Using residual areas for geometrically nonlinear structural analysis

•Three new constraint equations are formulated.•These relations are utilized to analyze the structure with nonlinear behavior.•The capacity of each strategy in passing the limit points is assessed.•Findings prove the high capability of the authors׳ schemes.

Incremental–iterative methods are widely used for tracing the equilibrium paths of structures. To determine the nonlinear structural response, an iteration process is required. In this paper, some residual areas are employed for the base of iteration steps. By setting each area to zero, and minimizing its perimeter separately, some new constraint equations can be achieved. After developing the related formulations, several geometric nonlinear analyses of frames, shell and trusses are performed to evaluate the robustness of the suggested methods. Findings prove the high capability of the authors׳ first scheme compared to other new proposed methods and cylindrical arc-length technique. Additionally, the capacity of each strategy in passing the limit points is assessed.