Topology optimization of high frequency vibration problems using the EFEM-based approach

The energy finite element method (EFEM) provides researchers with an efficient tool to analyze high-frequency vibrating solid structures with less calculation and clear distribution of the energy density. However, the corresponding applications in structure optimization mainly focus on modifying the size and material properties, and it leaves a scientific gap that the topology flexibility is not addressed enough in the optimization. Therefore, this work aims at establishing an explicit level-set based topology optimization framework for the energy finite element method. A series of basic technical aspects, including the explicit level set description method, customized finite element mesh, mathematical model, and sensitivity analysis, are presented. With these basic studies, an original EFEM-based topology optimization framework for thin-walled structures is established for the first time. It is a basic work to conduct topology optimization in terms of energy. Additional applications in curved surfaces, spatial structures, and compound materials can also be developed only by modifying the description and EFEM module. Finally, the proposed optimization is applied to classic stiffened plates. Further analyses indicate that the proposed EFEM-based topology optimization can improve the dynamic performance of high-frequency vibrating structures by 20%–80%.