Objectives The dynamic ultimate strength of a hull girder is a crucial parameter for assessing ship safety. In the context of ships being subjected to dynamic loads such as wave-induced and slamming loads during navigation, making accurate calculation of the dynamic ultimate strength of the hull girder is of great significance for ship designers to predict structural performance and ensure ship safety. However, existing research on the calculation of the dynamic ultimate strength of the hull girder remains limited, and traditional methods often face challenges in terms of computational efficiency. Therefore, this study aims to address the challenge of efficiently calculating the dynamic ultimate strength of a hull girder and proposes a more efficient calculation method.

Methods The proposed approach is the dynamic Smith method, which is based on the traditional Smith method. Firstly, considering the strain rate effect of materials under dynamic load, the Cowper−Symonds model is introduced to modify the yield strength of materials. This modification is essential as the dynamic yield strength of materials increases with the increase of strain rate. Secondly, the stress−strain relationship of stiffened plate elements under different strain rates is taken into account. Xiong's empirical formula for the dynamic ultimate strength of stiffened plates is adopted to correct the stress−strain curve, ensuring more accurate calculation of member stress. Finally, the inertia force generated during the dynamic response of the hull girder structure is considered. By calculating the acceleration caused by the change of the neutral axis of the cross-section in the Smith method iteration process, the inertia force of each unit is obtained, and then the impact of inertia force on the dynamic ultimate strength is corrected.

Results The results show that when the angular velocity of the end-face rotation is less than 1, the error between the dynamic ultimate strength calculated by the dynamic Smith method and that by the finite element method is less than 10%. Specifically, for the box girder model and the hull girder model of a VLCC based on ISSC 2012, the dynamic Smith method shows strong agreement with the finite element results in the low-to-medium angular velocity range. However, when the angular velocity is greater than 1, the error between the two methods becomes larger.

Conclusions In conclusion, the dynamic Smith method is a significant extension of the traditional Smith method. Compared with the finite element method, it can remarkably improve the calculation efficiency for calculating the dynamic ultimate strength of a hull girder, especially when the end-face rotation angular velocity is less than 1. For the correction of the stress-strain relationship curve in the dynamic Smith method, when the strain rate is less than 0.4, the stress-strain curve is calculated based on strain rate hardening; when the strain rate is greater than or equal to 0.4, the empirical formula is used. This research provides a novel approach to ship safety assessment and provides valuable guidance for ship design and structural strength analysis.