Objective Stress concentration around web openings poses a critical local-response challenge in the deck transverse beams of roll-on/roll-off (Ro-Ro) ships, directly affecting the arrangement of openings, the extent of reinforcement, and structural reliability. Existing surrogate modeling approaches generally focus on a small number of characteristic stress values, while the full circumferential stress distribution along the opening boundary — which is essential for identifying peak stress locations and capturing local gradients — has seldom been reconstructed. To address this limitation, 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 K= 9, which maps stress curves with varying numbers of sampling points into a unified, fixed-dimensional spectral space. This spectral encoding mitigates interpolation artifacts and nonphysical smoothing that arise from inconsistent point densities across different hole diameters, while preserving dominant modes, peak stress locations, and overall distribution trends. To incorporate structural mechanics knowledge, the theoretical spectrum derived from Vierendeel truss theory was introduced as a physics-based baseline approximation of the opening-induced stress pattern. Instead of directly regressing finite-element stress curves, a spectral-domain residual learning network was developed to predict the discrepancy between the theoretical and finite-element spectra, thereby reducing learning complexity and enhancing model interpretability under limited training data. A harmonic confidence weighting scheme was further implemented, based on the statistical deviation of individual harmonics between theoretical and finite-element solutions. This approach prioritizes low-order harmonics that govern the principal stress pattern while adaptively suppressing high-order components susceptible to noise 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 peak-stress relative error, mean relative curve L_2 error, and median peak-angle error are reduced by 25.61%, 63.96%, and 84.62%, respectively. Compared with the spectral-supervised curve model, the peak-stress relative error, mean relative curve error, and median peak-angle error are reduced by 43.95%, 48.45%, and 84.62%, respectively. Ablation studies confirm that both the residual learning structure and the harmonic confidence weighting scheme are essential for accurate distribution reconstruction and precise peak stress localization. The proposed model also demonstrates strong generalization 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 integrating 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.
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