Eliminate localized eigenmodes in level set based topology optimization for the maximization of the first eigenfrequency of vibration

Maximizing the fundamental eigenfrequency of vibration is an important topic in structural topology optimization. Previous studies of such a topology optimization problem should always be cautious of the “artificial localized mode” as it makes the optimization fail. In the present work, a level set based topology optimization is proposed to address such an issue. The finite element analysis is conducted on the actual structure by using a body-fitted mesh and without artificial weak material, thus localized mode that conventionally arises due to low-density region is prevented. In the present study, attention is turned to localized mode occurred gradually during the optimization. Such kind of localized mode results from the emergence of isolated area or cracked structure member produced by topological changes. A mode recognition technique based on the volume ratio of vibration-free region to the entire structure is proposed to identify such localized mode. Numerical examples of 2D structures are investigated.