A theoretical study investigating the effects of both anisotropic and isotropic surface roughness on the convective stability of the boundary-layer flow over a rotating disk is described. Surface roughness is modelled using a partial-slip approach, which yields steady-flow profiles for the relevant velocity components of the boundary-layer flow which are a departure from the classic von Kármán solution for a smooth disk. These are then subjected to a linear stability analysis to reveal how roughness affects the stability characteristics of the inviscid Type I (or cross-flow) instability and the viscous Type II instability that arise in the rotating disk boundary layer. Stationary modes are studied and both anisotropic (concentric grooves and radial grooves) and isotropic (general) roughness are shown to have a stabilizing effect on the Type I instability. For the viscous Type II instability, it was found that a disk with concentric grooves has a strongly destabilizing effect, whereas a disk with radial grooves or general isotropic roughness has a stabilizing effect on this mode. In order to extract possible underlying physical mechanisms behind the effects of roughness, and in order to reconfirm the results of the linear stability analysis, an integral energy equation for three-dimensional disturbances to the undisturbed three-dimensional boundary-layer flow is used. For anisotropic roughness, the stabilizing effect on the Type I mode is brought about by reductions in energy production in the boundary layer, whilst the destabilizing effect of concentric grooves on the Type II mode results from a reduction in energy dissipation. For isotropic roughness, both modes are stabilized by combinations of reduced energy production and increased dissipation.

We summarise results of a theoretical study investigating the distinct convective instability properties of steady boundary-layer flow over rough rotating disks. A generic roughness pattern of concentric circles with sinusoidal surface undulations in the radial direction is considered. The goal is to compare predictions obtained by means of two alternative, and fundamentally different, modelling approaches for surface roughness for the first time. The motivating rationale is to identify commonalities and isolate results that might potentially represent artefacts associated with the particular methodologies underlying one of the two modelling approaches. The most significant result of practical relevance obtained is that both approaches predict overall stabilising effects on type I instability mode of rotating disk flow. This mode leads to transition of the rotating-disk boundary layer and, more generally, the transition of boundary-layers with a cross-flow profile. Stabilisation of the type 1 mode means that it may be possible to exploit surface roughness for laminar-flow control in boundary layers with a cross-flow component. However, we also find differences between the two sets of model predictions, some subtle and some substantial. These will represent criteria for establishing which of the two alternative approaches is more suitable to correctly describe experimental data when these become available.

The stress concentration factor in a plate with a hole is very important for joints. There are many different types of joints and forms. Plates are usually connected with bolted, riveted and pin joints. Connection parts need to consist of hole/holes to make a joint using these machine elements. Machine parts are exposed to different stresses. In this study, the stress concentration factor in a plate with a circular hole under axial tension stresses was invegistated. The emprical (Peterson's) stress concentration factor (Kt) was compared with the results of analytical model, regression analysis (REGA), finite element analysis (FEA), artificial neural network (ANN) model. The stress concentration factor (Kt) was modeled using 5 different methods and the accuracy of Peterson's model was tested. The best results were obtained using ANN model. The emprical results and ANN predictions were compared by using statistical error analyzing the absolute fraction of variance (R² = 0.999999788), root mean square error (RMSE = 0.000934125) and mean error percentage (MEP = 0.033902049) with the test data. ANN model can be used instead of Peterson's model. K_t was determined by the ANN with an acceptable accuracy.