A Plastic Path-following Method That Handles the Continuous Spreading of Elastic Unloading

This work deals with the numerical determination of equilibrium paths in geometrically and physically non-linear problems. The aim of this paper is to propose, present the formulation and illustrate the application of a path-following method which is able to handle the continuous spreading of elastic unloading and, therefore, is particularly well suited to solve plastic buckling problems. The proposed method involves an incremental solution technique characterized by (i) the use of both the configuration quantities and their rates as independent variables, (ii) the simultaneous solution of the total and incremental equilibrium equations and (iii) the definition of an estimated configuration history throughout an increment, on the basis of the initial and final values of the configuration quantities and their rates. In order to clarify the concepts introduced and to illustrate the application and capabilities of the path-following method formulated, a study of the buckling behaviour of an elastic-plastic column is presented. It is shown that, for the numerical example analysed, the implementation of the proposed solution technique always leads to more accurate results than the ones yielded by a standard technique. Manuel Ritto-Corrêa and Dinar Camotim. 2