Multi-voltage topology optimization for precise deformation control in piezoelectric composite structures

The piezoelectric composite structures combine traditional materials with piezoelectric smart materials, enabling active structural control and offering considerable potential for aerospace applications. Specific deformation control can be achieved by applying multiple voltage layouts to the surface of a piezoelectric structure. However, achieving accurate control over arbitrarily specified deformation shapes remains challenging with traditional design methods. This study introduces a topology optimization approach for precise deformation control of piezoelectric structures with multiple voltage layouts, leveraging a multi-material topology optimization model. In this method, the objective function is defined as the weighted sum of deviations between the actual and target deformation shapes, providing a measure of discrepancy. Different actuating voltages, including zero voltage across all piezoelectric finite elements, are selected as design variables to achieve an optimal multi-voltage layout for arbitrarily specified structural deformations. The Discrete Material Optimization (DMO) interpolation model, combined with the Heaviside projection function, is used to implement multi-voltage selection and filtering during optimization. Explicit sensitivity analysis of the objective and constraint functions with respect to the design variables is derived, and the optimization problem is solved using mathematical programming algorithms. Numerical examples validate the effectiveness of the proposed optimization algorithm in accurately controlling various pre-specified deformation shapes. The proposed method can improve the control accuracy of piezoelectric active-deformation composites while lowering their control energy consumption.