Integrated optimization of structural topology and control for piezoelectric smart plate based on genetic algorithm

The integrated optimization of structural topology, number and positions of the actuators and control parameters of piezoelectric smart plates is investigated in this paper. Based on the optimal control effect in the independent mode control and singular value decomposition of the distributed matrix of total performance index for all physical control forces for piezoelectric smart plate, a new criterion, where several large values in singular values are selected, is put forward to determine the optimal number of the assigned actuators in the coupled modal space control. Furthermore, the optimal positions of actuators are ascertained by singular value decomposition of the modal distributing matrix. The integrated optimization model, including the optimized objective function, design variables and constraint functions, is built. The design variables include the logic design variables of structural topology, the number and positions of actuators as well as the control design parameters. Some optimal strategies based on genetic algorithm (GA), such as structural connection checking and structural checkerboard checking and repairing technique, are used to guide the optimization process efficiently. The results of two numerical examples show that the proposed approach can produce the optimal solution with clear structural topology and high control performance.