Partitioned analysis and approximations in optimization of mechanical systems: A focus on electronic packages.

摘要

Mechanical systems; in general, are computationally expensive to analyze. Electronic packages are examples of complex mechanical systems. The analysis of electronic packages is usually complicated because of factors such as: nonlinear behavior of materials (e.g. plastic and creel) deformations of solder), complicated package construction, large number of interconnections (e.g. a high-end area-array package can have more than 1000 solder joints) and other complications in analysis (e.g. a nonlinear contact analysis of a Land Grid Array connector). Conventional analysis techniques, such as finite element analysis, are computationally inefficient for quick design decision. Optimal designs are even inure expensive to determine since optimization techniques are iterative. Efficiency in analysis of these systems can be achieved by using design or analysis related approximations, but this approach may lead to inaccuracies in the solution. The need for efficient as well as accurate techniques for analysis of complex mechanical systems in general and electronic packages in particular is obvious. The current trend in electronic packages is towards very high density of interconnections. With increasing density and decreasing size of the package, the need for an efficient analysis and design technique is even more severe.; In the research presented here, techniques that enable efficient as well as accurate analysis, and therefore efficient optimization, are developed. The research presented in this thesis represents efficient analysis and optimization techniques at two different levels. The first set of techniques is aimed at efficient analysis at subsystem level. In case of electronic packages, this applies to the second level packaging or the interconnect level. The second set of techniques is aimed at the system level. A novel decomposition-based methodology is proposed: the whole system is partitioned into subsystems and an efficient system level solution is obtained by coordinating the subsystem level solutions. The decomposition methodology presented here is a combination of traditional design and domain decomposition, and it fills an existing gap in these two types of decompositions. Other important aspects of the methodology are: no need for mesh correspondence at the interface, linking together of independently analyzed subsystems, and system-independent, subsystem modules.; Although the methods developed here are demonstrated on electronic packaging problems, they have potential applications in other engineering systems such as automotive and aerospace systems.