Maximizing the first eigenfrequency of structures subjected to uniform boundary erosion through the level set method

Abstract

Erosion of structure may result in non-trivial loss of performance. For instance, erosion may make structure members break apart and results in localized vibration eigenmodes, which will make the first eigenfrequency of eroded structure become smaller. To obtain a robust design whose first eigenfrequency is not disproportionately affected by boundary erosion, we first examine a generic deterministic structural optimization problem defined in the level-set framework. Relying on the analysis of the first-order shape derivative and the optimality conditions, several important conclusions are obtained. Then, the optimization problem of maximizing the first eigenfrequency of structures subjected to uniform erosion is introduced. In each iteration of optimization, erosion is intentionally created, and a mode recognition technique is employed to identify the actual first eigenfrequency, i.e., not belonging to localized eigenmodes. The boundary of the un-eroded structure is optimized to improve the performance of the eroded structure. The shape derivative defined on the boundary of the eroded structure is mapped to the boundary of the un-eroded one by resorting to velocity extension of the level set method.