Finite Element Analysis of Shock & Vibration of a Printed Circuit Board Assembly Using the Beam Elements to Model the Solder Joints

This paper presents a finite element analysis (FEA) of shock & vibration (S&V) with the solder balls modeled by the beam elements instead of the traditional solid elements. The modeling degree of freedom is reduced by 2 orders in magnitude thus the computing time can be reduced from days to hours while the modeling accuracy is acceptable. To avoid spurious oscillations of nodal responses at the interface of different types of elements with degree-of-freedom mismatch, the appropriate tied contact is used between beam or shell elements and solid elements. It is found the beam elements can present the local bending moment and shear forces over each solder ball well but cannot present the axial force over the solder ball. The planar assumption of the beam theory is consistent with the deformation of majority area of the cross section of a solder but cannot reflect the normal stress concentration near the solder ball rim. Therefore, there is certain error on stress calculation from the beam theory. However, the relative relationship of the solder ball stresses calculated from the beam theory are consistent with that obtained from using solid elements on the solder balls. This strategy provides a quick alternative to perform FEA on a complicated board with multiple BGA to assess the risks of solder joint reliability during S&V.