A FEM-BEM coupling scheme for elastic dynamics problems in electronic packaging

In the field of electronic packaging structure reliability research, the Finite Element Method (FEM) is recognized as an effective and reliable approach for numerical simulation. Concurrently, the Boundary Element Method (BEM) is noted for its unique advantage of requiring discretization only at the boundary, which significantly reduces the degrees of freedom and potentially enhances the accuracy of analyses. This characteristic makes BEM particularly useful for analyzing multiscale structures in electronic packaging. Nevertheless, both methods have their limitations: FEM necessitates elements within the internal domain, making it computationally intensive, while BEM is most effective with linear problems and can be less versatile with nonlinear issues. Considering these factors, this paper introduces a FEM-BEM coupling algorithm designed to address the transient elastic dynamic response problem in electronic packaging structures. This approach is designed to leverage the strengths and mitigate the limitations of both the FEM and BEM. During the numerical simulation, the model is initially segmented into FE and BE domains. The FE domain is solved using ABAQUS, while the BE domain is analyzed through a self-written boundary element program. The BE domain functions as a specialized type of finite element, where its equivalent stiffness and load are determined by invoking the boundary element program via the User-Defined Element subroutine (UEL). These results are then integrated into the finite element system. Numerical examples demonstrate that the proposed FEMBEM coupling method is both effective and feasible for analyzing the dynamic response of electronic packaging structures.