Advanced Methods of Fundamental Solutions applied to Problems in Computational Mechanics
George Fam has successfully passed his MPhil Viva at WIT with a thesis on “Advanced Methods of Fundamental Solutions applied to Problems in Computational Mechanics”.
George presented new developments in the Method of Fundamental Solutions (MFS) for two-dimensional potential problems and three-dimensional elastostatics problems.
The conventional monopole MFS formulation for two-dimensional potential problems was reviewed. The effect of different problem parameters including the number of boundary points, the number of sources and their placement was studied. Dipole formulation for two-dimensional potential problems was introduced and the derivation of the corresponding kernels was given in explicit form. This new formulation in addition to a mixed version including both monopoles and dipoles were implemented in a computer code.
The conventional formulation for the Method of Fundamental Solutions with three-dimensional elastostatics and monopoles, was reviewed. The Dipole formulation was then introduced in the MFS for 3D elastostatics and corresponding kernels for displacement, strain, stress and traction were derived. The formulation was applied to several problems and results were verified against other numerical and analytical techniques.
A treatment of body forces within the MFS for 3D elastostatics was developed. The gravitational body load was represented by means of analytical particular solutions. The formulation was extended to take into account spring boundary conditions.
An advanced MFS formulation for 3D elastostatics was developed, based on the continuous collocation approach. A mixed collocation approach was then developed. It was found that such formulation helped in modelling (linear, quadratic, …etc) boundary conditions. Several examples, including such boundary conditions distributions, thin structures, and calculation of tangential stressed on the boundaries, were presented.
George presented an excellent MPhil thesis as a result of his research, and was congratulated by the external examiner, Prof. Derek Ingham, Professor of Mathematics at Leeds University, and Dr Viktor Popov, internal examiner, for the high standard of his work. He is now returning to Cairo where he is to further his career as a professional engineer.