This paper investigates the behaviour of an underwater elastic toroidal shell storage container filled with compressible fluid under constraint volume condition. The fundamental form of the surface is used to define the geometry of a toroidal shell under an initial unstrained state (IUS), reference state (RS), and deformed state (DS). In the reference state, it is assumed that the toroidal shell storage container has a circular cross section. In the deformed state, the displacements of the shell are assumed to be large. The energy functional of the underwater toroidal shell storage container can be established based on the principle of virtual work, and it can be rearranged in an appropriate form that can conveniently be implemented in a finite element formulation. The nonlinear static analysis of the elastic toroidal storage container under external hydrostatic pressure can be performed by the nonlinear finite element method (FEM) via the fifth-order polynomials shape functions. The nonlinear responses under the variable water depth to cross-sectional radius, cross-sectional radius to wall thickness, and cross-sectional bend radii ratio are demonstrated and discussed. The results revealed that the change of internal pressure is indicated by the value of the Lagrange multiplier, which is calculated using the iterative method for finding the equilibrium configuration under the constraint volume requirement.

本文研究了在约束体积条件下充满可压缩流体的水下弹性环形壳储存容器的行为。表面的基本形式用于定义初始无应变状态 (IUS)、参考状态 (RS) 和变形状态 (DS) 下环形壳的几何形状。在参考状态下，假设环形壳存储容器具有圆形横截面。在变形状态下，假设壳的位移很大。水下环壳储存容器的能量泛函可以根据虚功原理建立，并可以重新排列成合适的形式，便于在有限元公式中实现。外部静水压力下弹性环形存储容器的非线性静力分析可以通过非线性有限元法 (FEM) 通过五阶多项式形状函数进行。演示和讨论了在可变水深与横截面半径、横截面半径与壁厚以及横截面弯曲半径比下的非线性响应。结果表明，内部压力的变化由拉格朗日乘子的值表示，该乘子是使用迭代方法计算的，以在约束体积要求下找到平衡配置。演示和讨论了在可变水深与横截面半径、横截面半径与壁厚以及横截面弯曲半径比下的非线性响应。结果表明，内部压力的变化由拉格朗日乘子的值表示，该乘子是使用迭代方法计算的，以在约束体积要求下找到平衡配置。演示和讨论了在可变水深与横截面半径、横截面半径与壁厚以及横截面弯曲半径比下的非线性响应。结果表明，内部压力的变化由拉格朗日乘子的值表示，该乘子是使用迭代方法计算的，以在约束体积要求下找到平衡配置。