Load coupling mechanism and plastic deflection prediction of pre-pierced clamped plates under simultaneous double-charge underwater explosions with varying charge spacings

Simultaneous double-charge underwater explosions generate spacing-dependent coupled loading that governs the global plastic deformation of thin-walled structures. Underwater explosion experiments and validated S-ALE simulations were combined to investigate fully clamped steel plates at a fixed standoff distance of R = 100 mm, considering charge spacings of 50–300 mm, small symmetric pre-pierced holes, and air- or water-backed boundaries. Under air-backed conditions, the maximum residual deflection first increases and then decreases with charge spacing; among the discrete spacings considered, the largest response occurs at S = 200 mm. Quantitative load decomposition indicates that shock-wave loading contributes more than 85 % of the final maximum deflection, whereas the bubble-induced increment remains below 15 %. Within the investigated small-hole and global plastic deformation regime, pre-piercing does not substantially alter the global central-depression mode or maximum deflection. In contrast, the water-backed boundary markedly suppresses deformation accumulation and weakens the spacing dependence of the final deflection. A symmetry-plane-averaged equivalent shock-wave pressure and a dynamic–plastic model are proposed for first-order prediction of the global maximum deflection of air-backed plates. The model captures the spacing-dependent deflection trend with relative errors of 6–11 % for intact plates and 2–5 % for pre-pierced plates, providing an efficient engineering estimate within the investigated configuration.