Smart capabilities of a laminated piezoelectric plate model

Abstract

This paper focuses on the modelling and analysis of actuator and sensor effects for thin laminated plates, which are formed by stacking several layers of different piezoelectric materials. We first discuss features and properties of a two-dimensional asymptotic model for a piezoelectric anisotropic plate, whose unknowns are the Kirchhoff-Love displacement and the electric potential. We prove that the latter is a quadratic polynomial of the plate’s thickness. The polynomial’s coefficients depend on the tangential and transverse displacements of the plate’s middle plane and the material coefficients. The asymptotic laminated plate model is discretized using finite elements. To investigate its smart capabilities we use two discrete optimization problems: the first one, focusing on the actuator effect, aims at obtaining a maximum displacement of the plate’s middle plane; the second one that corresponds to the sensor effect intends to maximize the electric potential at a predefined thickness of the plate. The optimization variables are the thicknesses of the layers, their ordering as well as the location of the applied electric potential (for the actuator problem) or the location of the applied mechanical forces (for the sensor problem). Since we also want to minimize the number of these locations (besides maximizing the above objectives), we obtain a multi-objective optimization problem that we solve using genetic algorithms. Several numerical results are reported.