AXISYMMETRIC STATIC AND DYNAMIC BUCKLING OF SPHERICAL CAPS DUE TO CENTRALLY DISTRIBUTED PRESSURES

Sanders’ axisymmetric nonlinear elastic shell theory, including provision for general orthotropy along the shell meridian, is approximated by finite difference equations including the Houbolt backward difference formulation in time. The equations are then applied to the nonlinear response of an isotropic shallow spherical cap subjected to static and dynamic loads. Axisymmetric static buckling is determined by investigating the convergence characteristics of the static numerical solution as the “top of the knee” buckling point is reached. Dynamic buckling is defined as the threshold load at which large increases in the peak amplitude of the average dynamic displacement occur. Axisymmetric buckling loads are given for a spherical cap subjected to a constant static pressure or step pulse of infinite duration distributed axisymmetrically over a portion of the center of the shell. The influence of the size of the loaded area and of moment and inplane boundary conditions on both static and dynamic buckling is studied, as well as the use of various criteria to define the threshold load for dynamic buckling. © 1969 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.