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.

Viscoelastic artificial boundary elements are one of the most commonly used artificial boundaries when solving dynamic soil-structure interactions or near-field wave propagation problems. However, due to the lack of clear and practical stability criteria for the explicit algorithm that considers the influence of viscoelastic artificial boundary elements, the determination of the stable time increment in such numerical analyses is still a challenge. In this study, we proposed a numerical stability analysis method for the explicit algorithm with a 3D viscoelastic artificial boundary element based on the idea of a subsystem. Through this method, the artificial boundary subsystem that controls the stability of the overall numerical system is determined, and the analytical solution for the stability condition of the explicit integration algorithm with 3D viscoelastic artificial boundary elements is obtained. On this basis, the maximum time increment for solving dynamic problems with viscoelastic artificial boundary elements can be determined.

This study examines the dynamic response of bottom-sitting steel shell structures subjected to underwater shock waves. A computational framework integrating the Arbitrary Lagrangian Eulerian (ALE) method was implemented in finite-element analysis to simulate three-dimensional interactions between shock waves and curved shell geometries (hemispherical and cylindrical configurations). An analysis of the impacts of shock-wave propagation media, explosive distance, charge equivalence, hydrostatic pressure, and shell thickness on the dynamic response of these bottom-sitting shell structures is conducted. The findings reveal that the deformation of semi-spherical steel shells subjected to underwater shock waves is significantly greater than that of shells subjected to air shock waves, with effective stress reaching up to 831.4 MPa underwater. The mechanical deformation of curved steel shells exhibits a gradual increase with increasing explosive equivalents. The center displacement of the hemispherical shell at 800 kg equivalent is 6 times that at 50 kg equivalent. Within the range of 0 to 2.0092 MPa, hydrostatic pressure leads to an approximate 26.34% increase in the center vertical displacement of the semi-cylindrical shell compared with 0 MPa, while restricting horizontal convex deformation. Increasing thickness from 0.025 m to 0.05 m results in a reduction of approximately 60% in the center vertical displacement of the semi-cylindrical shell. These quantitative correlations provide critical benchmarks for enhancing the blast resilience of underwater foundation systems.

To investigate the anti-explosion performance of steel beam-slab protective door under underwater explosion impact, a three-dimensional numerical model for the steel beam-slab protective door under underwater impact load was established, and the effects of constraint conditions, height and thickness of the flat web in the skeleton beam, width and thickness of the flange plate on its anti-explosion performance were analyzed. The calculation results demonstrate that the frame beam at the edge of the protective door is the most vulnerable component in terms of anti-explosion performance. It is susceptible to various failure modes, including buckling deformation of local frame beam, overall flexural failure, compression-bending failure, and warping failure of frame beams on both sides; the variation in constraint conditions has a notable influence on the anti-explosion performance of the structure; increasing the height and thickness of the flat web results in a reduction of approximately 20% in the peak displacement of the structure. But simply increasing the width and thickness of the flange plate has a limited impact on the structural resistance to explosions.

To investigate the dynamic response of shell structure under underwater shock wave load, a three-dimensional numerical model for the typical shell structure under underwater shock wave load was established based on Arbitrary Lagrangian Eulerian algorithm. The dynamic response, deformation and failure mode of steel prefabricated hemispherical and semi-cylindrical sitting-bottom shell structures under different explosive equivalent and explosive distance were analyzed. The calculation results demonstrate that the peak displacement, deformation and effective stress increase with the increase of explosive equivalent and the decrease of explosive distance. The semi-cylindrical steel shell has obvious deformation in the mid-span area, the upper part of the bottom side constraints and the side walls at both ends. The upper part of the bottom constraints of the hemispherical steel shell deforms outward, but the overall deformation is small. When the explosive distance lower than 5m and the explosive equivalent lower than 200kg, the maximum effective stress of the hemispherical steel shell and the semi-cylindrical steel shell does not exceed the ultimate strength of Q690 steel.