深海潜器的核心部件之一是耐压壳，其结构的安全性至关重要。针对耐压壳的主尺度（半径、长度、板厚等）与结构响应之间一直没有比较简单且准确的经验公式，但其在深海潜器的结构设计中具有重要作用，提出预测在给定外压下球柱结合耐压壳强度的数学表征公式。首先，根据耐压壳的几何结构确定设计参数，利用拉丁超立方技术设计1000组耐压壳结构型式；其次，基于Python对Abaqus的二次开发进行参数化建模与结果批量后处理；最后，根据耐压壳结构应力极值位置，分析推导出母型公式，基于机器学习进行回归预测。与有限元计算结果相比，运用机器学习得出耐压壳的主尺度与结构的强度响应之间数学表征，平均预测误差为2.53%。因此，耐压壳的主尺度与结构的强度响应之间存在简易的数学表达，研究成果可为深海潜器的结构设计提供一定参考。
The pressure hull is a critical component of deep-sea submersibles, and its structural safety is of paramount importance. However, a simple yet accurate empirical formula describing the relationship between the main dimensions of the pressure hull (e.g., radius, length, and plate thickness) and its structural response remains unavailable, despite its critical role in structural design. This study develops a mathematical representation for predicting the strength of spherical-cylindrical pressure hulls under given external pressure. First, the design parameters were identified based on the geometric structure of the pressure hull, and 1,000 structural configurations were generated using the Latin hypercube sampling technique. Second, Python was utilized to perform secondary development of Abaqus for parametric modeling and batch post-processing. Finally, the mathematical formula was derived by analyzing stress extremities and further refined using machine learning-based regression prediction. Compared to finite element results, the proposed approach achieves an average prediction error of 2.53%. This study confirms the existence of a straightforward mathematical relationship between the main dimensions of the pressure hull and its strength response, offering practical guidance for the structural design of deep-sea submersibles.
2025,47(15): 44-50 收稿日期：2024-10-28
DOI：10.3404/j.issn.1672-7649.2025.15.008
分类号：U661.43；U663.1
基金项目：中核集团领创科研项目
作者简介：张峥林(1999-),男,硕士,研究方向为深潜器尺度极限数学表征及结构智能优化设计
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