CONTINUITY AND COLLOCATION EFFECTS IN THE BOUNDARY ELEMENT METHOD

The presence of singularities in the integral operators of the boundary element methods requires that the density functions must satisfy certain continuity requirements if the displacements and stresses are to be bounded. Quite often the continuity conditions, particularly on the derivatives of the density functions, are relaxed at the element ends for the sake of simplicity in approximating the unknown density functions. In this paper, a numerical study on the effects of satisfying or violating the continuity requirements and the effect of the boundary condition collocating point on three different BEM formulations is presented. Two are indirect formulations using force singularities and displacement discontinuity singularities, and the third is Rizzo's direct formulation. The two integral operators in the direct BEM appear individually in the two different formulations of the indirect BEM. This makes it possible to study the numerical error and other problems in each integral operator and the interaction of the two integral operators in the direct BEM. The impact of the study on numerical modelling for the three BEM formulations is presented in the paper. © 1997 by John Wiley & Sons, Ltd.     

Component allocation to balance workload in printed circuit card assembly systems

Component allocation in printed circuit card assembly systems is a special case of the classical mixed-model assembly line balancing problem and involves assigning component types to machines to achieve specific production objectives. In this paper the component allocation problem is considered for the scenario where there are two or more placement machines (possibly nonidentical) and the objective is to balance, for every card type, a combination of the card assembly time and the machine setup time. A mathematical formulation of the problem is developed for a class of placement machines. Two alternative solution approaches are presented: a list-processing-based heuristic for a simple version of the problem, and a linear-programming-based branch-and-bound procedure for the general component allocation problem. Industrial case study results are presented for each approach that indicate expected throughput improvements of up to 8-10% over the company's current procedure, with much less direct effort required by the process engineer.