Stress‐Constrained Topology Optimization of Sweep‐Frequency Harmonic Vibration Problems Using a B‐Spline‐Parameterized Topology Description Function Method

ABSTRACT This paper presents a novel B‐spline‐parameterized topology description function (TDF) method to tackle the challenging problem of stress‐constrained topology optimization under sweep‐frequency harmonic excitations. The proposed method employs B‐spline coefficients as design variables, enabling a smooth and implicit representation of evolving topologies. A two‐layer aggregation strategy with a dynamically adjusted correction coefficient is introduced to condense the spatial‐frequency peak stress into a single, smooth, and differentiable global stress constraint. A rigorous error analysis of the introduced two‐layer aggregation strategy is provided. The sensitivities of the global spatial‐frequency stress constraint and the volume objective with respect to the B‐spline coefficients are derived in detail. Furthermore, the model reduction technique based on the modified Gram‐Schmidt orthonormalization is introduced to reduce the cost of repeated harmonic‐response analyses at multiple frequencies. Finally, three numerical examples, including an L‐shaped beam, a U‐shaped beam, and a corbel structure, are investigated to validate the proposed approach. The results show that the developed method effectively controls local stress concentrations under sweep‐frequency harmonic vibrations, providing a robust tool for designing lightweight structures subjected to variable‐frequency dynamic loads.