The shape of a liquid's surface is determined by both the body force and surface force of the liquid. In this report, the body force is solely from the gravitational force. The surface force is generated from the movement of an elastic interface between the solid and liquid. To obtain the shape of the surface, both asymptotic analysis and numerical approaches are used in this report. The asymptotic analysis is applied on the potential flow. The initial conditions are chosen to be the function of the shape of the interface between the solid and liquid and the free stream velocity far away from the interface. The time dependent contributions from the fluid system are also considered. The initial condition changes according to the function of the calculated velocity potential. The numerical approach includes two parts: calculation the velocity potential and a formalism of the change of the system as time evolves. For the first part, two idealized vertical boundaries are utilized to give a unique solution of the Laplace equation. The boundary conditions are determined as the flow under linear viscosity. For the second part, the flow is first assumed to be a potential flow, and a boundary layer is considered to make the no-slip condition valid and to give a more precise approximation for the shear stress.

Deforming a complex generic shape into a representation of another complex shape is investigated. An initial study is done on the effect of cranial shape variation on masticatory induced stress. A finite element analysis is performed on two different skull geometries. One skull geometry has a prognathic shape, characterised by jaws protruding forward, while the other has a non-prognathic form. Comparing the results of the initial nite element analyses, the effect of an undesired variation in shape and topology on the resulting stress field is observed. This variation in shape and topology can not be attributed to the cranial shape variation that is investigated. This means that the variation in the masticatory induced stress field that is due to the relative degree in prognathism can not be quantified effectively. To best compare results, it would be beneficial to have a computational domain for the different skull geometries that have one-to-one correspondence. An approach to obtain a computational domain that represents various geometries with the exact same mesh size and connectivity between them does exist. This approach involves deforming a generic mesh to represent different target shapes. This report covers an introductory study to register and deform a generic mesh to approximately represent a complex target geometry. Various procedures are investigated, implemented and combined to specifically accommodate complex geometries like that of the human skull. A surface registration procedure is implemented and combined with a feature registration procedure. Feature lines are extracted from the surface representation of each skull as well as the generic shape. These features are compared and an initial deformation is applied to the generic shape to better represent the corresponding features on the target. Selective feature preserved elastic surface registration is performed after the initial feature based registration. Only the registration to surfaces of featureless areas and matched feature areas are allowed along with user selected areas during surface registration. The implemented procedures have various aspects that still require improvement before the desired study regarding prognathism's effect on masticatory induced stress could truly be approached pragmatically. Focus is only given to the use of existing procedures while the additional required improvements could be addressed in future work. It is however required that the resulting discretised domain obtained in this initial study be of sufficient quality to be used in a finite element analysis (FEA). The implemented procedure is illustrated using the two original skull geometries. Symmetric versions of these geometries are generated with a one-to-one correspondence map between them. The skull representations are then used in a finite element analysis to illustrate the appeal of having computational domains with a consistent mapping between them. The variation in the masticatory induced stress field due to the variation in cranial shape is illustrated using the consistent mapping between the geometries as part of this example. / Dissertation (MEng)--University of Pretoria, 2011. / Mechanical and Aeronautical Engineering / unrestricted