On the Large Deformation of a Rigid-Plastic Spherical Shell Compressed by a Rigid Plate

Abstract

The behavior of a rigid perfectly plastic spherical shell loaded by means of contact with a flat rigid surface is investigated. The predictions of the analysis are restricted to overall displacements lying between a few thicknesses and about one tenth the shell radius. At each stage of deformation an approximate limit load and corresponding velocity field are found for an assumed deformed shape of the shell, which later is shown to be very close to the calculated deformed shape. A simple formula relating the total axial force on the shell to the displacement of the shell is derived, and its range of validity is investigated. Finally, the results of some static tests of shells are shown to agree favorably with the theory.