Collapse Mode of Elastic‐Plastic Structures

Abstract

For a structure of elastic‐perfectly plastic material subjected to steady and cyclic loads exceeding shakedown limit, the possibility to predict collapse mode, without making a complete analysis, is illustrated. This goal is achieved by using the kinematical part of the solution to the shakedown load factor problem, and by considering that it is proportional to the gradient of the elastic‐plastic, steady‐state response to cyclic loads at the shakedown limit. A bounding technique, which allows the approximate assessment of any desired measure of plastic deformation occurring in the steady‐state phase, is presented. Such technique differs from the usual bounding techniques because the preventive determination of only one bound on a suitable proportionality factor is requested. On the grounds of such bound value, it is possible to compute (with a very small computational effort) other bounds on any chosen measure of plastic deformation, by using the solution of the shakedown load factor problem.