Shipboard equipment must survive the transient loads of underwater explosions. The U.S. Navy certifies such equipment with the Dynamic Design Analysis Method (DDAM), a modal response analysis driven by Navy shock design spectra. DDAM is well established as a verification tool, yet it is rarely used as a design driver in topology optimization. The design spectrum depends on the modal mass, a non-smooth coupling that classical sensitivity formulations do not address. This paper presents a complete differentiable formulation of the DDAM criterion for gradient-based topology optimization. Eigenvalue sensitivities follow the Fox-Kapoor method, and eigenvector sensitivities follow Nelson's method. The chain rule covers a spectral displacement that depends on both the natural frequency and the modal participation factor. Automatic differentiation assembles the sensitivity, and the engineer can certify components inside the optimization loop rather than after design. Three certification problems on a representative shipboard equipment frame demonstrate the workflow. In each, the optimizer removes 43.2% to 46.1% of the design-domain material and holds the certifying NRL Sum within 0.41% of the Navy allowable. Two companion studies follow. A compliance-optimized frame of nearly the same mass has a 5.2 Hz fundamental, outside the range the certification can qualify. Its nominal response also exceeds the allowable by a factor of 2.75. A lower bound on the mean of the two lowest eigenvalues separates the repeated pair that the demonstrations drive onto the frequency floor. The response then stops oscillating across the acceptance boundary. It ends at most 0.5% above the allowable, at a cost of under two percentage points of volume fraction.

翻译：暂无翻译