ASYMPTOTIC ANALYSIS OF A BUCKLING PROBLEM FOR AN EMBEDDED SPHERICAL SHELL

The axisymmetric buckling of a spherical shell embedded in an elastic medium with uniaxial compression at infinity is examined in the limit of small shell thickness ratio. An asymptotic method is developed by considering the paradigm problem of a beam attached to a Winkler substrate of variable stiffness, which in the small aspect ratio limit displays the same behavior as the shell. The asymptotic method is then applied to the Euler-Lagrange equations corresponding to shell buckling. The system is analyzed in two distinguished limits, displaying good agreement with the full numerical results. © 2009 Society for Industrial and Applied Mathematics