Complexity of mixed shop scheduling problems: A survey

We survey recent results on the computational complexity of mixed shop scheduling problems. In a mixed shop, some jobs have fixed machine orders (as in the job shop), while the operations of the other jobs may be processed in arbitrary order (as in the open shop). The main attention is devoted to establishing the boundary between polynomially solvable and NP-hard problems. When the number of operations per job is unlimited, we focus on problems with a fixed number of jobs.

CFD approach for solid mechanics analysis

A cell-centred finite volume(CC-FV) solid mechanics formulation, based on a computational fluid dynamics(CFD) procedure, is presented. A CFD code is modified such that the velocity variable is used as to the displacement variable. Displacement and pressure fields are considered as unknown variables. The results are validated with finite element(FE) and cell-vertex finite volume(CV-FV) predictions based on discretisation of the equilibrium equations. The developed formulation is applicable for both compressible and incompressible solids behaviour. The method is general and can be extended for the simultaneous analysis of problems involving flow-thermal and stress effects.

Modelling induction melting energy savings

Electromagnetic processing of liquid metals involves dynamic change of the fluid volume interfacing with a melting solid material, gas or vacuum, and possibly a different liquid. Electromagnetic field and the associated force field are strongly coupled to the free surface dynamics and the heat-mass transfer. We present practical modelling examples of the flow and heat transfer using an accurate pseudo-spectral code and the k-omega turbulence model suitable for complex and transitional flows with free surfaces. The 'cold crucible' melting is modelled dynamically including the melting front gradual propagation and the magnetically confined free surrounding interface. Intermittent contact with the water-cooled segmented wall and the radiation heat losses are parts of the complex problem.

Modelling the fluid dynamics and coupled phenomena in arc weld pools

A 3D model of melt pool created by a moving arc type heat sources has been developed. The model solves the equations of turbulent fluid flow, heat transfer and electromagnetic field to demonstrate the flow behaviour phase-change in the pool. The coupled effects of buoyancy, capillary (Marangoni) and electromagnetic (Lorentz) forces are included within an unstructured finite volume mesh environment. The movement of the welding arc along the workpiece is accomplished via a moving co-ordinator system. Additionally a method enabling movement of the weld pool surface by fluid convection is presented whereby the mesh in the liquid region is allowed to move through a free surface. The surface grid lines move to restore equilibrium at the end of each computational time step and interior grid points then adjust following the solution of a Laplace equation.

Characterisation of weldpool shapes in the laser welding of thick plates

We consider the problem of finding the heat distribution and the shape of the liquid fraction during laser welding of a thick steel plate using the finite volume CFD package PHYSICA. Since the shape of the keyhole is not known in advance, the following two-step approach to handling this problem has been employed. In the first stage, we determine the geometry of the keyhole for the steady-state case and form an appropriate mesh that includes both the workpiece and the keyhole. In the second stage, we impose the boundary conditions by assigning temperature to the walls of the keyhole and find the heat distribution and the shape of the liquid fraction for a given welding speed and material properties. We construct a fairly accurate approximation of the keyhole as a sequence of include sliced cones. A formula for finding the initial radius of the keyhole is derived by determining the radius of the vaporisation isotherm for the line heat source. We report on the results of a series of computational experiments for various heat input values and welding velocities.

A model to predict the life of pneumatic conveyor bends

A new approach to the prediction of bend lifetime in pneumatic conveyors, subject to erosive wear is described. Mathematical modelling is exploited. Commercial Computational Fluid Dynamics (CFD) software is used for the prediction of air flow and particle tracks, and custom code for the modelling of bend erosion and lifetime prediction. The custom code uses a toroidal geometry, and employs a range of empirical data rather than trying to fit classical erosion models to a particular circumstance. The data used was obtained relatively quickly and easily from a gas-blast erosion tester. A full-scale pneumatic conveying rig was used to validate a sample of the bend lifetime predictions, and the results suggest accuracy of within ±65%, using calibration methods. Finally, the work is distilled into user-friendly interactive software that will make erosion lifetime predictions for a wide range of bends under varying conveying conditions. This could be a valuable tool for the pneumatic conveyor design or maintenance engineer.

Three-phase computations of the continuous casting process

In this paper, the continuous casting process for steel slab production is modelled using a mult-physics approach. For this purpose, a Finite Volume (FV) numerical model was constructed in 3D, with the following characteristics: Time dependent, turbulent fluid flow and heat transfer in the molten steel and flux regions, solidification of the skin layer, under prescribed heat loss boundary conditions, particle tracking simulation of argon bubbles injected with the metal into the mould, full coupling between bubbles and liquid through buoyancy and interfacial forces using a novel gas accumulation technique, and a full transient simulation of flux-metal interface behaviour under the influence of gravity and fluid inertial forces and bubble plume buoyancy. The unstructure mesh FV code PHYSICA developed at Greenwich was used for carry out the simulations with physical process data and properties supplied by IRSID SA.

