Large Deflection of Axisymmetrically Loaded Spherical Caps

Abstract

SummaryThis study is an investigation of the non-linear behaviour of an elastic spherical cap under the assumption of axisymmetric deformation. The types of axisymmetric loading under consideration are partially loaded uniform pressure, line load, “cosine” load with the maximum intensity at the apex and the combined action of uniform pressure and line load. The edge of the cap is assumed to be rigidly clamped, hinged, and unrestrainedly simply-supported. The method of solution is an extension of the iterative procedure for the integral equations formulated by Budiansky for uniformly loaded, clamped caps. In the cases of hinged and unrestrainedly simply-supported edges, the critical loads for the axisymmetric snap-buckling are presented for different types of loading and various values of the geometrical cap parameter. In the case of a clamped edge the load-deflection curves are established until no solution can be found for further increasing the load. The load corresponding to the limit point on the load-deflection curve is the critical load if the axisymmetric snap-buckling exists. The graphical results are presented for load-deflection curves, deflection profiles, bending moments, transverse shear and interaction of buckling pressures and buckling line loads. The present results are in good agreement with available data for uniform pressure distributed over the entire surface of the cap with three sets of edge conditions and over the central portion of a clamped cap.