Topology optimization of a piezoelectric actuator on an elastic beam

The purpose of this study is to investigate the optimal topology of a piezoelectric actuator in reducing the tip deflection of a static cantilever beam under a concentrated tip load. Optimized topologies are obtained for both statically loaded and harmonically excited cases. The beam is modeled using the commercial finite element code ABAQUS, and a proportional control law is implemented through modification of the stiffness matrices. Parameter studies varying the gain and volume of the piezoelectric material are conducted. Optimal topologies show substantial improvement over equivalent uniform piezoelectric layers. This study also demonstrates the possibility of using a commercial FE code for studying structural control with piezoelectric materials.