Dynamic Shape Control And Design Optimization For Piezoelectric Curve Shell Structures

With the rapid development of microelectronic mechanical, aerospace, precision instrument and other fields, the study of active control system of smart materials and structures have increasingly important. As piezoelectric material is suitable for the high accuracy shape and vibration controls of structure due to its excellent operating performance, fast response and sensitive features, much of the research in the piezoelectric material has focused on shape control of structures equipped with actuators. Some dynamic shape control researches were represented in recent years when static shape control had been unable to meet the needs of engineering which needed to take the load changes and posture adjustment of the structure design into consider. Curve shell structures are used in many engineering fields, while most of shape control are accomplished in flat structures, which means that it will increases the computing costs and control costs for curved structure shape control, so the dynamic shape control of piezolaminated curved shell and optimization of piezoelectric actuators is presented in this paper.This paper firstly presents a finite element formulation of 8-node curve shell element, and forms a dynamic finite element equation for spatial structure with curve shell piezoelectric actuators by connecting the host shells and actuators with constraint equations. In order to achieve the dynamic shape control of structures with actuators voltage as control variables, the time domain discrete equations of structural dynamic shape control based on the Newmark integral method is derived by minimizing the difference between the ideal and computed structure shape. Kuhn-Tucher condition is introduced to solve the equations to obtain the optimal voltage distribution of actuators.Then, the single layer isotropic host material is expanded to anisotropic composite material based on the spatial curve shell, and the finite element formulation of the piezolaminated curve shell structure is derived by subsection integrating in thickness direction based on the hierarchical theory for solving the element stiffness matrix. The dynamic shape control of piezolaminated curve shell structure is achieved using Newmark integration and the Kuhn-Tucher condition.Finaly, with the actuators voltage and thickness as design variables together, the hierarchical optimization model of structural dynamic shpe control is developed by optimizing the voltage in the inner optimization step and optimizing the actuators thickness in the outer optimization step with the simulated annealing algorithm. The actuator thickness is optimizated as continuous variables and discrete variables respectly to achieve the optimization of piezolaminated curve shell structure shape control. Besides, the optimal placement of actuators is achieved in dynamic shape control of curve shell structure by minimizing the number of actuators.