Topology optimization for improving stability of a rotating thin plate

Increasing the critical angular speed of a rotating structure can enlarge working range and enhance operating safety. To achieve this purpose, a topology optimization approach is proposed to increase the critical angular speed of a rotating thin plate in this paper. Firstly, the stability analysis of a rotating thin plate is performed by using the absolute nodal coordinate formulation modeling scheme, which can accurately account for the large deformation and large rotation of the rotating thin plate. In order to overcome the difficulty of non-differentiability of the critical angular speed with respect to the design variables, an alternative density-based topology optimization model for improving stability is then established by minimizing the real part of the eigenvalues of the rotating thin plate. A successive approximation dynamic programming method is therefore proposed to approaching the critical angular speed by repeatedly solving the aforementioned topology optimization problem. Finally, one dynamic example and two optimization examples are presented to respectively demonstrate the accuracy of the stability analysis procedure and the effectiveness of the proposed topology optimization problem.