A nested finite element methodology (NFEM) for stress analysis of electronic products - Part I: Theory and formulation

In this gaper, the authors present a stress analysis technique based on a novel nested finite element methodology (NFEM). The NFEM is similar in concept to an earlier. proposed multi-domain Rayleigh-Ritz methodology (Ling, S., 1997, "A Multi-Domain Rayleigh-Ritz Method for Thermomechanical Stress Analysis of Surface Mount Interconnects in Electronic Assemblies," Ph.D. dissertation, Univ., of Maryland), that is based on a nested multi-field displacement assumption. The nested multifield displacement technique may be viewed as a localized cascading of the p-type refinement in conventional finite element analysis. The concept and formulation of NFEM are presented in this paper while the application of NFEM to analyze the viscoplastic stress-state in two popular surface mount electronic interconnect styles is presented in Part II of this series. To illustrate the concept of NFEM, the formulation and results are provided for a one-dimensional viscoplastic example.