Geometric non-linear analyses are performed utilising two main control factors, including load and displacement parameters. In this paper, a new incremental-iterative scheme without predictor step is suggested. Using the obtained constraint equation, the load factor increment is calculated. It is assumed that the path corresponding to the iterative analysis is a parabolic curve. Two different mathematical procedures are developed in order to form this new constraint equation. In the first formulation, two reasonable assumptions are considered for the parabolic path. The length of iterative steps’ curve is minimised in the second scheme. To corroborate the efficiency and capability of the proposed technique, several structures with complex non-linear behaviour are solved.

Keywords