Research Interests

I have a strong interest in structural buckling phenomena, particularly those leading to localizations and spatial chaos. Typical examples are the buckling of long, thin cylindrical shells under axial compression and struts resting on softening foundations. Such behaviour is inherently nonlinear and non-periodic but can be successfully modelled using methods from dynamical-systems theory.

Under certain loading conditions, such elastic structures can be analysed using both classical techniques developed in the past few decades based on the total potential energy functional and part-numerical methods which utilize some of the above results but also take advantage of modern numerical and symbolic computational tools. Here are some typical localized profiles for a strut resting on a softening foundation. I have tried to explain a little more about the behaviour of the strut problem here.

A new research front is the investigation of localization and ovalization of tubes in flexure. You can read about that here.

I have experience in the the application of bifurcation theory, the use of perturbation methods, numerical methods and computer programming.

Current research fronts:

• Double-scale perturbations;
• Variational methods;
• Extensions to the Rayleigh-Ritz and Galerkin techniques;
• Application of solitary-wave-type solutions to structural problems;
• Multi-modal homoclinic solutions (multi-humped localizations as soliton interactions). Use of exponential asymptotics;
• Modelling of the elastic bending of tubes.

Research grants held

Title	Duration	Co-investigator	Associated Researcher	Amount	Funding body
Elastic localization and restabilization in the post-buckling of model structures	2000-2003	Dr Andrew Bassom	Dr Ciprian D. Coman (Oct 2000-Oct 2002) Dr Andreas A. Aigner (Jan 2003-Dec 2003)	£ 138K	EPSRC GR/N05666/01

Ph. D. students

Olivier Meuric	1996-98	Numerical modelling of fluid flow in drilling processes
Edward Hirons	2007-	Auxetic tubes and buckling of aeronautical structures

External travel funding

Event	Date	Location	Sponsor	Value
Third Biennial European Joint Conference on Engineering Systems Design and Analysis organized by ASME	1-4 July 1996	Montpellier, France	The Royal Academy of Engineering	£ 300
Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation organized by SIAM	1-5 June 1998	Colorado School of Mines, Golden CO, USA	The Royal Academy of Engineering	£ 200
Workshop on Nonlinear Elasticity organized by Prof. Ray Ogden, Dr Yibin Fu and Dr Hui-Hui Dai	6-9 April 2000	City University of Hong Kong, China	The Royal Academy of Engineering	£ 300
ICIAM 2003	7-11 July 2003	Sydney, Australia	The Royal Academy of Engineering	£ 800
Visiting academic appointment, University of Western Australia	July-August 2006	Perth, Australia	The Royal Society of London	£ 1000
Visiting academic appointment, University of Western Australia	July-August 2008	Perth, Australia	The Royal Academy of Engineering	£ 500

Peer Review Activities: I have acted as a referee for the following:

• Grant applications submitted to EPSRC;
• Papers submitted to
  • Proceedings of the Royal Society of London (Series A)
  • International Journal of Solids and Structures
  • IMA Journal of Applied Mathematics
  • International Journal of Nonlinear Mechanics

Here are some nonlinear links to follow (shamelessly stolen from my brother, Ahmer (Overconfidentii vulgaris)).

UK Nonlinear News
UK Nonlinear Dynamics Groups
University of Bath School of Mathematical Sciences
University College London Centre for Nonlinear Dynamics
University of Bristol Research in Applied Nonlinear Mathematics

Some links to learned and professional organizations.

The Royal Society of London
The Royal Academy of Engineering
The Engineering Council
The Institution of Structural Engineers
The Institution of Civil Engineers
The Institute of Mathematics and its Applications
The Society for Industrial and Applied Mathematics