Abstract
Compared with static shape control, dynamic shape control is more difficult due to its time-varying nature. To improve the control precision and reduce the number of actuators needed, an integrated design optimization model of structure and control is proposed. The following three sets of design variables are considered to minimize the time domain variance between the controlled and desired dynamic shapes: the time-varying actuator voltages, the actuator layout and the structural ply parameters. To satisfy the engineering performance requirements to the greatest extent possible, constraints on the structural mass, the energy, the maximum transient voltage and the number of actuators are considered. Because the control voltages are varying in time, a two-level optimization strategy is adopted. In the inner optimization problem, the Newmark integral method is applied to derive discrete time domain expressions for the shape control equations, and then, the Kuhn-Tucker condition is introduced to calculate the optimal time-varying voltage distribution. To solve the outer optimization problem, because of the coexistence of discrete variables and continuous variables, a simulated annealing algorithm is used. To address the shape control of complicated curved shells, a finite element formulation for an eight-node laminated curved shell element with piezoelectric actuators is derived. Numerical examples show that the proposed integrated design optimization method can significantly improve the control effect and that the optimization of the structural ply parameters plays an important role. Moreover, the control system can be simplified by taking the minimum number of actuators as the objective function when the control accuracy allows.
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Funding
The research project is supported by the National Natural Science Foundation of China (U1508209, 11072049), the Liaoning BaiQianWan Talents Program, and the Dalian Science and Technology Innovation Fund (2018J11CY003). The authors would like to acknowledge the support of these funds.
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Detailed code and model data for shape control process are available in the Online Resources. The code and data for the remaining sections are available from the corresponding author on reasonable request.
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Zheng, H., Zhang, S. & Zhao, G. Integrated design optimization of actuator layout and structural ply parameters for the dynamic shape control of piezoelectric laminated curved shell structures. Struct Multidisc Optim 63, 2375–2398 (2021). https://doi.org/10.1007/s00158-020-02818-7
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DOI: https://doi.org/10.1007/s00158-020-02818-7