The response of structures can contain material  and geometric non-linearity when limit states of strength and / or serviceability is approached.   

The methods of analysis of structures with non-linear behaviour often lead to load-deflection relationships which are complex and require excessive computational effort. Solutions are usually found iteratively and often pose convergence problems when structural failure is reached. This is because the actual structure instability is reflected in mathematical model.  

A simple and efficient approach for analysing frame structures with material and geometric non-linear response has been applied successfully to a wide range of problems.  A summary of the method, originally developed by Saleh, Stutzki & Lopetegui is presented in [1] & [2].  The method utilises a set of orthogonal Load-Deflection States of a structure as a substitute of a non-linear structure stiffness matrix.

1. Saleh, A. and Lopetegui, J., " Non linear Analysis using Linear Elements" , Proceedings of the Sixth International Conference in Australia on Finite Element Methods, July 8th - 10th, 1991, Sydney, Australia.

2. Saleh, A. Collapse Analyses of Skeletal Structures using Load Deflection States. Proceedings of First China-Australia Symposium on Computational Mechanics CASCM’95, Dalian, P.R. China, August 7-11, 1995..