Bifurcation phenomena in spherical shells under concentrated and ring loads.
Finite prebuckling deformations are accounted for in the calculation of bifurcation loads for spherical shells under concentrated loads and ring loads. In the case of clamped caps with in ward-directed point loads, good agreement is obtained with the test results of Penning and Thurston and the analytical results reported by Budiansky and Hutchinson. The analysis of simply supported caps is in qualitative agreement with the test results of Evan-Iwanowski et al. Further calculations show that bifurcation in the case of complete spherical shells occurs with 3 circumferential waves. The critical value of the dimensionless load parameter PR/Et is independent of the radius-to-thickness ratio R/t for R/t greater than about 100, and it decreases with decreasing R/t. Spherical shells with outward-directed point loads buckle with 8 circumferential waves at loads 18 to 24 times the critical in warddirected loads. As the diameter increases, of the ring over which the tensile load is applied, the critical load increases; the number of circumferential waves increases and results from linear theory approach those from the nonlinear theory.