# Professor Rade VignjevicProfessor - Structural Integrity

Howell Building 107

## PhD projects for research students

### Modelling damage and failure of structural glass panels based on a hybrid plate element

The tensile strength of thin glass panels/plates used in building structures is of great importance due to the designer’s increasing demands for such structures, regarding size, shape and weight of the panels. It is well known that the intrinsic, (for panels with perfect surfaces) tensile strength of a panel greatly exceeds the tensile strength of real panels with surfaces flaws such as surface cracks and pits. Such surface flaws can arise from manufacture of a glass panel, during handling or installation on a building, or by impact damage from wind driven debris during its service life. A major difficulty in determining the panel tensile strength in situ is the fact that the number, size and the location of the flaws on the panel surfaces are not known. Thus, in modelling a panel one requires not only numerical methods such as finite elements, but also statistical methods to predict the probability of failure for a real panel with the surface flaws subjected to a specific loading regime.

We are seeking a PhD student with appropriate background to work on the development of a modelling approach based on Kirchhoff plate theory where the biharmonic operator is split allowing for separation of the damage effects from the response of the perfect plate with no imperfections leading to coupled second order PDEs. This will enable calculation of the deformation of the plates with the randomly located and increasing number of surface flows (cracks & pits). In this the effect of the change of surface shape on the deformation is treated by having in the PDE the effect of the changing shape contained on the right-hand side of the continuous problem and the resulting matrix system in the FE computation. The random location of the increasing number of the flows are calculated using Monte-Carlo method. This new computational tool will be validated and applied to selected industrial problems.

The research involves applied mathematics and scientific computing (in, for example, Fortran or C/C++). Applicants are expected to have at least a 2.1 BSc/BEng honours degree or equivalent in Mathematics, Mechanical Engineering or a related subject.

The ideal candidate will have experience of numerical approximation of partial differential equations, although candidates lacking that specific experience should not be deterred from applying.

Note that a condition of the appointment is the requirement to complete the Graduate Learning and Teaching Programme (or equivalent) and the appointee may be required to successfully pass selected taught modules run by Brunel University London and/or the London Taught Course Centre.

This research will be carried out in at the National Structural Integrity Research Centre (NSIRC Brunel) in Cambridge and consequently the student will work at NSIRC for a certain percentage of time.

### Improvement of Eulerian form of SPH

This is proposal for a PhD project on reformulation of the Eulerian form of the Smooth Particle Hydrodynamics (ESPH) method and the development of methods for stabilisation of ESPH. This is intended for modelling of damage and failure of solids mainly the specific case of quasi-static and dynamic elasticity. The stable form of the ESPH should allow for more accurate modelling of damage initiation, evolution and localisation as well as crack initiation, propagation and branching. The research project will focus first on problems posed in two-dimensional spatial domains, with the later intention to extend and implement the work in a 3D SPH code. This new computational tool will be validated and applied to selected industrial problems such as modelling of bird strike on composite aircraft structures and modelling of crack propagation in pressurised pipes. The research involves applied mathematics, solid mechanics and scientific computing (in, for example, Fortran or C/C++). The ideal candidate will have experience of numerical approximation of partial differential equations, although candidates lacking that specific experience should not be deterred from applying.

### SPH/FEM coupling for transient analysis

We are seeking a PhD student with appropriate background to work on the development of methods for the coupling of total Lagrangian SPH (Smooth Particle Hydrodynamics) methods to FEM (Finite Element Methods) in the specific case of quasi-static and dynamic elasticity. The SPH/FEM coupling should allow for more accurate modelling of: damage initiation, evolution and localisation; crack initiation, propagation, and branching. Initially, the developments will be done in 2D with intention to be extended and implemented into a 3D non-linear finite element/SPH code. The new developments will be validated and applied to selected industrial problems.

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