Integrated optimization of material layout and control voltage for piezoelectric laminated plates

Topology optimization techniques have recently been successfully applied to the design of piezoelectric smart structures. However, in previous formulations, the material layout is optimized under the condition of given electric actuation voltages. This imposes a restriction to the design problem and may consequently limit application of these approaches, particularly in complex shape control problems. The present article investigates the integrated optimization of structural topology and control voltage of piezoelectric laminated plates. The finite element analysis formulation of laminated plates with surface bonded piezoelectric layers is introduced first. The optimal design problem is then formulated based on an artificial material model with penalization for both mechanical and piezoelectric properties. In the formulated problem, the topologies of both host and actuation layers are optimized simultaneously with spatial distribution of control voltage. Several special cases of the proposed design problem are considered, and numerical techniques for sensitivity analysis and optimal solutions are proposed. Numerical examples are presented to demonstrate the validity and applicability of the proposed methods.