The single most difficult aspect for thermo-mechanical analysis at the board level lies in to an accurate accounting for interactions among boards and small features such as solder joints and secondary components. It is the large number of small features populated in a close neighborhood that proliferates the computational intensity. This paper presents an approach to stress analysis for boards with highly populated small features (solder joints, for example). To this end, a generalized self-consistent method, utilizing an energy balance framework and a three-phase composite model, is developed to obtain the effective properties at board level. The stress distribution inside joints and components are obtained through a back substitution. The solutions presented are mostly in the closed-form and require a minimum computational effort. The results obtained by present approach are compared with those by finite element analysis. The numerical calculations show that the proposed micromechanics approach can provide reasonably accurate solutions for highly populated printed circuit boards.
Chip- and board-level optical interconnections using rigid flexible optical electrical printed circuit boards
