Journal of Theoretical
and Applied Mechanics

41, 3, pp. 575-591, Warsaw 2003

Stability of inelastic bilayered conical shells

Piotr Paczos, Jerzy Zielnica
The paper deals with the derivation of the basic stability equations of bilayered elastic-plastic conical shells and a approximate solution to these equations, both theoretically and by numerical procedures. The subject of the analysis is a bilayered open conical shell under a combined load comprising longitudinal forces and external pressure. Kirchhoff-Love's hypotheses hold for the layers, and use is made of constitutive relations in the form of generalized Hooke's law for the elastic stability analysis, and the Prandtl-Reuss incremental plasticity theory for the stability analysis in the elastic-plastic range. The stability equations are derived using the virtual work principle, and Ritz's method is applied to solve the equations. An iterative computer algorithm has been developed which made it possible to analyse the shells in the elastic, elastic-plastic or totally plastic prebuckling state of stress. The numerical results are presented in diagrams.
Keywords: elasto-plasticity; stability; shell theory; geometrical nonlinearity; critical load; stress-strain relations