Axisymmetric buckling of thin shallow circular spherical shells under uniform pressure for large values of geometric parameter λ

Abstract

The problem of axisymmetric buckling of thin shallow circular spherical shells under uniform pressure with the edge either rigidly clamped or simply supported is studied. The Newton-spline function method is used to solve the non-linear differential equations of thin shallow circular spherical shells. Numerical results of upper and lower critical loads for shells with the value of geometric parameter λ as great as 50 are obtained. The character of prebuckling and postbuckling and the problem of finding critical points is discussed. This problem is called the very large geometric parameter λ buckling problem of a shallow circular spherical shell, whose results had been predicted by Budiansky. Here we confirm his results as being reasonable. Relations between the buckling model and the geometric parameter λ which improve Karman and Tsien's suggestion are discussed.