Efficient robust topology optimization of piezoelectric energy harvesters with smooth boundaries and reduced computational cost

• Robust topology optimization for piezoelectric energy harvesters • KL–SGC uncertainty propagation cuts sampling cost by ∼10 × • Floating-projection yields smooth, fabrication-ready boundaries • Reduced stress localization and improved load transfer in designs • Benchmarks show robust performance without accuracy loss This study introduces a robust topology optimization (RTO) framework for piezoelectric energy harvesters (PEHs) to ensure reliable performance under uncertainties in material properties, loading conditions, and excitation frequency. Topology optimization under uncertainty involves two main challenges: (1) the prohibitive computational cost arising from the high dimensionality of the uncertainty space, and (2) the difficulty of obtaining designs with optimized mean performance, low variance, and smooth manufacturable boundaries. To address these issues, the proposed framework integrates the Karhunen–Loève (KL) expansion with the sparse grid collocation (SGC) method to reduce problem dimensionality and solution time, while the floating projection technique is used to reduce the response variance and stress concentration by creating smooth boundaries. This integration enables robust PEH optimization with smooth manufacturable designs, reduced variance, and fewer order-of-magnitude samples than conventional tensor-product grids. Numerical simulations across various configurations demonstrate that the proposed RTO-smooth framework yields a design with smoother boundaries, lower stress concentrations, and improved computational efficiency compared to existing methods.