Body-fitted iso geometric topology optimization for maximizing phononic band gaps

We present a novel body-fitted iso geometric topology optimization framework for maximizing phononic band gaps, featuring an accurate boundary representation of evolving geometries. Analytical design sensitivities are derived, with particular focus on a narrow band of control points near the interface, shown to be critical due to the underlying physical mechanisms of Bragg scattering. Benchmark comparisons against density-based finite element approaches confirm the superior convergence behavior and predictive accuracy of our method. These highlight the main contributions of this work, namely: high reliability and engineering credibility, achieved by generating computational results that are directly manufacturable without post-processing and with no performance degradation; and substantially faster convergence rates in the numerical evaluation of band gap simulations compared to conventional FEM-based methods. Numerical examples demonstrate the advantages of the proposed framework, positioning it as a reliable computational tool for band gap engineering in phononic materials.