On the Automatic Limit and Shakedown Optimal Plastic Design of Frames

This paper on "On the Automatic Limit and Shakedown Optimal Plastic Design of Frames" was presented at the NAFEMS World Congress on Design, Simulation & Optimisation: Reliability & Applicability of Computational Methods - 9-11 April 1997, Stuttgart, Germany.

Summary

A fully automatic way towards the optimal plastic limit and shakedown design of plane frames is presented. The approach is based on the force method, which provides certain computational advantages over the displacement method in linear programming applications. An algorithm is presented which uses the graph representation of the frame and forms cycles by finding the shortest path between the end nodes of its members. The algorithm provides an easy computer implementation, because of the simple way the generated cycle is checked for independence. This is done by fictitiously increasing the lengths of the members of a cycle. The cycle basis helps to form a statical basis which is then used to express the contribution of the hyperstatic forces to the stress resultants of the frame. The quickest way to the ground for each load is used to satisfy equilibrium with this load.