Modeling and optimal design for static shape control of smart reflector using simulated annealing algorithm

Abstract

This article presents a finite element formulation for static shape control and optimal design of smart reflector with distributed piezoelectric actuators. The finite element model is developed based on the higher-order shear deformation theory where the displacement field in the model accounts for a parabolic distribution of the shear strain, and the shear correction factor is not involved. The Hamilton variational principle is used to formulate the governing equation of the system. A four-node element with seven mechanical degrees of freedom for each node and one electrical potential degree of freedom for each piezoelectric actuator element is used in the finite element formulation. The optimization model for finding the optimal control voltages is derived, and the control voltages can be determined using Lagrange multipliers. The optimal design of actuator locations using simulated annealing algorithm is also investigated. Finally, numerical examples are given to demonstrate the effectiveness of the present model and optimization scheme. The obtained results show that the use of piezoelectric actuators for static shape control of smart reflector can greatly improve the root mean square error, and the optimal location of actuators can be determined effectively using simulated annealing algorithm.