## 2 Experimental Studies of Spherical Shells
### Experimental Studies of PVC Spherical Shells Performed by [PERSON]  
In May 1962, [PERSON] published a paper entitled \"The nature of buckling in thin spherical shells\" [10], which was part of his doctoral dissertation. The paper included both theoretical considerations on the buckling capacity of spherical shells and the results of extensive experimental studies. The experimental study used 40 samples of spherical shells composed of polyvinyl chloride (PVC) with different parameters. These shells had different base radii: 15, 25, 35, 45, and 80 inches. The thickness of each shell was determined as the arithmetic average of measurements at the top of the shell and at points at the center of the four selected meridians. The nominal radius of curvature of each shell was calculated from the shell's height, which is the distance of the top from the base of the shell. In the experiments conducted, two different types of testing were used. The first type consisted of a constant control of the displacement of the shell, while the second consisted of a constant control of the hydrostatic pressure applied to the top surface of the shell. The  
Figure 2: Comparison of the test results of [PERSON] and [PERSON] [9] with proposed B&M buckling capacity curves. experimental results were converted to SI units. A schematic of the test stand is shown in Figure 3 below. Figure 4 shows buckling capacity curves for different classes of manufacturing quality using material parameters corresponding to the PVC used. The experimental results are shown as points on the graph (40 points in total). A comparison of the experimental results with the proposed B&M calculation procedure shows that the buckling phenomenon of real spherical shells was well described by the calculation formulas. The experimental results were higher than all three buckling capacity  
Figure 4: Comparison of the test results of [PERSON] [10] with proposed B&M buckling capacity curves. Figure 3: Schematic of the test apparatus. According to [10]. curves for the fabrication quality parameter Q = 16, 25 and 40 except for two specimens, which provided results slightly below the buckling capacity curve corresponding to the worst fabrication quality class, with Q = 16. See Figure 4 below. Experimental Studies of Aluminum Spherical Shells Performed by [PERSON] and [PERSON]  
In August 1963, [PERSON] and [PERSON] published a scientific report [11] entitled \"Tests of Stiffened and Unstiffened Machined Spherical Shells Under External Hydrostatic Pressure\", in which they presented the results of experimental tests on spherical shells. These tests included as many as 102 samples, 73 of which were unstiffened spherical shells with different opening angles (from \(5^{\circ}\) to \(120^{\circ}\)). The tested shells were composed of 7075-T6 aluminum with material parameters as follows: yield strength _fyk_ = 80,000 psi, elastic modulus \(E\) = 10.8\(\cdot\)10\({}^{6}\) psi, and [PERSON]'s ratio \(v\) = 0.30. A tool specifically designed to accurately generate internal spherical surfaces was used to generate the internal contours. The spherical shell and support ring of each model were composed as a unit. All the samples were subjected to hydrostatic pressure, which was gradually increased at one-minute intervals until the tested shell buckled. The pressure value at the point of buckling was read and considered the critical pressure. A schematic of the test stand is shown in Figure 5 below. The experimental results were converted to SI units and presented in tables and graphs. Figure 6 shows buckling capacity curves for different classes of manufacturing quality using material parameters corresponding to the aluminum used. The material parameters are \(E\) = 74,463.4 MPa, _fyk_ = 551.6 MPa, and \(v\) = 0.30. The experimental results are shown as points on a graph (59 points in total).