A robust updated normal plane scheme for geometric non-linear structural analysis

A new normal plane constraint for assessing the geometric non-linear behaviour of structures is proposed. In this procedure, the vector passing through a point placed on the equilibrium path and the iteration point is perpendicular to the locus of the iterative points. The capability of the suggested constraint equation was investigated numerically. To compare its abilities with other well-known techniques (the normal plane, cylindrical arc-length and updated normal plane methods), several planar and space trusses, plate and shells were analysed. The results proved the high accuracy and efficiency of the developed scheme. The powers of the methods in passing the limit points were also investigated. In addition, to assess the capabilities of the methods more accurately, they were all ranked based on the total number of increments and iterations required.