PhD Scholarship on Mathematics for Manufacturing

Robustness-performance optimisation for automated composites manufacture
Supervisors: Profs. Frank Ball, Andrew Cliffe and Michael Tretyakov, School of Mathematical Sciences (Nottingham)

Multidisciplinary collaborations are a critical feature of material science research enabling integration of data collection with computational and/or mathematical modelling. This PhD study provides an exciting opportunity for an individual to participate in a project spanning research into composite manufacturing, stochastic modelling and statistical analysis, and scientific computing. The project is integrated into the EPSRC Centre for Innovative Manufacturing in Composites, which is led by the University of Nottingham and delivers a co-ordinated programme of research at four of the leading universities in composites manufacturing, the Universities of Nottingham, Bristol, Cranfield and Manchester.

This project focuses on the development of a manufacturing route for composite materials capable of producing complex components in a single process chain based on advancements in the knowledge, measurement and prediction of uncertainty in processing. The necessary developments comprise major manufacturing challenges. These are accompanied by significant mathematical problems, such as numerical solution of coupled non-linear partial differential equations with randomness, the inverse estimation of composite properties and their probability distributions based on real-time measurements and the formulation and solution of a stochastic model of the variability in fibre arrangements. The outcome of this work will enable a step change in the capabilities of composite manufacturing technologies to be made, overcoming limitations related to part thickness, component robustness and manufacturability as part of a single process chain, whilst yielding significant developments in mathematics with generic application in the fields of stochastic modelling and inverse problems.

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The specific aims of this project are: (i) Stochastic simulation of multi-dimensional non-linear stochastic problems; (ii) Stochastic and statistical modelling of fibre variability in Automated Fibre Placement to permit the predictive simulation of range of potential outcomes conditional on monitoring observations made during the process; (iii) Solution of the anisotropic conductivity inverse problem under uncertainty to translate monitoring and simulation of observable parameters to uncertainty quantification of critical unobservable variables.

The PhD programme contains a training element, which includes research work as well as traditional taught material. The exact nature of the training will be mutually agreed by the student and their supervisors and will have a minimum of 30 credits (approximately ¼ of a Master course/taught component of an MSc course) of assessed training. The graduate programmes at the School of Mathematical Sciences and the EPSRC Centre for Innovative Manufacturing in Composites provide a variety of appropriate training courses.

We require an enthusiastic graduate with a 1st class degree in Mathematics (in exceptional circumstances a 2(i) class degree can be considered), preferably of the MMath/MSc level, with good programming skills and willing to work as a part of an interdisciplinary team. A candidate with a solid background in statistics and stochastic processes will have an advantage.

The studentship is available for a period of three and a half years from September/October 2013 and provides an annual stipend of £13,726 and full payment of Home/EU Tuition Fees. Students must meet the EPSRC eligibility criteria.

Informal enquiries should be addressed to Prof. Michael Tretyakov, email:

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To make an application, please click the ‘Apply‘ button below. Please ensure you quote ref: SCI/1262. This studentship is open until filled. Early application is strongly encouraged. 

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