Axissymmetric Buckling of Hollow Spheres And Hemispheres
Axissymmetric Buckling of Hollow Spheres And Hemispheres
Louis Bauer
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Thus for example, the branch joining B^ „ at its lower critical pressure should be called Br o' But since Br n bifurcates from P^ we also call it Bk -, . The notation in Table II is now rather obvious if we merely observe that most critical pressures, P . Or P . , have dual representations. On the branches bifurcating from unsymmetric eigenvalues the eigenvalues are also upper or lower critical pressures, that is, P = P . Or P = P -, . '^ ' ' n n, l n n, l In Figures 3 and ^ we show how the sol...utions for P decreasing on the lowest symmetric bifurcation branch Br -, go over continuously to the solutions for P increasing on the adjacent branch B^ „. There is an obvious difference in the shapes and stresses between the states on branches Br -, and Br q for P > 0. 05; compare Figures 3a and ^a with Figures 3c and 4c. However, for P near Pg -, - ^ ({ n ~ 0. 0105 the shapes on both branches are quite similar. Thus there is no abrupt change in mode (see Figures 3b and 4b). As P Increases the states on Br Q develop a boundary layer near 9 = tt/2.
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