Underwater bottom-sitting shell structures face threats from underwater explosion shock waves. To investigate the damage characteristics and dynamic response of bottom-sitting shell structures under underwater explosion shock waves, three-dimensional numerical models of semi-spherical and semi-cylindrical bottom-sitting reinforced concrete (RC) shells under underwater shock waves were established based on the Arbitrary Lagrangian–Eulerian (ALE) algorithm using LS-DYNA software. The influences of the shock wave transmission medium, explosive equivalent, explosive distance, hydrostatic pressure, and reinforcement on the damage characteristics and dynamic response of semi-spherical and semi-cylindrical bottom-sitting RC shell structures were studied. The results indicated that the damage and center vertical deformation of RC shells under underwater shock waves are significantly greater than those under air shock waves. With an increase in explosive equivalent or decrease in explosive distance, the damage and center vertical deformation of RC shells are increased. The damage to the inner surface of RC shells is more severe than the outer surface. The damage and center vertical deformation of RC shells can be reduced by bottom reinforcement and an increase in the diameter of the steel bar. The ‘hoop effect’ caused by hydrostatic pressure restrains the horizontal convex deformation and slightly decreases the macroscopic damage and vertical center deformation of the semi-spherical RC shell with an increase in hydrostatic pressure within the range of 0–2.0092 MPa. The hydrostatic pressure restrains the horizontal convex deformation of the semi-cylindrical RC shell. However, inward concave deformation of the shell center is increased by hydrostatic pressure, inducing an increase in the damage to and center vertical deformation of the semi-cylindrical RC shell. These findings may offer a reference for the construction and design of protective measures for underwater bottom-sitting shell structures.

A quasi-static finite cavity cylindrical expansion model is proposed to investigate the lateral boundary effect during long-rod penetration. Analytical solutions for the cavity pressure in the elastic–plastic stage and plastic stage are obtained, through which a decay function for the lateral boundary effect is constructed. The resistance of the target with finite diameter R_T is obtained by multiplying the decay function with the resistance of infinite target R_T*. Then, a theoretical model for the penetration into the metal targets with finite diameters by long rods is proposed by substituting R_T into the Alekseevskii–Tate model. The proposed model is verified by comparison with existing experimental results. Furthermore, the effect of the target diameter, initial impact velocity and yield criterion on the penetration depth and resistance are investigated. The results showed that the lateral boundary effect should be taken into account if the ratio of the target radius to the rod radius (r_t0/R_P) is less than 25.