Inelastic buckling process of axially compressed cylindrical shells subject to edge constraints

Abstract

In this paper the effects of prebuckling deformation caused by edge constraints, and non linear strain displacement relationships, on the inelastic buckling process of axially compressed cylindrical shells are studied. By Drucker's postulate of positive work in plastic deformation, a modified incremental theory of plasticity on the stress-strain relationships expressed in terms of Kirchhoff stress and Green strain rates is developed. A variational principle in the Lagrangian description and for quasi-static problems of finite plasticity is developed, and the existence of an extremum principle for a material having a sufficiently great hardening rate is shown. In addition a criterion for the stability of a body under dead load is established.The variational principle in conjunction with the incremental Rayleigh-Ritz technique is used to determine the deformation process of an idealized cylindrical shell composed of four thin load carrying sheets made of a general work hardening material. The theoretical predictions obtained numerically by digital computer compare favorably with available experimental results.