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%.

能量有限元方法（EFEM）为研究人员提供了一种有效的工具，可以以较少的计算量和清晰的能量密度分布来分析高频振动固体结构。但是，结构优化中的相应应用主要集中在修改尺寸和材料属性上，并且在科学上存在空白，即拓扑灵活性在优化中得不到充分解决。因此，这项工作旨在为能量有限元方法建立基于显式水平集的拓扑优化框架。介绍了一系列基本技术方面，包括显式水平集描述方法，定制的有限元网格，数学模型和灵敏度分析。有了这些基础研究，首次建立了基于EFEM的原始薄壁结构拓扑优化框架。根据能量进行拓扑优化是一项基础工作。仅通过修改说明和EFEM模块，也可以开发曲面，空间结构和复合材料中的其他应用程序。最后，将所提出的优化应用于经典加筋板。进一步的分析表明，所提出的基于EFEM的拓扑优化可以将高频振动结构的动态性能提高20％–80％。只能通过修改说明和EFEM模块来开发复合材料。最后，将所提出的优化应用于经典加筋板。进一步的分析表明，所提出的基于EFEM的拓扑优化可以将高频振动结构的动态性能提高20％–80％。只能通过修改说明和EFEM模块来开发复合材料。最后，将所提出的优化应用于经典加筋板。进一步的分析表明，基于EFEM的拓扑优化建议可以将高频振动结构的动态性能提高20％–80％。