The ocean is full of resources for human development. However, traditional ocean observation technologies like ship-based observations, ocean buoys, and ocean satellites are no longer able to meet the current needs of ocean exploration due to the urgent need for further in-depth development of underwater resources. For the development of marine resources, high-pressure marine exploration equipment will, therefore, be essential. Submersible detectors come in a variety of shapes and sizes, but they are all made up of three basic parts: a connecting structure, an internal framework platform structure, and a pressure-resistant structure [
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7]. Considering that it makes up between a quarter and a half of the submersible’s total weight, the pressure-resistant shell structure is one of its most important parts. The primary duty of this structure is to tolerate high water pressure from the outside. To achieve the best pressure resistance performance and floating weight ratio, it is crucial to research and optimize the materials and structural forms of pressure-resistant shells.
Reducing the weight or minimizing the total weight of pressure-resistant shells while keeping the necessary strength and stability for operation is the major goal of optimization.
MingYang et al. [
8] used the theory of thin shells to build a mechanical model of spherical pressure-resistant shells, which they then used to combine the Penalty Function Method (PFM) with the Multi-Population Genetic Algorithm (MPGA) to optimize the thickness, strengthening ribs, width of the strengthening ribs, and intersection angle of spherical pressure-resistant shells. A. S. Bhanu Prasan et al. [
9] also used the PSO algorithm to optimize the quality of an entire pressure-resistant shell under specified buckling pressure and frequency constraints. Muhammad Imran et al. [
10] optimized the pressure-resistant shell of a spherical submersible using the genetic algorithm (GA) in ANSYS, and then performed nonlinear buckling analysis on the pressure-resistant shell using a modified RIKS program in ABAQUS. In order to reach the maximum operating depth, Elsayed Fathallah et al. [
11] optimized the entire pressure-resistant shell by reducing the elliptical submersible’s buoyancy coefficient. The design variables that were utilized were the longitudinal beam size, elliptical radius, and thickness of the pressure-resistant shell, all of which were subject to the limitations of failure criteria and shell buckling strength. Muhammad Imran et al. [
12] introduced composite materials into cylindrical pressure-resistant shells, aiming to minimize buoyancy coefficients and maximize buckling load coefficients as optimization research objectives, and executed them through a coupled multi-objective genetic algorithm (MOGA). In order to optimize design variables and obtain the optimal cylindrical pressure-resistant shell, Cheng Wang et al. [
13] proposed a cylindrical pressure-resistant shell with non-uniform arch ribs. Based on the parameterization model of the response surface method, they established an approximate model for the output response of ship mass. Honglei Liu et al. [
14] proposed an adaptive morphogenesis algorithm based on the growth mechanism of leaf veins. They then applied this method to the design of stiffened plate and shell structures, resulting in a distinct stiffener distribution pattern. Paweł Foryś [
15] addressed the impact of geometric defects on the form of equilibrium paths, employed an enhanced particle swarm optimization method (MPSO) for numerical optimization, and utilized the finite element method (FEM) to model and solve cylindrical shell structures. Ghasemi et al. [
16] investigated the impact of hydrostatic pressure on cylindrical shells and their preparation by combining a genetic algorithm with geometric, structural, stress, and buckling constraints. Additionally, they used penalty functions to get rid of weak models. In the end, they suggested the best model, taking into account the least amount of weight under pressure. An optimization technique based on a free form was developed by Masatoshi et al. [
17] and is especially useful for shape optimization in the out-of-plane direction. The buckling coefficient is the optimization’s objective function. The optimization results show that the buckling coefficient can be greatly increased using this method. Wu et al. [
18] used the Newton–Lapson iteration method to perform a nonlinear static finite element analysis of axially compressed reinforced cylindrical shell structures with the goal of determining the ultimate load of structural instability. Mahdi et al. [
19] optimized the shell and rib parameters under weight and frequency constraints using a genetic algorithm. They also improved the ribs’ material composition and shape, and the outcomes demonstrated that the improved shell had superior vibration characteristics. In order to optimize underwater pressure-resistant shells, Akl et al. [
20] used a max–min multi-objective optimization strategy. The optimization objectives included shell vibration, noise, and quality. Sofiyev AH et al. [
