Non‐linear programming for the plastic analysis of local deformations in shell structures

Abstract

AbstractThe paper presents an analysis of the response of plastic spherical and cylindrical shells subjected to loads applied through a rigid boss. Special emphasis is placed on following the load‐deflection behaviour of these structures after the application of the yield‐point load in order to predict the appearance of any snapping action.The method of analysis assumes that upper bound calculations are applicable and that the associated velocity fields can be represented by a series of piecewise continuous polynomials. The internal dissipation of energy for the structures are then written in terms of the coefficients of these polynomials and the values appropriate to the solution are found by using a non‐linear programming routine.The results of this analysis are correlated with a non‐dimensional boss size parameter p and compared with the results of experimental investigations. Mention is also made of the possible effects of initial imperfections.