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Stability Research at Imperial College London


Imperial College London
Geometric modelling of nonlinear instabilities in structural mechanics
Ahmer Wadee

December 2015


Slender structural elements under certain geometric configurations can be highly susceptible to a range of complex post-buckling phenomena. Systems studied by our group at Imperial College London in the UK have included sandwich structures, layered structures and materials, thin-walled structural components, prestressed stayed columns and trusses, as well as conventional beams and columns. The principal behavior observed in these components is between global and local modes of buckling which when combined can give highly imperfection sensitive responses even when the individual modes may be stable in terms of their post-buckling response. Moreover, certain features in such components, although observed commonly in physical experiments, can be very difficult to model using standard numerical techniques such as the finite element method. These phenomena include: symmetry breaking, the localization of post-buckling modes and progressive cellular buckling. The latter is sometimes known as "snaking" and is also an important topic in nonlinear systems which pervades branches of applied mathematics, solid mechanics and physics (especially nonlinear optics). It is crucially important to model such phenomena if the true loadcarrying capacity of the components needs to be established for structural design.


Analytical geometric modelling is the primary approach that the group implements. The behaviour of the structural components have been studied primarily through energy principles, shear deformation bending theories, the Rayleigh-Ritz method and numerical continuation techniques. Depending on the problem, sometimes the models are modelled using variational techniques whereas some can be reduced to a very limited number of variables while describing the systems with discrete linear and nonlinear springs in conjunction with rigid link elements. Both perfect and imperfect systems are routinely analysed since this provides deeper understanding of how the model parameters affect the structural response. The models are then validated using physical experimentation or with the judicious use of the finite element method; the ultimate aim has then been to determine the structural configurations that provide most severely destabilizing behavior such that these may be avoided in calibrated design procedures. 


The interaction between lateral-torsional buckling (LTB) and local buckling in thin-walled beams has been investigated through the development of an analytical model which was validated through experimental studies. This has been subsequently extended to investigating the behaviour of axially compressed I-sections and stringer-stiffened plates. There has also been parallel work on prestressed stayed columns where it has been identified that the case which was deemed in the literature to be the most optimal is in fact that the most vulnerable to nonlinear modal interactions. Moreover, some recent work on modelling kink band instabilities and deformation in laminated composites has been developed by extending previous work on modelling confined friction layers for which detailed experiments revealed the excellence of the analytical study. 


Amongst several highlights, the findings from the research have revealed for the first time that cellular buckling is fairly commonplace in interactive buckling problems in thin-walled structures and in layered structures and materials. This has a profound influence on the structural response and our work has provided methodologies to establish the most severe configurations. Moreover, the group have recently devised a calibrated methodology for designing a class of prestressed stayed columns, which is currently being extended to more complex column and bridge deck arrangements.

Selected Publications

1. Hunt, GW and Wadee, MA, 1998. Localization and mode interaction in sandwich structures.
Proc. R. Soc. A, 454:1197-1216.
2. Wadee, MA and Hunt, GW, 1998. Interactively induced localized buckling in sandwich
structures with core orthotropy. J. Appl. Mech. - Trans. ASME, 65:523-528.
3. Wadee, MA, 2000. Effects of periodic and localized imperfections on struts on nonlinear
foundations and compression sandwich panels. Int. J. Solids Struct., 37:1191-1209.
4. Hunt, GW, Peletier, MA, Champneys, AR, Woods, PD, Wadee, MA, Budd, CJ and Lord, G J,
2000. Cellular buckling in long structures. Nonlinear Dyn. 21(1):3-29.
5. Wadee, MA and Blackmore, A, 2001. Delamination from localized instabilities in compression
sandwich panels. J. Mech. Phys. Solids, 49:12 81-1299.
6. Wadee, MA, Hunt, GW and Peletier, MA, 2004. Kink band instability in layered structures. J.
Mech. Phys. Solids, 52(5):1071-1091.
7. Wadee, MA and Edmunds, R, 2005. Kink band propagation in layered structures. J. Mech.
Phys. Solids, 53(9):2017-2035.
8. Edmunds, R and Wadee, MA, 2005. On kink banding in individual PPTA fibres. Compos. Sci.
Technol., 65(7-8):1284-1298.
9. Saito, D and Wadee, MA, 2008. Post-buckling behaviour of prestressed steel stayed
columns. Eng. Struct. 30:1224-1239.
10. Saito, D and Wadee, MA, 2009. Numerical studies of interactive buckling behaviour in
prestressed steel stayed columns. Eng. Struct. 31:432-443.
11. Wadee MA, Yiatros, S and Theofanous, M, 2010. Comparative studies of localized buckling
in sandwich struts with different core bending models. Int J. Non-Linear Mech., 45:111-120.
12. Wadee, MA and Völlmecke C, 2011. Semi-analytical modelling of buckling driven
delamination in uniaxially compressed damaged plates, IMA J. Appl. Math., 76(1):120-145.

Core Competencies

  • Stability of solids and structures
  • Nonlinear systems
  • Analytical structural modelling
  • Buckling, post-buckling and structural failure
  • Differential equations
  • Numerical continuation
  • Finite element analysis
  • Experimental techniques

Left: A physical example of lateral-torsional buckling and local buckling mode interaction. Right: An analytical model solution from Wadee and Gardner, Proc. R. Soc. A, 2012.

Dr Ahmer Wadee

Current PhD Students
Li Bai
Maryam Farsi
Jonathan Gosaye Fida Kaba
Elizabeth Liu
Fernando Madrazo-Aguirre
Jialiang Yu

Recent PhD Graduates
Dr Fumiaki Kimura 
Dr Finian McCann
Dr Adelaja Osofero
Dr Daisuke Saito
Dr Christina Völlmecke
Dr Stylianos Yiatros

Academic Collaborators
Professor Dinar Camotim
Professor Leroy Gardner
Dr Ana Girão Coelho
Professor Giles Hunt
Professor Mark Peletier
Dr Pedro Simão
Professor Luis Simões da Silva