Conical Shell Inversion—An Approximate Energy Analysis

Abstract

The plastic inversion of a simply supported conical shell is considered. The shell is loaded through a rigid central collar. The material is assumed to be elastic-perfectly plastic and to obey the Tresca yield criterion. Upper and lower bound calculations are presented for the collapse load of the inverted configuration. The steady state load-deflection behavior for the large deflection inversion process is determined through a continuous application of the upper bound calculation. Minimization of the upper bound serves not only to determine an accurate characterization of the load-deflection curve but also provides a realistic measure of the bend radius associated with the mode of deformation assumed. Experimental results are presented and compared with the theory.