Erratum: "Elastic Stability of Near-Perfect Shallow Spherical Shells"

The Geometric Role of Precisely Engineered Imperfections on the Critical Buckling Load of Spherical Elastic Shells

“…where E is the Young's modulus, is the Poisson's ratio, and g ¼ R=t is the dimensionless radius of the shell, of radius R and thickness t. For decades, this theoretical prediction was found to be in disagreement with the experimental results [5][6][7][8][9][10], and attempting to reconcile the two has been a cornerstone in structural mechanics [3]. Throughout this paper, we focus exclusively on spherical shells.…”

“…Kaplan and Fung [6] showed that the nonlinear buckling behavior of a shallow spherical shell is set by k, and subsequent studies have tended to present the buckling pressure as a function of this geometric quantity [6][7][8][9]. In the results presented in Sec.…”

“…(1), presumably due to significant material and geometric imperfections imparted through the fabrication process. By contrast, high-precision shells fabricated by machining aluminum [9] tended to attain higher buckling pressures (0:45 < j d < 0:9), but still with considerable scatter. Note that most of these experimental investigations were conducted with shallow spherical shell caps.…”

“…The equations for that theory for a spherical shell are immediately obtained as follows: one omits u 2 r in the strains in Eq. (9), and the in-plane displacements, u x and u h , are also neglected in the rotations in Eq. (6).…”

“…1 Experimental results of the knockdown factor, j d , versus the radius-to-thickness ratio, g 5 R=t, of spherical shells. Most of the previous experiments [5][6][7][8][9] (open symbols) were conducted with shallow spherical segments and resulted in a large variation in j d 5 0.17-0.9. Carlson et al [10] used complete spherical shells and increased the knockdown factor from 0.05 to 0.86 by improving the shell surface and loading conditions.…”