Elastoplastic axially asymmetric deformation of shells with curvilinear openings

Abstract

The fundamental results of an analysis of the stress deformed state of elastic shells with stress concentrators of different forms are generalized in [8]. Currently, the solutions of a series of nonlinear (including elastoplastic) problems for stress concentrators in shells have been obtained; the majority of these results pertain to a study of axially symmetric deformation of shells with active stress processes. Solutions of two-dimensional nonlinear stress concentrator problems have been obtained in various works in which the results are based on either theoretical [2-5, 7-9] or experimental [i, 6, 8, 10] techniques. Numerical data on calculations for inelastic deformation of shells have been primarily done for rectangular openings [3, 5]. For shells with circular openings, analyses have been done for axial stretching (compressing) forces. In this study, the theories of thin shells and deformation plasticity are used to obtain nonlinear resolvent equations, and the techniques for solving these equations are given. An algorithm is formulated for solving two-dimensional elastoplas=ic problems involving thin-walled structures with stress concentrators. Fundamental nonlinear equations are given for asymmetric deformation of arbitrary shells with curvillnear (circular, elliptic, etc.) openings whose profile is reinforced by an element (a ring). Results obtained on a computer are presented.