2018 年 84 巻 868 号 p. 18-00343
In this study, we propose a parameter-free optimization method to control time-dependent responses of a shell structure, where the optimal thickness distribution is determined without design parameterization. The design objective is to minimize the vibration displacements or to control the dynamic responses at arbitrary domains and times for an arbitrary time-dependent loading under the volume constraint. The unsteady optimum design problems are formulated as distributed-parameter optimization problems and the sensitivity functions with respect to the thickness variation are derived based on the variational method, Lagrange multiplier method and the adjoint variable method. The derived sensitivity function is applied to the H1 gradient method with Poisson's equation, a gradient method in the function space newly proposed in this study to determine the optimal variation of the thickness distribution. With the proposed method, the optimal thickness distribution for time-dependent response problems such as a forced-vibration, a free-vibration or a transient response is obtained while minimizing the objective functional and maintaining the smooth thickness distribution of a shell structure. Several numerical design examples including a continuous dynamic force or an impulse force as an input force are demonstrated to show the effectiveness of the proposed method, and the results are discussed.
