In this paper, an efficient nonstandard finite difference scheme for the numerical solution of chaotic fractional-order Chen system is developed. In the new method, an appropriate nonlocal framework in conjunction with the Grünwald-Letnikov approximation are applied for the discretization of fractional differential system. By constructing the discretization with the nonstandard finite difference scheme, high resolution of the system can be obtained, and the numerical instabilities of the nonlinear fractional-order Chen chaotic system can be also addressed to some extent. In addition, a new fractional derivative of the Caputo type is employed in the context of fractional-order Chen system to further decrease the computational complexity in the long-term treatment of fractional model. Numerical simulations demonstrate the applicability, accuracy and efficiency of the developed method.

Accurately assessing ice loads is a fundamental issue in the field of structural design for ships in ice-covered regions. In this paper, we conducted research on extreme ice load estimation for icebreaking ships, combining stochastic theory with numerical simulation. Firstly, using sea ice data from the Arctic region of the United States National Snow and Ice Data Center, a stochastic ice field model was established under Arctic sea ice conditions using non-parametric estimation and the rejection sampling method, and ice field data were generated stochastically. Then, based on the stochastic ice field data, a three-dimensional numerical model of the interaction between the ice field and the ship hull was established, and the reliability of the numerical model was verified by experimental results. Finally, based on the numerical model of the interaction between the ice field and the ship hull, asymptotic methods were used to study the extreme ice load estimation in different parts of the ship hull, revealing the variation law of the extreme ice load in different parts of the ship hull. This study provides basic theory and technical support for the structural design of ships in polar regions and has engineering application value.

At present, the calculation method of ice load on surface navigation ships has been very mature, but the calculation method of submarine ice load is very few. The reasonable evaluation of submarine ice load has become an urgent problem to be solved. In this paper, the mechanical characteristics of the submarine surfacing ice-breaking process are systematically analyzed. Based on the theory of plate and shell, the theoretical calculation models of ice-breaking resistance of the submarine command tower and hull are established, respectively, and the ice load calculation method of the command tower and the hull is obtained. Then, the submarine model SUBOFF is used to perform the numerical simulation of the submarine’s ice-breaking and surfacing process. The numerical result is compared with the ice-breaking resistance calculation model. The results show that the ice-breaking resistance calculation model proposed in this paper is consistent with the numerical simulation results, and the influence of parameters such as ice mechanical properties, the upper area of the command tower, and initial crack length on ice-breaking resistance is established. The calculation model in this paper can provide a theoretical reference for the optimization design of polar submarine structures.

The estimation of ship resistance in ice is a fundamental area of research and poses a substantial challenge for the design and safe use of ships in ice-covered waters. In order to estimate the ice resistance with greater reliability, we develop in this paper an improved Lindqvist formulation for the estimation of bending resistance in level ice based on the superposition of double-plates. In the developed method, an approximate model of an ice sheet is firstly presented by idealizing ice sheeta as the combination of a semi-infinite elastic plate and an infinite one resting on an elastic foundation. The Mohr–Coulomb criterion is then introduced to determine the ice sheet’s failure. Finally, an improved Lindqvist formulation for estimation of ice resistance is proposed. The accuracy of the developed formulation is validated using full-scale test data of the ship KV Svalbard in Norway, testing the model as well as the numerical method. The effect of ice thickness, stem angle and breadth of bow on ship resistance is further investigated by means of the developed formulation.

The trans-media aircraft water entry process generates strong slamming loads that will seriously affect the stability and safety of the aircraft. To address this problem, we design a fixed-wing aircraft configuration and employ numerical simulations with the volume of fluid (VOF) multiphase flow model, standard k-epsilon turbulence model, and dynamic mesh technique. We explore the characteristics of aircraft subjected to bang loads under different conditions. The results show the following: the pressure load on the aircraft surface increases with higher water entry velocity; larger entry angles lead to more drastic changes in the aircraft’s drag coefficient, demonstrating strong nonlinear characteristics; the greater the angle of attack into the water, the greater the pressure load on the root underneath the wing, with little effect on the pressure load on the head; and the water entry drag coefficient and average pressure load follow an increasing order of conical head, hemispherical head, and flat head. These findings provide theoretical references for studying the load characteristics during trans-media water entry of various flying bodies and optimizing fuselage structural strength.