This paper presents a global–local methodology for predicting mechanical deformation and fatigue durability of solder joints in electronic packaging systems subject to cyclic thermal loading. It involves a global deformation analysis, a local critical solder–joint analysis, and a fatigue life analysis. The global deformation analysis includes a new optimization formulation for determining an equivalent model. The methodology developed was applied to fine pitch ball grid array (fpBGA) and super ball grid array (SBGA) packages. Selective experimental efforts were also undertaken to evaluate the predicted deformation characteristics of the fpBGA package. A good agreement was obtained between the simulated deformation results and experimental observations. For the durability analysis, the total fatigue life predicted using the energy-based method is larger than 2500 cycles—a trend observed experimentally for both packages entailing widely different designs. Based on proposed modeling and simulation results and package designs studied, the SBGA package is more durable than the fpBGA package.

This paper presents a new method to construct response surface function and a new hybrid optimization method. For the response surface function, the radial basis function is used for a zeroth-order approximation, while new bases is proposed for the moving least squares method for a first-order approximation. For the new hybrid optimization method, the gradient-based algorithm and pattern search algorithm are integrated for robust and efficient optimization process. These methods are based on: (1) multi-point approximations of the objective and constraint functions; (2) a multi-quadric radial basis function for the zeroth-order function representation or radial basis function plus polynomial based moving least squares approximation for the first-order function approximation; and (3) a pattern search algorithm to impose a descent condition. Several numerical examples are presented to illustrate the accuracy and computational efficiency of the proposed method for both function approximation and design optimization. The examples for function approximation indicate that the multi-quadric radial basis function and the proposed radial basis function plus polynomial based moving least squares method can yield accurate estimates of arbitrary multivariate functions. Results also show that the hybrid method developed provides efficient and convergent solutions to both mathematical and structural optimization problems.