Optimization of Vibration-Shock Responses of BGA Solder Joints under Complex Dynamic Loads

TIAN Zhengyang; ZHONG Yuan; ZHU Yixin; SU Yutai

doi:10.7643/issn.1672-9242.2026.07.002

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Equipment Environmental Engineering ›› 2026, Vol. 23 ›› Issue (7) : 11-21. DOI: 10.7643/issn.1672-9242.2026.07.002

Special Topic——Research on Application of Complex Dynamic Environment Analysis and Fine Adaptability Verification Technique for Precise Mother-Daughter UAV System

Optimization of Vibration-Shock Responses of BGA Solder Joints under Complex Dynamic Loads

TIAN Zhengyang^1a, ZHONG Yuan², ZHU Yixin^1b, SU Yutai^1a,*

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Abstract

The work aims to propose a vibration-shock response prediction and optimization method for BGA solder joint arrays to reduce the integrated critical response of the solder joint array under typical dynamic load cases, so as to address the problems of random-vibration-induced Mises stress concentration and shock-induced plastic strain accumulation in BGA solder joints of aircraft electronic assemblies under complex dynamic load environments. Driven by two load cases, random vibration and shock, a parametric model consisting of a PCB a 15×15 BGA solder joint array, and surrounding components was established. PCB thickness, solder joint stand-off height, solder joint diameter, pad diameter, and the x- and y-direction offsets of the BGA solder pad array were selected as design variables. A total of 300 samples were generated using Latin hypercube sampling. Random Mises stress was adopted for the random vibration case, while equivalent plastic strain was used to characterize the plastic response of solder joints under shock loading. A U-Net surrogate model for array responses was further constructed to rapidly predict the 15×15 solder joint array response field from structural parameters. Based on a reference design, the maximum random Mises stress under random vibration and the maximum equivalent plastic strain under shock loading were normalized, and a vibration-shock integrated objective function with equal weighting was formulated. The adaptive opposition-based spiral search algorithm was then employed for optimization. The finite element validation results showed that, after optimization, the maximum equivalent plastic strain of the BGA solder joint array under shock loading was reduced by 40.31%, the maximum random Mises stress under random vibration was reduced by 67.82%, and the integrated objective function was reduced by 54.07%. These results indicated that the optimized design could effectively improve the response level of the solder joint array under the two dynamic load cases. The proposed method enables rapid prediction and parameter optimization of vibration-shock responses of BGA solder joint arrays with limited simulation samples. It can effectively reduce the critical responses of solder joints under two typical dynamic load cases and provide a reference for environmental worthiness design and reliability analysis of aircraft electronic assemblies under complex dynamic load environments.

Key words

complex dynamic load / BGA solder joint / random vibration / shock response / equivalent Mises stress / equivalent plastic strain / U-Net surrogate model / response optimization

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TIAN Zhengyang, ZHONG Yuan, ZHU Yixin, SU Yutai. Optimization of Vibration-Shock Responses of BGA Solder Joints under Complex Dynamic Loads[J]. Equipment Environmental Engineering. 2026, 23(7): 11-21 https://doi.org/10.7643/issn.1672-9242.2026.07.002

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Funding

National Natural Science Foundation of China (52505158); Chuang Yuan High-level Innovation and Entrepreneurship Talent Project (QCYRCXM-2022-306); Xi'an Science and Technology Plan Project under the Key Core Technology Research Program (2026JH-GJHXG-0020)