21] introduced the stability of non-uniform nanocomposite cylindrical shells (INCCSs) under hydrostatic pressure in a hot environment. The effective material properties of non-uniform nanocomposite cylindrical shells were modeled based on extended mixing rules. Based on the effective performance of the materials, the basic relationship and stability equation of the thermal environment were derived. The analytical expressions for the hydrostatic buckling pressure of INCCSs under the framework of FSDT and classical shell theory (CST) were obtained through solutions based on the Galerkin program. Wang M et al. [
22] introduced the design and optimization of a pressure cylindrical shell composed of carbon/epoxy resin and glass/epoxy resin composite materials. A method for analyzing composite-pressure cylindrical shells was proposed, and the strength and buckling of composite-pressure cylindrical shells with different rib numbers were analyzed. The effects of thickness and layer angle on critical buckling and strength failure stress were studied. Yang Z et al. [
23] used experimental methods to study the buckling pressure and failure strength of non-reinforced fiber-reinforced composite cylindrical shells under external hydrostatic pressure. They collected and discussed strain and pressure data. The results indicate that the improvement in buckling pressure by the ring reinforcement structure is more significant than the increase in failure pressure. The experimental burst pressure of the annular rigid cylindrical shell increased by 23.2%. Zhang X et al. [
24] proposed a pressure shell with a corrugated structure to significantly improve its compressive performance. Seven pressure shells were prepared, including six inner corrugated pressure shells and one cylindrical pressure shell, and hydrostatic pressure tests were conducted. The results indicate that the corrugated structure can significantly increase the critical buckling load of the shell. Zhang Y et al. [
25] proposed a novel bidirectional corrugated sandwich structure to improve the load-bearing capacity of cylindrical shells. The static and buckling analyses of sandwich shells and unreinforced cylindrical shells with the same volume-to-weight ratio were studied through numerical simulation. The results indicate that the proposed sandwich shell can effectively reduce the ratio of circumferential stress to axial stress from 2 to 1.25, increasing the critical buckling load by approximately 1.63 times. Numerical simulations show that optimizing and adjusting structural parameters can significantly improve the advantages of sandwich shells.
The ultra-high deep-water pressure environment that occurs tens of thousands of meters deep is typically ignored in current research. The standard uniform ribbed method for cylindrical shells may not be able to form unstable half-waves in the radial direction when encountering overall instability in the ultra-deep-water static pressure environment. This could lead to an insufficient ability of the pressure-resistant shell to resist instability. We suggest a technique to modify the internal rib stiffness in order to enhance the pressure-resistant shell’s overall anti-instability capabilities in order to address this general instability scenario. However, in terms of lightweight qualities, conventional, ordinary pressure-resistant materials like aluminum alloy 6061T6, resin-based carbon fiber T700, silicon nitride ceramics, etc. cannot be substituted for the titanium alloy TB9 material used to meet the pressure resistance conditions while minimizing volume at depths of tens of thousands of meters. An orthogonal topology optimization method is proposed to further reduce costs by optimizing the inner rib section after adjustment, given the high density and high cost of titanium alloy TB9 material. By combining the second-generation genetic algorithm, NSGA-2, for additional lightweight design in order to obtain the ideal pressure-resistant shell parameters, a multi-objective optimization design of the pressure-resistant shell is also proposed.
In the context of deep-sea high-pressure cylindrical shell structures, the standard uniform ribbed method for cylindrical shells may encounter issues with unstable half-waves in the axial direction when overall instability arises. Additionally, the method is unable to form unstable half-waves in the radial direction, which leaves the pressure-resistant shell with insufficient ability to withstand instability. The idea behind this article is to improve the overall instability resistance of the pressure-resistant shell by adjusting the uneven stiffness of the ribs inside using a method based on the Liz method. This paper suggests using the second-generation fast non-dominated genetic algorithm (NSGA-2) for the multi-objective optimization design of the pressure shell structure in order to obtain the optimal design parameters for the pressure shell. This will allow for the optimization of the inner rib section while maintaining good anti-instability ability and lead to a lightweight design of the entire device.