowski AJ, 2016, Local–global mode interaction in thin-walled rectangular hollow section struts, EMI/PMC 2016

CONFERENCE PAPER

Shen J, Wadee MA, Sadowski AJ, 2016, Local-global mode interaction in box-section struts under axial compression, Coupled Instabilities in Metal Structures, Publisher: CIMS

An analytical model describing the interactive buckling of a thin-walled box-section strut under axial compression, where global buckling is critical, is formulated based on variational principles. A system of nonlinear differential and integral equations subject to boundary conditions are derived and solved using numerical continuation. The results show that when the local buckling load is close to the global buckling load, unstable interactive buckling dominates. Equilibrium behaviour, characterized by the equilibrium paths and the progressive change in local buckling wavelength, is highlighted. The results from the analytical model have been validated using the finite element method in conjunction with the static Riks method and show excellent comparisons.

CONFERENCE PAPER

Wadee MA, Madrazo-Aguirre F, Li P, Yu Jet al., 2016, Analytical modelling of structural components and systems vulnerable to interactive buckling: Recent developments, Pages: 220-226

© 2016 Taylor & Francis Group, London. Some recent developments regarding the application of analytical modelling of systems susceptible to interactive buckling are presented. The aim of the current work is to highlight some advantages of mathematical modelling for interpreting the mechanical response of practical nonlinear problems in structural engineering and mechanics. Two applications where prestressing is combined with nonlinear instability are presented. The presented cases have been used to validate numerical simulations and allow insights into the fundamental parameters that control large deflection behaviour.

CONFERENCE PAPER

Wadee MA, Yu J, 2016, Mode jumping and snaking in prestressed stayed columns, Metz, France, 2016 EMI International Conference, Publisher: University Press of Universite de Lorraine, Metz, France, Pages: 308-308

CONFERENCE PAPER

Yu J, Wadee MA, 2016, Nonlinear mechanics of prestressed stayed columns with multiple bays, Pages: 257-263

© 2016 Taylor & Francis Group, London. An analytical study of multi-bay prestressed stayed columns is presented. The model is formulated with potential energy principles in conjunction with the Rayleigh-Ritz method. Both linear and nonlinear buckling responses are investigated using the numerical continuation package Auto to solve the derived system of nonlinear equilibrium equations. The results are compared with numerical models developed within the commercial finite element package Abaqus. It is found that the distinct buckling eigenmodes do not necessarily control the post-buckling behaviour, especially when the critical mode has an antisymmetric profile where interactive buckling is found to govern the mechanical response.

CONFERENCE PAPER

Zschernack C, Wadee MA, Völlmecke C, 2016, Nonlinear buckling of fibre-reinforced unit cells of lattice materials, Composite Structures, Vol: 136, Pages: 217-228, ISSN: 1879-1085

Truss-based lattice materials are cellular materials with an outstanding potential for multi-functional use. This is owing to properties of high compressive strength to density ratios combined with a periodic and open structure. However, such structures at low relative densities are particularly vulnerable to elastic buckling failure. Fibre-reinforcement that increases the buckling strength of lattice materials is proposed and the behaviour of unit cells that are tessellated within the lattice is investigated. A two-dimensional square orientated unit cell and a three-dimensional tetrahedron-shaped unit cell are both modelled discretely using energy principles with the nonlinear interactive buckling behaviour being analysed. The analytical approach, based on a perturbation method, exhibits excellent agreement for the mechanical response when compared to results from numerical continuation for moderately large displacements. A fundamental understanding of the mechanical behaviour of a unit cell can be upscaled in future work. It is postulated that this will enable the determination of the constitutive behaviour of such lattice materials.

JOURNAL ARTICLE

Bai L, Wadee MA, 2015, Mode interaction in thin-walled I-section struts with semi-rigid flange-web joints, International Journal of Non-Linear Mechanics, Vol: 69, Pages: 71-83, ISSN: 0020-7462

A recently developed variational model that describes the nonlinear interaction between the global and local buckling of a thin-walled I-section strut under pure compression is extended to include semi-rigid flange--web connections. 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. Cellular buckling, observed in the case where the web is assumed to provide no more than a simple support to the flanges, is found to be rapidly eroded by increasing the connection rigidity, although the local buckling wavelength still reduces as the post-buckling deformation is increased. The model is validated using finite element analysis; the results compare very well particularly when a high rigidity between the section web and flanges is simulated.

