Singular stresses at the tip of a crack terminating at frictional interface of fibre reinforced composites

The stress singularities at the tip of a crack that terminates at a frictional interface between two layers in anisotropic composites are investigated. The order of stress singularities is determined by solving the characteristic equations obtained from the boundary conditions and the frictional interface conditions for the cases concerned. The interface is assumed to be governed by Coulomb's law of friction. Numerical results are presented for the cases with a crack terminating at a frictional interface of a fibre reinforced composite, and it is shown that there is a big difference of stress singularities between cases with and without considering friction along the interface.

An application of quasi-Newton methods for the numerical solution of interface problems

Quasi-Newton methods are applied to solve interface problems which arise from domain decomposition methods. These interface problems are usually sparse systems of linear or nonlinear equations. We are interested in applying these methods to systems of linear equations where we are not able or willing to calculate the Jacobian matrices as well as to systems of nonlinear equations resulting from nonlinear elliptic problems in the context of domain decomposition. Suitability for parallel implementation of these algorithms on coarse-grained parallel computers is discussed.

Nonlinear MHD stability of aluminium reduction cells

An industrial electrolysis cell used to produce primary aluminium is sensitive to waves at the interface of liquid aluminium and electrolyte. The interface waves are similar to stratified sea layers [1], but the penetrating electric current and the associated magnetic field are intricately involved in the oscillation process, and the observed wave frequencies are shifted from the purely hydrodynamic ones [2]. The interface stability problem is of great practical importance because the electrolytic aluminium production is a major electrical energy consumer, and it is related to environmental pollution rate. The stability analysis was started in [3] and a short summary of the main developments is given in [2]. Important aspects of the multiple mode interaction have been introduced in [4], and a widely used linear friction law first applied in [5]. In [6] a systematic perturbation expansion is developed for the fluid dynamics and electric current problems permitting reduction of the three-dimensional problem to a two dimensional one. The procedure is more generally known as “shallow water approximation” which can be extended for the case of weakly non-linear and dispersive waves. The Boussinesq formulation permits to generalise the problem for non-unidirectionally propagating waves accounting for side walls and for a two fluid layer interface [1]. Attempts to extend the electrolytic cell wave modelling to the weakly nonlinear case have started in [7] where the basic equations are derived, including the nonlinearity and linear dispersion terms. An alternative approach for the nonlinear numerical simulation for an electrolysis cell wave evolution is attempted in [8 and references there], yet, omitting the dispersion terms and without a proper account for the dissipation, the model can predict unstable waves growth only. The present paper contains a generalisation of the previous non linear wave equations [7] by accounting for the turbulent horizontal circulation flows in the two fluid layers. The inclusion of the turbulence model is essential in order to explain the small amplitude self-sustained oscillations of the liquid metal surface observed in real cells, known as “MHD noise”. The fluid dynamic model is coupled to the extended electromagnetic simulation including not only the fluid layers, but the whole bus bar circuit and the ferromagnetic effects [9].

Investigating the representation of merging behavior at the floor–stair interface in computer simulations of multi-floor building evacuations

In this article, the representation of the merging process at the floor— stair interface is examined within a comprehensive evacuation model and trends found in experimental data are compared with model predictions. The analysis suggests that the representation of floor—stair merging within the comprehensive model appears to be consistent with trends observed within several published experiments of the merging process. In particular: (a) The floor flow rate onto the stairs decreases as the stair population density increases. (b) For a given stair population density, the floor population's flow rate onto the stairs can be maximized by connecting the floor to the landing adjacent to the incoming stair. (c) In situations where the floor is connected adjacent to the incoming stair, the merging process appears to be biased in favor of the floor population. It is further conjectured that when the floor is connected opposite the incoming stair, the merging process between the stair and floor streams is almost in balance for high stair population densities, with a slight bias in favor of the floor stream at low population densities. A key practical finding of this analysis is that the speed at which a floor can be emptied onto a stair can be enhanced simply by connecting the floor to the landing at a location adjacent to the incoming stair rather than opposite the stair. Configuring the stair in this way, while reducing the floor emptying time, results in a corresponding decrease in the descent flow rate of those already on the stairs. While this is expected to have a negligible impact on the overall time to evacuate the building, the evacuation time for those higher up in the building is extended while those on the lower flows is reduced. It is thus suggested that in high-rise buildings, floors should be connected to the landing on the opposite side to the incoming stair. Information of this type will allow engineers to better design stair—floor interfaces to meet specific design objectives.

Time-dependent modelling and experimental validation of the metal/flux interface in a continuous casting mould

A finite volume computer model of the continuous casting process for steel flat products has been developed. In this first stage, the model concentrates on the hydrodynamic aspects of the process and in particular the dynamic behavior of the metal/slag interface. The model was validated against experimental measurements obtained in a water model apparatus.