Numerical simulation and optimization of smart piezoelectric structures

Abstract

In this paper an overview about a finite-element-based simulation tool for smart structures is given, which includes also optimization procedures (e.g., for sensor/actuator placement) as well as control strategies. The focus of the paper is on piezoelectric materials (wafers and fibers) as active components, which are controlled by electric fields and consequently, the coupled electro-thermo-mechanical field equations have to be solved. The element library contains 1-D, 2-D, and 3-D multifield finite elements as well as special layered elements to simulate thin-walled structures with different layers of passive and active materials based on a layerwise constant shear angle theory. A substructure/superelement technique can be used in static as well as dynamic applications. In the optimization of actuator distributions a discrete-continuous optimization procedure will be presented, where the actuator positions at the structure are described by dicrete 0-1 variables, and the control parameters are included as continuous variables. Mathematical solution algorithms for nonlinear, mixed optimization problems are used to solve the optimization problem. Test examples (e.g., active vibration damping to reduce noise radiation) and comparisons with experimetal results will be presented to discuss the quality of the finite-element simulation and optimization tool.