A Finite Step Updating Method for Elastoplastic Analysis of Frames

Abstract

A numerical method is developed for analysis of elastoplastic frames. Yielding is represented by concentrated displacement discontinuities with extension and rotation components. The possible yield points are located at the ends of the beam elements. The corresponding plastic degrees of freedom are added to the system as they arise, increasing the size of the global system of equations but avoiding refactorization. The yield deformations follow a hardening plastic rule. By using a piecewise linearized (polyhedral) yield surface and linear hardening a formulation is developed in which the gradual development of yielding of the frame is computed as a sequence of linear problems, each leading to the formation of a new yield hinge or change of an existing yield hinge. The method has been implemented in the C programming language with fully dynamic memory allocation but can be used to extend existing linear frame analysis programs.