Post-buckling behavior of a closed spherical shell: PMM vol. 35, n≗ 5, 1971, pp. 840–847

Abstract The question of new equilibrium modes of a uniformly compresses closed elastic spherical shell for loading values close to the critical one is considered for which the membrane state of stress loses stability. The problem [1] reduces to constructing solutions branching off from the trivial solution in the neighborhood of the bifurcation point, for the equations in [2]. The investigation is carried out by the Liapunov-Schmidt method for a broad class of operator equations in Banach space [3]. The author of [4, 5] used the analytical Liapunov-Schmidt method earlier to construct new equilibrium modes in the case of plates and shallow shells. The problem of the bifurcation of the trivial solution of a shallow spherical segment by the Poincare method was Investigated in [6], where meridian stress resultants in equilibrium with the uniformly distributed surface pressure are given on the edge, whereupon a membrane equilibrium mode always exists. For the problem of an uniformly compressed closed sphere when the spectrum is simple, the behavior of the solutions in the neighborhood of the bifurcation point has been studied in [7] numerically on a computer by using the method of “adjustment”. The survey [8] is devoted to mis same problem.