Multi-Objective Optimization of an Adaptive Composite Beam Using the Physical Programming Approach

The objective of this paper is to present the optimization of an adaptive composite structure using the physical programming approach. To this end, a multi-objective optimization problem of an adaptive composite beam with piezoelectric actuators bonded to its surface is performed. The goal is to optimize the size and placement of the actuator pairs, in order to maximize the performance of their actuation power, to minimize the mass of the piezoelectric material and to maintain the required actuation voltages below maximum operating values. A generalized tri-dimensional version of the Heaviside function has been used to represent the distribution of the piezoelectric actuators. A closed form solution for the equations of equilibrium is presented. Physical programming presents the following advantages over the more conventional optimization methodologies: reduced computational effort and time, elimination of both iterative selection of weights and prioritization of objective functions.