An EFEM-based topology optimization for curved structures with high-frequency vibration

The increasing operating velocities of advanced equipment, such as aerospace vehicles, new-concept engines, and hypersonic vehicles, have made high-frequency vibrations a critical issue. Energy-based vibration analysis is a primary tool for high-frequency vibration studies. However, energy reflection leads to discontinuous energy fields, which are rarely addressed in topology optimization studies. Moreover, as a fundamental feature of thin-walled structures, curved surface induces coupling between energy reflection and wave conversion, making energy-based topology optimization more challenging. Additionally, the topological evolution of arbitrary curved thin-walled structures requires highly flexible modeling methods. It is another challenge in the optimization of high-frequency vibrating curved structures. Therefore, the topology optimization of curved structures with high-frequency vibration is still open. The innovation of this study lies in the integration of EFEM with topology optimization techniques for curved structures. On the one hand, a modified EFEM is developed to handle energy reflection and wave-type conversion in curved structures, and overcome mesh failure issues in discontinuous fields. On the other hand, an explicit topology optimization for curved discontinuous fields is also provided. It can model stiffener layouts in arbitrarily curved surfaces and drive free topological changes within discontinuous energy density fields. To verify the applicability of the proposed method, a series of cases where the curvature and topology vary from simple to complex are studied. The cases indicate that the proposed method can effectively suppress high-frequency vibrations and achieve lightweight designs. This conclusion is further confirmed by modal, sweep frequency, and fixed-frequency experiments.