Computational modelling of metals forming processes

The computational modelling of metal forming processes is now well established. In this work

A case based model to assist in the design process in the manufacture of furniture products

This paper describes progress on a project to utilise case based reasoning methods in the design and manufacture of furniture products. The novel feature of this research is that cases are represented as structures in a relational database of products, components and materials. The paper proposes a method for extending the usual "weighted sum" over attribute similarities for a ·single table to encompass relational structures over several tables. The capabilities of the system are discussed, particularly with respect to differing user objectives, such as cost estimation, CAD, cutting scheme re-use, and initial design. It is shown that specification of a target case as a relational structure combined with suitable weights can fulfil several user functions. However, it is also shown that some user functions cannot satisfactorily be specified via a single target case. For these functions it is proposed to allow the specification of a set of target cases. A derived similarity measure between individuals and sets of cases is proposed.

Scheduling batches with simultaneous job processing for two-machine shop problems

We consider the problem of scheduling independent jobs on two machines in an open shop, a job shop and a flow shop environment. Both machines are batching machines, which means that several operations can be combined into a batch and processed simultaneously on a machine. The batch processing time is the maximum processing time of operations in the batch, and all operations in a batch complete at the same time. Such a situation may occur, for instance, during the final testing stage of circuit board manufacturing, where burn-in operations are performed in ovens. We consider cases in which there is no restriction on the size of a batch on a machine, and in which a machine can process only a bounded number of operations in one batch. For most of the possible combinations of restrictions, we establish the complexity status of the problem.

Dynamics of magnetically suspended fluid

Magnetic suspension is a technique for processing pure or reactive materials without contact to walls. This work is concerned with the flow in the rapidly deforming liquid volume, suspended in an AC magnetic field. Intense flow motion due to the induced electromagnetic force distorts dynamically the droplet envelope. The relative positional change between the liquid surface and the surrounding coil means that fluid flow and magnetic field computations need to be closely coupled. The computed results are compared against a physical experiment and nearly spherical analytic solutions. A comparison between the "magetic pressure" approximation and the full electromagnetic force solutions shows fundamental differences; the full electromagnetic force is necessary for accurate results in most practical applications of this technique. The physical reason for the fundamental discrepancy is the difference in the electromagnetic force representation: only the gradient part of the full force is accounted for in the "magnetic pressure" approximation.

Investigation of the cold crucible melting process: experimental and numerical study

The dynamic process of melting different materials in a cold crucible is being studied experimentally with parallel numerical modelling work. The numerical simulation uses a variety of complementing models: finite volume, integral equation and pseudo-spectral methods combined to achieve the accurate description of the dynamic melting process. Results show the temperature history of the melting process with a comparison of the experimental and computed heat losses in the various parts of the equipment. The free surface visual observations are compared to the numerically predicted surface shapes.

Details of an integrated approach to three-dimensional dynamic fluid structure interaction

Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, wind response of buildings, flows in elastic pipes and blood vessels. Numerical modelling of dynamic fluid-structure interaction (DFSI) involves the coupling of fluid flow and structural mechanics, two fields that are conventionally modelled using two dissimilar methods, thus a single comprehensive computational model of both phenomena is a considerable challenge and until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply. A single, finite volume unstructured mesh (FV-UM) spatial discretisation method has been employed on a single mesh for the entire domain. The Navier Stokes equations for fluid flow are solved using a SIMPLE type procedure and the Newmark b algorithm is employed for solving the dynamic equilibrium equations for linear elastic solid mechanics and mesh movement is achieved using a spring based mesh procedure for dynamic mesh movement. In the paper we describe a number of additional computation issues for the efficient and accurate modelling of three-dimensional, dynamic fluid-structure interaction problems.

A finite volume approach to geometrically non-linear stress analysis

In this past decade finite volume (FV) methods have increasingly been used for the solution of solid mechanics problems. This contribution describes a cell vertex finite volume discretisation approach to the solution of geometrically nonlinear (GNL) problems. These problems, which may well have linear material properties, are subject to large deformation. This requires a distinct formulation, which is described in this paper together with the solution strategy for GNL problem. The competitive performance for this procedure against the conventional finite element (FE) formulation is illustrated for a three dimensional axially loaded column.