A General Finite Element Scheme for Limit State Analysis and Optimization

This paper on "A General Finite Element Scheme for Limit State Analysis and Optimization" was presented at the NAFEMS World Congress on Effective Engineering Analysis - 25-28 April 1999, Newport, Rhode Island, USA.

Abstract

Limit State analysis which is based on a perfect plastic material behaviour is used in many different applications primarily within Structural Engineering and Geotechnics. The calculation methods have not reached the same level of automation such as Finite Element Analysis for elastic structures. The computer based systems are more ad hoc based and are typically not well-integrated with pre- and postprocessors well-known from commercial Finite Element codes.
A finite element based formulation of limit state analysis is presented which allows an easy integration with standard Finite Element codes for elastic analysis. In this way the user is able to perform a limit state analysis on the same model used for elastic analysis only adding data for the yield surface.
The method is based on the lower-bound theorem and uses stress-based elements with a linearized yield surface. The mathematical problem is an optimization problem a so-called Linear Programming problem. The optimization gives the optimal stress distribution and through the primal-dual concept a collapse mode can be determined. The formulation can also be used for material optimization which can be used in connection with reinforcement of plates and slabs. Examples of applications are given for frames, plates and slabs.