A Gradient Mesh Analysis of Numerical Ship Model With Two-Way Stiffened Plate Equivalence

Abstract With the development of ships in recent years, the ship size becomes larger and the hull structure becomes complicated. The entire ship should be modeled to study the dynamic responses as the key equipment may be located away from the loading area, leading to a dramatic increase in the number of numerical model elements. The stiffener, which is attached to the hull plate, may further make the numerical simulation time-consuming even difficult to converge and stabilize. Thus, it is necessary to reduce the element number of stiffened plates in the ship model. Current approaches may only consider the single in-plane or out-of-plane stiffness equivalence to smear the stiffener onto the plating. Besides, the applicability may be limited to the one-way stiffened plate. In this study, a simplified approach considered the coupling effect of in-plane and out-of-plane stiffnesses for two-way stiffened plate is proposed. Firstly, the equilibrium and compatibility equations are used to equal the stiffness of stiffened plate to the single plate with orthotropic material properties. Then the coupled load-deformation relationship of the equivalent single plate is derived based on the orthotropic material parameters and first-order shear deformation theory. Based on the mechanical property equivalence, the transverse stiffener and the longitudinal stringer of numerical ship model can be removed. Subsequently, the simplification of stiffener can amplify the maximum mesh size from stiffener spacing to web frame spacing, which can further reduce the number of elements. The fine mesh can be used for the loading and focus regions of the model, while the coarse mesh can be used for the rest region. Finally, the various dynamic evaluations are conducted to discuss the applicability of the approach. The results show that the equivalent single plate combined with the gradient mesh method can improve the computational efficiency and stability with high accuracy.