JOURNAL ARTICLE

Bai L, Wadee MA, 2015, Imperfection sensitivity of thin-walled I-section struts susceptible to cellular buckling, International Journal of Mechanical Sciences, Vol: 104, Pages: 162-173, ISSN: 0020-7403

A variational model that describes the nonlinear interaction between global and localbuckling of an imperfect thin-walled I-section strut under pure compression is developed.An initial out-of-straightness of the entire strut and an initial local out-of-plane displacementin the flanges are introduced as a global and a local type of imperfection respectively.A system of differential and integral equilibrium equations is derived for the structuralcomponent from variational principles, an approach that was previously validated. Imperfectionsensitivity studies focus on cases where the global and local critical loads aresimilar. Numerical results reveal that the strut exhibiting cellular buckling (or ‘snaking’) ishighly sensitive to both types of imperfections. The worst forms of local imperfection areidentified in terms of the initial wavelength, amplitude and degree of localization and thesechange with the generic imperfection size and highlight the potential dangers of unsafepredictions of actual load-carrying capacity.

JOURNAL ARTICLE

Hanley KJ, O'Sullivan C, Wadee MA, Huang Xet al., 2015, Use of elastic stability analysis to explain the stress-dependent nature of soil strength, ROYAL SOCIETY OPEN SCIENCE, Vol: 2, ISSN: 2054-5703

JOURNAL ARTICLE

Liu EL, Wadee MA, 2015, Mode interaction of global and local buckling in thin-walled I-section struts with rigid flange-web joints, Eighth International Conference on Advances in Steel Structures (ICASS) 2015

A variational model describing the behaviour of a thin-walled I-section compression membersuffering from local–global buckling mode interaction is presented. Using the Rayleigh–Ritz methodcombined with displacement functions, a system of differential and integral equations is derived to describethe equilibrium states of the strut. In the present work, the interaction is between the criticalglobal (Euler) buckling mode about the weak axis and local buckling in the flange and web simultaneously,where the flange to web connection is assumed to be free to rotate as a rigid body. The initialeigenmode is shown to be destabilized at a secondary bifurcation where interactive buckling is triggered.A progressive change in the buckling mode is then observed, initially with local buckling in the compressionflange. Owing to the nature of the flange to web connection, this also triggers local buckling inthe web, which displaces in sympathy with the flange. The results from the analytical model have beenvalidated using the commercial finite element software ABAQUS, with good comparisons presented forthe post-buckling behaviour.

CONFERENCE PAPER

Liu EL, Wadee MA, 2015, Interactively induced localization in thin-walled I-section struts buckling about the strong axis, Structures, Vol: 4, Pages: 13-26, ISSN: 2352-0124

A variational model describing the behaviour of a thin-walled I-section strut suffering from local–global buckling mode interaction is presented where global (Euler) buckling about the strong axis is the critical mode. A system of differential and integral equations is derived that describe the equilibrium states from variational principles and are solved numerically using the continuation and bifurcation software Auto-07p for the perfect case. Initially stress relieved out-of-straightness imperfections are subsequently introduced and the nonlinear response is modelled. The modelled interaction is between the critical global buckling mode about the strong axis and local buckling in the flange and web simultaneously, where the flange–web joint is assumed to be free to rotate as a rigid body. The initial eigenmode is shown to be destabilized at a secondary bifurcation where interactive buckling is triggered. A progressive change in the buckling mode is then observed, initially with local buckling localizing at the mid-span of the compression flange, which also triggers sympathetic local buckling in the web. The results from the analytical model have been validated using the commercial finite element (FE) software Abaqus with good comparisons presented for the initial post-buckling behaviour. The strut also exhibits sensitivity to initial out-of-straightness imperfections, with a notable decrease in the ultimate load as the imperfection size increases. The ultimate loads for a range of imperfection amplitudes are found using both analytical models and FE analysis, with very good correlation observed.

JOURNAL ARTICLE

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