On a simplified inelastic analysis of structures

Abstract

In this paper two main problems are considered: the derivation of cyclic constitutive relations during inelastic regime where hardening, softening and creep can occur, and the development of the eventual periodical state in the structure during cyclic thermodynamical loadings. We give a very simple and practical framework to solve these problems in one unique manner. Its essential feature consists in the introduction of a family of internal parameters which characterize local inelastic mechanisms and the family of transformed internal parameters which are linearly linked to the previous ones through a symmetrical non-negative matrix and are indeed the opposite of the associated residual stresses. Thanks to that, the treatment of the local plastic or viscoplastic yield conditions can be easily made from only the classical simple purely elastic (or viscoelastic) analysis. This property allows important results during cyclic loadings: conditions for elastic shakedown, plastic shakedown, ratcheting and bounds for the limiting state. Several examples are given in the text.