Topology optimization of high-frequency vibrating structures in thermal environments using the energy finite element method

The dynamic optimization of high-frequency vibrating structures under thermal effects is attracting increasing attention in engineering applications. To address this challenge, the energy finite element method (EFEM) has been widely adopted due to its low computational cost and accurate vibration analysis in the high-frequency band. However, studies combining topology optimization and the EFEM with thermal impact are rare, creating a scientific gap in the thermo-vibration coupling design of high-frequency vibrating structures. This study, for the first time, establishes an EFEM-based topology optimization framework for high-frequency vibrating thin stiffened plates under thermal environments. A series of basic technologies are provided, including thermo-vibration coupling analysis, explicit topology description, optimization models, and sensitivity analysis. The proposed optimization method is validated through multiple case studies under varying thermal conditions. Further analyses indicate that the optimization results vary with changes in the thermal environment, and the dynamic performance of high-frequency vibrating structures in different thermal environments can be improved by 13.58 %–60.42 %. It provides a digital design method for thermal vibration optimization design of engineering structures.