# The Ultimate Strength of Fully Transparent Pressure-Resistant Spherical Cabins
## 1 Introduction  
In recent decades, deep-sea exploration and development have received increasing attention. The manned submersible (HOV) is an advanced equipment for scientific research and exploration of the deep-sea resources [1]. These submersibles usually need to work in high-pressure and highly corrosive environments, so they are generally designed with an anti-corrosive metal shell structure. In order to facilitate the operator's observation of the external environment, the submersibles will use optical cameras and transparent windows to observe the external environment [2]. However, the narrow perspective of the observation window makes it difficult for the diver to observe, and it can easily lead to blind spots and service delays [3]. Therefore, a fully transparent cabin to improve vision and driving experience is a good practice to expand the range of observation as shown in Figure 1, which is a schematic figure of a submersible with a fully transparent cabin [4]. Figure 1: A schematic figure of a manned submersible with fully transparent cabin. In 1970, the US Navy launched a spherical PMMA submersible called NEMO [5], which means that the concept of using transparent material PMMA to manufacture the entire pressure-resistant shell is completely feasible. After decades of development, fully transparent submersibles have achieved success in the commercial field of sightseeing submersibles, such as the Trion submersible in the United States, C-Quester in the Netherlands, and DW2000 in collaboration with NASA in Canada [6]. Japan has also launched the \"Deep Sea 12000\" research program, while China put into operation the \"Huandao Jiaolong\" sightseeing submersible in 2015, making it the world's largest fully transparent passenger-carrying sightseeing submersible [7]. Because of this, the service safety of fully transparent structures is particularly important, whether from a scientific research perspective or with a focus on future commercial value. However, the maturity of the current design is being tested by service experience and the accumulated safety evaluation foundation is insufficient. Stability is a primary concern in the safety evaluation of pressure-resistant structures. Under the high outside pressure in deep-sea conditions, the pressure-resistant PMMA cabin may fail due to outside pressure exceeding its ultimate strength. The failure modes mainly include yield or fracture caused by insufficient material strength, which is called strength failure, or instability caused by insufficient structural stiffness, which is called buckling failure [8]. Generally speaking, the failure of thin shell structures usually is not related to the issue of strength failure, but thick shell structures may conform to both theories simultaneously. A pressure-resistant cabin requires relevant calculations based on different thicknesses to determine their failure mode, namely strength failure or buckling instability. Under external pressure, researchers have proposed various critical pressure calculation formulas for thick shell structures. [PERSON] originally proposed the formula for determining the buckling critical pressure of perfect spherical shells under external pressure [9]. This theoretical formula assumes that the structure is flawless, but various spherical shells manufactured in engineering practice cannot be flawless [10], which makes the buckling critical pressure obtained through experiments much smaller than the theoretical solution [11]. In 1934, [PERSON] proposed using nonlinear large deflection theory to analyze the post buckling state of thin-walled cylindrical shells when studying the torsional buckling problem [12], established a nonlinear cylindrical shell equation, obtained the critical buckling pressure, and obtained the post buckling waveform of the shell through experiments. In 1941, Based on [PERSON]'s study, [PERSON] and [PERSON] [13] studied the buckling problem of spherical shells., considering the initial defects of the spherical shell, and achieved breakthrough results.