Objective Stress concentration around web openings represents a critical local-response challenge in the deck transverse beams of roll-on/roll-off (Ro-Ro) ships, with direct implications for opening arrangement, reinforcement extent, and structural reliability. While existing surrogate modeling approaches typically focus on a small number of characteristic stress values, the full circumferential stress distribution along the opening boundary — essential for identifying peak locations and characterizing local gradients — has rarely been reconstructed. To address this gap, the present study proposes an interpretable and computationally efficient framework for predicting the circumferential von Mises stress distribution around circular web openings.

Method The stress field along the hole boundary is formulated as a periodic function in the angular domain and represented by a truncated Fourier series of order N = 9, mapping stress curves with varying numbers of sampling points into a unified fixed-dimensional spectral space. This spectral encoding avoids interpolation artifacts and nonphysical smoothing arising from inconsistent point densities across different hole diameters, while preserving dominant modes, peak positions, and overall distribution trends. To embed structural mechanics knowledge, the theoretical spectrum derived from Vierendeel mechanism theory is introduced as a physics-based baseline approximation of the opening-induced stress pattern. Rather than directly regressing finite-element stress curves, a spectral-domain residual learning network is developed to predict the discrepancy between the theoretical and finite-element spectra, reducing learning complexity and improving model interpretability under limited training data. A harmonic confidence weighting scheme is further designed based on the statistical deviation of individual harmonics between theoretical and finite-element solutions, so that low-order harmonics governing the principal stress pattern are prioritized while high-order components susceptible to noise are adaptively suppressed during optimization.

Results Trained on finite-element samples, the proposed method achieves a peak-stress error of 8.8%, a mean relative curve L_2 error of 0.133, and a median peak-angle error of 2° on the test set. Compared with a pointwise-supervised curve model, the mean relative curve L_2 error is reduced by 63.96%, the peak-location error by 84.62%, and the peak-stress error by 25.61%. Ablation studies confirm that both the residual learning structure and the harmonic confidence weighting are essential for accurate distribution reconstruction and precise peak localization. The proposed model also generalizes effectively to out-of-distribution opening positions. In terms of computational efficiency, a single prediction requires approximately 0.12 s, compared with roughly 3 hours for a conventional local finite-element analysis.

Conclusion By combining unified spectral encoding, theory-guided residual correction, and confidence-weighted optimization, the proposed framework offers a practical rapid-assessment tool for preliminary opening layout optimization, reinforcement design, and local-response screening in ship structural engineering.