Development of Initial Scantling Formulas for Submarine Deep Frames Based on Numerical Analysis

Submarine structures are typically classified into pressure hulls and non-pressure hulls. The pressure hull is a critical component designed to withstand external pressure at operational depths while ensuring internal structural integrity. It is generally composed of ring frames and bulkheads. However, in modern large-scale submarines, bulkheads are often replaced with deep frames to improve equipment layout flexibility. Deep frames serve as essential structural reinforcements, compensating for the loss of stiffness due to the absence of bulkheads. Despite their importance, research on the design of deep frames remains scarce, and in the absence of established design standards, engineers rely on conservative approaches based on practical experience. Therefore, the objective of this study is to propose initial scantling formulas for deep frames in submarine pressure hulls based on finite element analysis (FEA) and parametric studies. To this end, six design cases reflecting actual ship design ranges were selected, and the structural integrity of the pressure hull ring frames was verified through material and geometric nonlinear analysis using ANSYS Mechanical APDL. Subsequently, a total of 82,440 parametric studies were conducted with the reinforced shell thickness, effective length, height and thickness of the deep frame web, and the width and thickness of the deep frame flange as variables. As a result, the proposed formulas satisfied all Validation cases in terms of structural integrity and were found to be applicable within the section length range of 1.5 to 2.0 times the pressure hull diameter. The results of this study are expected to be effectively utilized in the initial design of deep frames for submarine pressure hulls.