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Extension of the Method of Difference Potentials to Problems of Elastic Plastic Mechanics

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  • Full or part time
    Dr Utyuzhnikov
    Dr Andrey Jivkov
  • Application Deadline
    No more applications being accepted
  • Funded PhD Project (UK Students Only)
    Funded PhD Project (UK Students Only)

Project Description

The method of Difference Potentials (DPM) proved to be a unique and very efficient tool for tackling many problems of mathematical physics. Its main advantage is that it allows boundary value problem to be reduced to a boundary equation in quite arbitrary domains without knowledge of Green’s function. This property is achieved via specially constructed difference projection operators and surface potentials. The potentials can be calculated in advance regardless the boundary conditions and forces. Therefore, the method is very efficient with respect to computational time for design problems in which multiple computations are needed for optimisation. The method is also quite universal since it can always be realised on rectangular structural grids with high accuracy regardless how complex the region is. Recently the method has been successfully applied to elastic problem with singular cracks (Woodward, Utyuzhnikov, Massin, Int. J. for Numerical Methods in Engineering, 2015).
This project is a following on work to extent DPM to nonlinear Mechanics. Although being a challenge, this problem is realistic because similar objectives were successfully achieved in fluid dynamics (Ryben’kii, Method of Difference Potentials and Its Applications, Springer, 2002). If successful the project will have high impact on non linear numerical analyses. It is supposed that the method should be implemented in the open source Code_Aster which has about 3,000 users. The project is supported by EDF and will be carried in close collaboration with the company.
The student will earn a unique experience in the very perspective field of elastic plastic fracture mechanics as well as the knowledge of the DPM. The student will be supervised at the University of Manchester but will also be guided by Dr P. Massin in EDF/CNRS (Paris)

Funding Notes

Project part-funded by EPSRC DTP and EDF.
Funding per year up to:
Home fees: £4,052
Stipend: £14,057 (RCUK Standard)
Additional stipend: £1,000

References

Additional skills required: Applicants must have strong mathematical and programming skills.

How good is research at University of Manchester in Aeronautical, Mechanical, Chemical and Manufacturing Engineering?
Mechanical, Aerospace and Manufacturing Engineering

FTE Category A staff submitted: 34.38

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