have been reached which help to explain the large disagreement between 

 theory and early experimental work. These conclusions provide design 

 tools for the naval architect or engineer. 



Because of the Model Basin's background of research in spherical 

 shells, the Office of Naval Research requested that an evaluation be made 

 of three spherical pressure hulls being fabricated for ALVIN, a two-man 

 oceanographic research vehicle designed for an operating depth of 6000 ft. 

 The pressure hull of this vehicle is an HY-100 steel sphere with five large 

 penetrations as shown in Figure 1. Although three spheres were fabricated, 

 present plans call for utilizing only one of these spheres as the actual 

 pressure hull for the vehicle. 



In this report, a brief review of recent tests of spherical shells 

 is given to provide a background for evaluating the effect of initial im- 

 perfections on the collapse of spherical shells. Actual measured deviations 

 from sphericity are presented for the three ALVIN pressure hulls as 

 finally constructed. Based on these measurements, hull thickness measure- 

 ments, .and available stress-strain curves, the collapse depths of the 

 pressure hulls are calculated. 



BACKGROUND 



The elastic buckling of complete spherical shells was first treated 

 y in 1915 and is 

 pressure p., is given by 



2 

 by Zoelly in 1915 and is presented by Timoshenko. His classical buckling 



p^ = 1.21 E (h/R)^ for u = 0.3 [1 ] 



where E is Young's Modulus, 



h is the shell thickness, and 



R is the radius to the midsurface of the shell. 



Early experiments showed wide disagreement with Equation [1]. Normally, 

 this disagreement may be attributed to initial imperfections, adverse 



boundary conditions, and residual stresses present in the experimental 



3-5 

 specimens. More recent tests conducted at the Model Basin on shells 



which more closely meet the assumption of the theory (i.e., near-perfect 



"TReferences are listed on page 37. 



2 



