Piezoelectric composite structures, extensively applied in diverse smart actuators, energy harvesting and conversion devices, demand flexible multiscale structural patterns but robust design methods. Topology optimization (TO) possesses the potential of fulfilling this task for the design of composite piezoelectric actuators and energy harvesters (PEHs) but is still not capable of simultaneously dealing with both multiscale and multi-phase design.

To maximize the functionality and efficiency of composites at both structural level and microscale, this paper proposes a concurrent multiscale TO framework to design PEHs with multiple integrated constituents, aiming at enhancing the electrical energy conversion efficiency (EECE). To avoid full-scale direct numerical simulations, the energy-based homogenization method is utilized to generate the structural material properties from characterizing heterogeneous microstructural parameters. The multi-material interpolation and void-solid interpolation are then defined at the macroscale and microscale, following which the sensitivity of the objective and constraint functions to the densities at the concurrent two scales is computed using the Lagrange multiplier-adjoint equation method. Subsequently, the method of moving asymptotes (MMA) is employed for bi-scale iteration to obtain the optimized solution of the objective function. Notably, an efficient Heaviside projection-based procedure is proposed to effectively eliminate grayscale issues in the microstructures, in the meantime reasonable constraints are imposed on the homogenized moduli to enhance the connectivity for the ease of additive manufacturing. A modified sensitivity filtering is further proposed to alleviate the special grayscale issue during the integrated TO process at the macroscale.